<?xml version="1.0" encoding="US-ASCII"?>
<!-- DFIN New ActiveDisclosure (SM) XBRL Schema Document - http://www.dfinsolutions.com/ -->
<!-- Creation Date :2026-08-04T15:17:54.3927+00:00 -->
<!-- Copyright (c) 2026 Donnelley Financial Solutions, Inc. All Rights Reserved. -->
<xsd:schema targetNamespace="http://grayscale.com/20260630" attributeFormDefault="unqualified" elementFormDefault="qualified" xmlns:dtr-types="http://www.xbrl.org/dtr/type/2024-01-31" xmlns:ecd-sub="http://xbrl.sec.gov/ecd-sub/2025" xmlns:ecd="http://xbrl.sec.gov/ecd/2025" xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:dei="http://xbrl.sec.gov/dei/2025" xmlns:hzen="http://grayscale.com/20260630" xmlns:xbrldt="http://xbrl.org/2005/xbrldt" xmlns:xbrli="http://www.xbrl.org/2003/instance" xmlns:us-types="http://fasb.org/us-types/2025" xmlns:enum2="http://xbrl.org/2020/extensible-enumerations-2.0" xmlns:srt="http://fasb.org/srt/2025" xmlns:us-gaap="http://fasb.org/us-gaap/2025" xmlns:xlink="http://www.w3.org/1999/xlink">
  <xsd:import schemaLocation="http://www.xbrl.org/2003/xbrl-instance-2003-12-31.xsd" namespace="http://www.xbrl.org/2003/instance"/>
  <xsd:import schemaLocation="http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd" namespace="http://www.xbrl.org/2003/linkbase"/>
  <xsd:import schemaLocation="http://www.xbrl.org/2005/xbrldt-2005.xsd" namespace="http://xbrl.org/2005/xbrldt"/>
  <xsd:import schemaLocation="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd" namespace="http://xbrl.sec.gov/ecd/2025"/>
  <xsd:import schemaLocation="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd" namespace="http://fasb.org/us-gaap/2025"/>
  <xsd:import schemaLocation="https://www.xbrl.org/2020/extensible-enumerations-2.0.xsd" namespace="http://xbrl.org/2020/extensible-enumerations-2.0"/>
  <xsd:import schemaLocation="https://www.xbrl.org/dtr/type/2024-01-31/types.xsd" namespace="http://www.xbrl.org/dtr/type/2024-01-31"/>
  <xsd:import schemaLocation="https://xbrl.fasb.org/us-gaap/2025/elts/us-types-2025.xsd" namespace="http://fasb.org/us-types/2025"/>
  <xsd:import schemaLocation="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd" namespace="http://fasb.org/srt/2025"/>
  <xsd:import schemaLocation="https://xbrl.sec.gov/ecd/2025/ecd-sub-2025.xsd" namespace="http://xbrl.sec.gov/ecd-sub/2025"/>
  <xsd:import schemaLocation="https://xbrl.sec.gov/dei/2025/dei-2025.xsd" namespace="http://xbrl.sec.gov/dei/2025"/>
  <xsd:import schemaLocation="https://www.xbrl.org/2023/calculation-1.1.xsd" namespace="https://xbrl.org/2023/calculation-1.1"/>
  <xsd:annotation>
    <xsd:appinfo>
      <link:roleType roleURI="http://grayscale.com/20260630/taxonomy/role/DocumentDocumentAndEntityInformation" id="DocumentDocumentAndEntityInformation">
        <link:definition>75000 - Document - Document and Entity Information</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://grayscale.com/20260630/taxonomy/role/StatementStatementsOfAssetsAndLiabilitiesUnaudited" id="StatementStatementsOfAssetsAndLiabilitiesUnaudited">
        <link:definition>75010 - Statement - STATEMENTS OF ASSETS AND LIABILITIES (UNAUDITED)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://grayscale.com/20260630/taxonomy/role/StatementStatementsOfAssetsAndLiabilitiesUnaudited2" id="StatementStatementsOfAssetsAndLiabilitiesUnaudited2">
        <link:definition>75020 - Statement - STATEMENTS OF ASSETS AND LIABILITIES (UNAUDITED) 2</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://grayscale.com/20260630/taxonomy/role/StatementStatementsOfAssetsAndLiabilitiesUnauditedParenthetical" id="StatementStatementsOfAssetsAndLiabilitiesUnauditedParenthetical">
        <link:definition>75030 - Statement - STATEMENTS OF ASSETS AND LIABILITIES (UNAUDITED) (Parenthetical)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://grayscale.com/20260630/taxonomy/role/StatementSchedulesOfInvestmentUnaudited" id="StatementSchedulesOfInvestmentUnaudited">
        <link:definition>75040 - Statement - SCHEDULES OF INVESTMENT (UNAUDITED)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://grayscale.com/20260630/taxonomy/role/StatementStatementsOfOperationsUnaudited" id="StatementStatementsOfOperationsUnaudited">
        <link:definition>75050 - Statement - STATEMENTS OF OPERATIONS (UNAUDITED)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://grayscale.com/20260630/taxonomy/role/StatementStatementsOfChangesInNetAssetsUnaudited" id="StatementStatementsOfChangesInNetAssetsUnaudited">
        <link:definition>75060 - Statement - STATEMENTS OF CHANGES IN NET ASSETS (UNAUDITED)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureOrganization" id="DisclosureOrganization">
        <link:definition>995455 - Disclosure - Organization</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureSummaryOfSignificantAccountingPolicies" id="DisclosureSummaryOfSignificantAccountingPolicies">
        <link:definition>995465 - Disclosure - Summary of Significant Accounting Policies</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureFairValueOfZen1" id="DisclosureFairValueOfZen1">
        <link:definition>995475 - Disclosure - Fair Value of ZEN</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureCreationsAndRedemptionsOfShares" id="DisclosureCreationsAndRedemptionsOfShares">
        <link:definition>995485 - Disclosure - Creations and Redemptions of Shares</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureIncomeTaxes1" id="DisclosureIncomeTaxes1">
        <link:definition>995495 - Disclosure - Income Taxes</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureRelatedParties" id="DisclosureRelatedParties">
        <link:definition>995505 - Disclosure - Related Parties</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureConcentrationRisk" id="DisclosureConcentrationRisk">
        <link:definition>995515 - Disclosure - Concentration Risk</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureFinancialHighlightsPerSharePerformance" id="DisclosureFinancialHighlightsPerSharePerformance">
        <link:definition>995525 - Disclosure - Financial Highlights Per Share Performance</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureIndemnifications" id="DisclosureIndemnifications">
        <link:definition>995535 - Disclosure - Indemnifications</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureSubsequentEvents" id="DisclosureSubsequentEvents">
        <link:definition>995545 - Disclosure - Subsequent Events</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureSummaryOfSignificantAccountingPoliciesPolicies" id="DisclosureSummaryOfSignificantAccountingPoliciesPolicies">
        <link:definition>995555 - Disclosure - Summary of Significant Accounting Policies (Policies)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureSummaryOfSignificantAccountingPoliciesTables" id="DisclosureSummaryOfSignificantAccountingPoliciesTables">
        <link:definition>995565 - Disclosure - Summary of Significant Accounting Policies (Tables)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureFairValueOfZenTables" id="DisclosureFairValueOfZenTables">
        <link:definition>995575 - Disclosure - Fair Value of ZEN (Tables)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureFinancialHighlightsPerSharePerformanceTables" id="DisclosureFinancialHighlightsPerSharePerformanceTables">
        <link:definition>995585 - Disclosure - Financial Highlights Per Share Performance (Tables)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureOrganizationAdditionalInformationDetail" id="DisclosureOrganizationAdditionalInformationDetail">
        <link:definition>995595 - Disclosure - Organization - Additional Information (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureSummaryOfSignificantAccountingPoliciesSummaryOfFairValueEstimatesDetail" id="DisclosureSummaryOfSignificantAccountingPoliciesSummaryOfFairValueEstimatesDetail">
        <link:definition>995605 - Disclosure - Summary of Significant Accounting Policies - Summary of Fair Value Estimates (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureSummaryOfSignificantAccountingPoliciesAdditionalInformationDetails" id="DisclosureSummaryOfSignificantAccountingPoliciesAdditionalInformationDetails">
        <link:definition>995615 - Disclosure - Summary of Significant Accounting Policies - Additional Information (Details)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureFairValueOfZenAdditionalInformationDetail" id="DisclosureFairValueOfZenAdditionalInformationDetail">
        <link:definition>995625 - Disclosure - Fair Value of ZEN - Additional Information (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureFairValueOfZenSummaryOfChangesInQuantityOfZenAndRespectiveFairValueDetail" id="DisclosureFairValueOfZenSummaryOfChangesInQuantityOfZenAndRespectiveFairValueDetail">
        <link:definition>995635 - Disclosure - Fair Value of ZEN - Summary of changes in quantity of ZEN and respective fair value (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureCreationsAndRedemptionsOfSharesAdditionalInformationDetail" id="DisclosureCreationsAndRedemptionsOfSharesAdditionalInformationDetail">
        <link:definition>995645 - Disclosure - Creations and Redemptions of Shares - Additional Information (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureIncomeTaxesAdditionalInformationDetail" id="DisclosureIncomeTaxesAdditionalInformationDetail">
        <link:definition>995655 - Disclosure - Income Taxes - Additional Information (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureRelatedPartiesAdditionalInformationDetail" id="DisclosureRelatedPartiesAdditionalInformationDetail">
        <link:definition>995665 - Disclosure - Related Parties - Additional Information (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureFinancialHighlightsPerSharePerformanceSummaryOfPerShareDataDetail" id="DisclosureFinancialHighlightsPerSharePerformanceSummaryOfPerShareDataDetail">
        <link:definition>995675 - Disclosure - Financial Highlights Per Share Performance - Summary of Per Share Data (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureSubsequentEventsAdditionalInformationDetail" id="DisclosureSubsequentEventsAdditionalInformationDetail">
        <link:definition>995685 - Disclosure - Subsequent Events - Additional Information (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:linkbase id="lnk">
        <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/all" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#all" xlink:type="simple"/>
        <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#dimension-default" xlink:type="simple"/>
        <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#dimension-domain" xlink:type="simple"/>
        <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/domain-member" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#domain-member" xlink:type="simple"/>
        <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#hypercube-dimension" xlink:type="simple"/>
        <link:arcroleRef arcroleURI="http://www.esma.europa.eu/xbrl/esef/arcrole/wider-narrower" xlink:href="http://www.xbrl.org/lrr/arcrole/esma-arcrole-2018-11-21.xsd#wider-narrower" xlink:type="simple"/>
        <link:arcroleRef arcroleURI="https://xbrl.org/2023/arcrole/summation-item" xlink:href="https://www.xbrl.org/2023/calculation-1.1.xsd#summation-item" xlink:type="simple"/>
        <link:roleRef roleURI="http://grayscale.com/20260630/taxonomy/role/DocumentDocumentAndEntityInformation" xlink:href="hzen-20260630.xsd#DocumentDocumentAndEntityInformation" xlink:type="simple"/>
        <link:roleRef roleURI="http://grayscale.com/20260630/taxonomy/role/StatementStatementsOfAssetsAndLiabilitiesUnaudited" xlink:href="hzen-20260630.xsd#StatementStatementsOfAssetsAndLiabilitiesUnaudited" xlink:type="simple"/>
        <link:roleRef roleURI="http://grayscale.com/20260630/taxonomy/role/StatementStatementsOfAssetsAndLiabilitiesUnauditedParenthetical" xlink:href="hzen-20260630.xsd#StatementStatementsOfAssetsAndLiabilitiesUnauditedParenthetical" xlink:type="simple"/>
        <link:roleRef roleURI="http://grayscale.com/20260630/taxonomy/role/StatementSchedulesOfInvestmentUnaudited" xlink:href="hzen-20260630.xsd#StatementSchedulesOfInvestmentUnaudited" xlink:type="simple"/>
        <link:roleRef roleURI="http://grayscale.com/20260630/taxonomy/role/StatementStatementsOfOperationsUnaudited" xlink:href="hzen-20260630.xsd#StatementStatementsOfOperationsUnaudited" xlink:type="simple"/>
        <link:roleRef roleURI="http://grayscale.com/20260630/taxonomy/role/StatementStatementsOfChangesInNetAssetsUnaudited" xlink:href="hzen-20260630.xsd#StatementStatementsOfChangesInNetAssetsUnaudited" xlink:type="simple"/>
        <link:roleRef roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureOrganization" xlink:href="hzen-20260630.xsd#DisclosureOrganization" xlink:type="simple"/>
        <link:roleRef roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureSummaryOfSignificantAccountingPolicies" xlink:href="hzen-20260630.xsd#DisclosureSummaryOfSignificantAccountingPolicies" xlink:type="simple"/>
        <link:roleRef roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureFairValueOfZen1" xlink:href="hzen-20260630.xsd#DisclosureFairValueOfZen1" xlink:type="simple"/>
        <link:roleRef roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureCreationsAndRedemptionsOfShares" xlink:href="hzen-20260630.xsd#DisclosureCreationsAndRedemptionsOfShares" xlink:type="simple"/>
        <link:roleRef roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureIncomeTaxes1" xlink:href="hzen-20260630.xsd#DisclosureIncomeTaxes1" xlink:type="simple"/>
        <link:roleRef roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureRelatedParties" xlink:href="hzen-20260630.xsd#DisclosureRelatedParties" xlink:type="simple"/>
        <link:roleRef roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureConcentrationRisk" xlink:href="hzen-20260630.xsd#DisclosureConcentrationRisk" xlink:type="simple"/>
        <link:roleRef roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureFinancialHighlightsPerSharePerformance" xlink:href="hzen-20260630.xsd#DisclosureFinancialHighlightsPerSharePerformance" xlink:type="simple"/>
        <link:roleRef roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureIndemnifications" xlink:href="hzen-20260630.xsd#DisclosureIndemnifications" xlink:type="simple"/>
        <link:roleRef roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureSubsequentEvents" xlink:href="hzen-20260630.xsd#DisclosureSubsequentEvents" xlink:type="simple"/>
        <link:roleRef roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureSummaryOfSignificantAccountingPoliciesPolicies" xlink:href="hzen-20260630.xsd#DisclosureSummaryOfSignificantAccountingPoliciesPolicies" xlink:type="simple"/>
        <link:roleRef roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureSummaryOfSignificantAccountingPoliciesTables" xlink:href="hzen-20260630.xsd#DisclosureSummaryOfSignificantAccountingPoliciesTables" xlink:type="simple"/>
        <link:roleRef roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureFairValueOfZenTables" xlink:href="hzen-20260630.xsd#DisclosureFairValueOfZenTables" xlink:type="simple"/>
        <link:roleRef roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureFinancialHighlightsPerSharePerformanceTables" xlink:href="hzen-20260630.xsd#DisclosureFinancialHighlightsPerSharePerformanceTables" xlink:type="simple"/>
        <link:roleRef roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureOrganizationAdditionalInformationDetail" xlink:href="hzen-20260630.xsd#DisclosureOrganizationAdditionalInformationDetail" xlink:type="simple"/>
        <link:roleRef roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureSummaryOfSignificantAccountingPoliciesSummaryOfFairValueEstimatesDetail" xlink:href="hzen-20260630.xsd#DisclosureSummaryOfSignificantAccountingPoliciesSummaryOfFairValueEstimatesDetail" xlink:type="simple"/>
        <link:roleRef roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureSummaryOfSignificantAccountingPoliciesAdditionalInformationDetails" xlink:href="hzen-20260630.xsd#DisclosureSummaryOfSignificantAccountingPoliciesAdditionalInformationDetails" xlink:type="simple"/>
        <link:roleRef roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureFairValueOfZenAdditionalInformationDetail" xlink:href="hzen-20260630.xsd#DisclosureFairValueOfZenAdditionalInformationDetail" xlink:type="simple"/>
        <link:roleRef roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureFairValueOfZenSummaryOfChangesInQuantityOfZenAndRespectiveFairValueDetail" xlink:href="hzen-20260630.xsd#DisclosureFairValueOfZenSummaryOfChangesInQuantityOfZenAndRespectiveFairValueDetail" xlink:type="simple"/>
        <link:roleRef roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureCreationsAndRedemptionsOfSharesAdditionalInformationDetail" xlink:href="hzen-20260630.xsd#DisclosureCreationsAndRedemptionsOfSharesAdditionalInformationDetail" xlink:type="simple"/>
        <link:roleRef roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureIncomeTaxesAdditionalInformationDetail" xlink:href="hzen-20260630.xsd#DisclosureIncomeTaxesAdditionalInformationDetail" xlink:type="simple"/>
        <link:roleRef roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureRelatedPartiesAdditionalInformationDetail" xlink:href="hzen-20260630.xsd#DisclosureRelatedPartiesAdditionalInformationDetail" xlink:type="simple"/>
        <link:roleRef roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureFinancialHighlightsPerSharePerformanceSummaryOfPerShareDataDetail" xlink:href="hzen-20260630.xsd#DisclosureFinancialHighlightsPerSharePerformanceSummaryOfPerShareDataDetail" xlink:type="simple"/>
        <link:roleRef roleURI="http://grayscale.com/20260630/taxonomy/role/DisclosureSubsequentEventsAdditionalInformationDetail" xlink:href="hzen-20260630.xsd#DisclosureSubsequentEventsAdditionalInformationDetail" xlink:type="simple"/>
        <link:roleRef roleURI="http://fasb.org/srt/role/srt-eedm/ExtensibleEnumerationLists" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-roles-2025.xsd#eedm1" xlink:type="simple"/>
        <link:roleRef roleURI="http://fasb.org/us-gaap/role/eedm/ExtensibleEnumerationLists" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-roles-2025.xsd#eedm" xlink:type="simple"/>
        <link:roleRef roleURI="http://grayscale.com/20260630/taxonomy/role/StatementStatementsOfAssetsAndLiabilitiesUnaudited2" xlink:href="hzen-20260630.xsd#StatementStatementsOfAssetsAndLiabilitiesUnaudited2" xlink:type="simple"/>
        <link:roleRef roleURI="http://www.xbrl.org/2009/role/negatedLabel" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedLabel" xlink:type="simple"/>
        <link:roleRef roleURI="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedTotalLabel" xlink:type="simple"/>
        <link:labelLink xlink:role="http://www.xbrl.org/2003/role/link" xlink:title="labelLink" xlink:type="extended">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityIncorporationStateCountryCode" xlink:label="dei_EntityIncorporationStateCountryCode"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_IncreaseDecreaseInNetAssetsFromOperationsAndCapitalShareTransactions" xlink:label="hzen_IncreaseDecreaseInNetAssetsFromOperationsAndCapitalShareTransactions"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityAbstract" xlink:label="us-gaap_EquityAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityCurrentReportingStatus" xlink:label="dei_EntityCurrentReportingStatus"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingExpensesAbstract" xlink:label="us-gaap_OperatingExpensesAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel2Member" xlink:label="us-gaap_FairValueInputsLevel2Member"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentCompanyFinancialHighlightsTableTextBlock" xlink:label="us-gaap_InvestmentCompanyFinancialHighlightsTableTextBlock"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_CryptoAssetDomain" xlink:label="srt_CryptoAssetDomain"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentFiscalPeriodFocus" xlink:label="dei_DocumentFiscalPeriodFocus"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityShellCompany" xlink:label="dei_EntityShellCompany"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:label="us-gaap_SegmentReportingPolicyPolicyTextBlock"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsNet" xlink:label="us-gaap_AssetsNet"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesIssued" xlink:label="us-gaap_CommonStockSharesIssued"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementTable" xlink:label="us-gaap_StatementTable"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentCompanyInvestmentIncomeLossFromOperationsPerShare" xlink:label="us-gaap_InvestmentCompanyInvestmentIncomeLossFromOperationsPerShare"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementLineItems" xlink:label="us-gaap_StatementLineItems"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenueFromContractWithCustomerPolicyTextBlock" xlink:label="us-gaap_RevenueFromContractWithCustomerPolicyTextBlock"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityFilerCategory" xlink:label="dei_EntityFilerCategory"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentOwnedBalanceContracts" xlink:label="us-gaap_InvestmentOwnedBalanceContracts"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventLineItems" xlink:label="us-gaap_SubsequentEventLineItems"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdditionalPaidInCapitalCommonStock" xlink:label="us-gaap_AdditionalPaidInCapitalCommonStock"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_InvestmentOwnedAccumulatedNetChangeInUnrecognizedUnrealizedAppreciationDepreciationNet" xlink:label="hzen_InvestmentOwnedAccumulatedNetChangeInUnrecognizedUnrealizedAppreciationDepreciationNet"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SignificantAccountingPoliciesTextBlock" xlink:label="us-gaap_SignificantAccountingPoliciesTextBlock"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskDisclosureTextBlock" xlink:label="us-gaap_ConcentrationRiskDisclosureTextBlock"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentCompanyTotalReturn" xlink:label="us-gaap_InvestmentCompanyTotalReturn"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_CryptoAssetsMiningNumberOfTransactionsPerSecond" xlink:label="hzen_CryptoAssetsMiningNumberOfTransactionsPerSecond"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdjustmentsForNewAccountingPronouncementsAxis" xlink:label="us-gaap_AdjustmentsForNewAccountingPronouncementsAxis"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntitySmallBusiness" xlink:label="dei_EntitySmallBusiness"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_InvestmentsOwnedNewContributions" xlink:label="hzen_InvestmentsOwnedNewContributions"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:label="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_AmendmentFlag" xlink:label="dei_AmendmentFlag"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate" xlink:label="us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressPostalZipCode" xlink:label="dei_EntityAddressPostalZipCode"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingCodmProfitLossMeasureHowUsedDescription" xlink:label="us-gaap_SegmentReportingCodmProfitLossMeasureHowUsedDescription"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleTable" xlink:label="us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleTable"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountingStandardsUpdate202308Member" xlink:label="us-gaap_AccountingStandardsUpdate202308Member"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CryptoAssetNumberOfUnits" xlink:label="us-gaap_CryptoAssetNumberOfUnits"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressAddressLine1" xlink:label="dei_EntityAddressAddressLine1"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateImmaterialEffect" xlink:label="us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateImmaterialEffect"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_NumberOfIncidentalRightsDistributedInPaymentOfSponsorsFee" xlink:label="hzen_NumberOfIncidentalRightsDistributedInPaymentOfSponsorsFee"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:label="us-gaap_FairValueByFairValueHierarchyLevelAxis"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentCompanyInvestmentIncomeLossFromOperationsPerShareAbstract" xlink:label="us-gaap_InvestmentCompanyInvestmentIncomeLossFromOperationsPerShareAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeAxis" xlink:label="us-gaap_InvestmentTypeAxis"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentType" xlink:label="dei_DocumentType"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByParent"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodSharesPeriodIncreaseDecrease" xlink:label="us-gaap_StockIssuedDuringPeriodSharesPeriodIncreaseDecrease"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityCentralIndexKey" xlink:label="dei_EntityCentralIndexKey"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventTypeDomain" xlink:label="us-gaap_SubsequentEventTypeDomain"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_InvestmentInZenMember" xlink:label="hzen_InvestmentInZenMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockParOrStatedValuePerShare" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TypeOfAdoptionMember" xlink:label="us-gaap_TypeOfAdoptionMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingCostsAndExpenses" xlink:label="us-gaap_OperatingCostsAndExpenses"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesAbstract" xlink:label="us-gaap_LiabilitiesAbstract"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_HorizenFoundationMember" xlink:label="hzen_HorizenFoundationMember"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_IndemnificationsDisclosureAbstract" xlink:label="hzen_IndemnificationsDisclosureAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealizedInvestmentGainsLosses" xlink:label="us-gaap_RealizedInvestmentGainsLosses"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_OwnershipDomain" xlink:label="srt_OwnershipDomain"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_CurrentFiscalYearEndDate" xlink:label="dei_CurrentFiscalYearEndDate"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_AccumulatedNetRealizedGainOnInvestment" xlink:label="hzen_AccumulatedNetRealizedGainOnInvestment"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentQuarterlyReport" xlink:label="dei_DocumentQuarterlyReport"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressStateOrProvince" xlink:label="dei_EntityAddressStateOrProvince"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentCompanyInvestmentIncomeLossRatio" xlink:label="us-gaap_InvestmentCompanyInvestmentIncomeLossRatio"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RisksAndUncertaintiesAbstract" xlink:label="us-gaap_RisksAndUncertaintiesAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes" xlink:label="us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventMember" xlink:label="us-gaap_SubsequentEventMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxLiabilityNotRecognizedAmountOfUnrecognizedDeferredTaxLiabilityPolicyholdersSurplus" xlink:label="us-gaap_DeferredTaxLiabilityNotRecognizedAmountOfUnrecognizedDeferredTaxLiabilityPolicyholdersSurplus"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SponsorFees" xlink:label="us-gaap_SponsorFees"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel3Member" xlink:label="us-gaap_FairValueInputsLevel3Member"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentCompanyGainLossOnInvestmentPerShare" xlink:label="us-gaap_InvestmentCompanyGainLossOnInvestmentPerShare"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnrealizedGainLossOnInvestments" xlink:label="us-gaap_UnrealizedGainLossOnInvestments"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_InvestmentMember" xlink:label="hzen_InvestmentMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionsAbstract" xlink:label="us-gaap_RelatedPartyTransactionsAbstract"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_InvestmentOwnedBalanceContractsNewContributions" xlink:label="hzen_InvestmentOwnedBalanceContractsNewContributions"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_HorizenDAOMember" xlink:label="hzen_HorizenDAOMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventsTextBlock" xlink:label="us-gaap_SubsequentEventsTextBlock"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:label="us-gaap_RelatedPartyTransactionsDisclosureTextBlock"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_DCGMember" xlink:label="hzen_DCGMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressAddressLine2" xlink:label="dei_EntityAddressAddressLine2"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueDisclosuresTextBlock" xlink:label="us-gaap_FairValueDisclosuresTextBlock"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentOwnedAtFairValue" xlink:label="us-gaap_InvestmentOwnedAtFairValue"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_NetRealizedAndUnrealizedGainLossAbstract" xlink:label="hzen_NetRealizedAndUnrealizedGainLossAbstract"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_InvestmentOwnedBalanceContractsNetChangeInUnrealizedDepreciationAppreciation" xlink:label="hzen_InvestmentOwnedBalanceContractsNetChangeInUnrealizedDepreciationAppreciation"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingCodmIndividualTitleAndPositionOrGroupOrCommitteeNameExtensibleEnumeration" xlink:label="us-gaap_SegmentReportingCodmIndividualTitleAndPositionOrGroupOrCommitteeNameExtensibleEnumeration"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfInvestmentsLineItems" xlink:label="us-gaap_ScheduleOfInvestmentsLineItems"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:label="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressCityOrTown" xlink:label="dei_EntityAddressCityOrTown"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_Quantityofhorizen" xlink:label="hzen_Quantityofhorizen"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_SecurityExchangeName" xlink:label="dei_SecurityExchangeName"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentOwnedAtCost" xlink:label="us-gaap_InvestmentOwnedAtCost"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeMember" xlink:label="srt_RangeMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentPeriodEndDate" xlink:label="dei_DocumentPeriodEndDate"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:label="us-gaap_FairValueMeasurementsFairValueHierarchyDomain"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementOfFinancialPositionAbstract" xlink:label="us-gaap_StatementOfFinancialPositionAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionRate" xlink:label="us-gaap_RelatedPartyTransactionRate"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Liabilities" xlink:label="us-gaap_Liabilities"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_IncreaseInNetAssetsFromCapitalShareTransactionsAbstract" xlink:label="hzen_IncreaseInNetAssetsFromCapitalShareTransactionsAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityFileNumber" xlink:label="dei_EntityFileNumber"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_CoverAbstract" xlink:label="dei_CoverAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeCategorizationMember" xlink:label="us-gaap_InvestmentTypeCategorizationMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NumberOfOperatingSegments" xlink:label="us-gaap_NumberOfOperatingSegments"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventTable" xlink:label="us-gaap_SubsequentEventTable"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfInvestmentsTable" xlink:label="us-gaap_ScheduleOfInvestmentsTable"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_OwnershipAxis" xlink:label="srt_OwnershipAxis"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeExtensibleEnumeration" xlink:label="us-gaap_InvestmentTypeExtensibleEnumeration"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentHoldingsScheduleOfInvestmentsTableTextBlock" xlink:label="us-gaap_InvestmentHoldingsScheduleOfInvestmentsTableTextBlock"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesOutstanding" xlink:label="us-gaap_CommonStockSharesOutstanding"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_CommonShareEquivalentOfHorizen" xlink:label="hzen_CommonShareEquivalentOfHorizen"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentTransitionReport" xlink:label="dei_DocumentTransitionReport"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_NumberOfIncidentalRightsHeld" xlink:label="hzen_NumberOfIncidentalRightsHeld"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfInvestmentsAbstract" xlink:label="us-gaap_ScheduleOfInvestmentsAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:label="us-gaap_StockholdersEquityNoteDisclosureTextBlock"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLoss" xlink:label="us-gaap_NetIncomeLoss"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_NonSponsorPaidExpensesMember" xlink:label="hzen_NonSponsorPaidExpensesMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsAbstract" xlink:label="us-gaap_AssetsAbstract"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_InvestmentsOwnedDistributions" xlink:label="hzen_InvestmentsOwnedDistributions"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentFiscalYearFocus" xlink:label="dei_DocumentFiscalYearFocus"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_CryptoAssetAxis" xlink:label="srt_CryptoAssetAxis"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_ChangeInSharesOutstandingAbstract" xlink:label="hzen_ChangeInSharesOutstandingAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xlink:label="us-gaap_FairValueMeasurementPolicyPolicyTextBlock"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueDisclosuresAbstract" xlink:label="us-gaap_FairValueDisclosuresAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentOwnedPercentOfNetAssets" xlink:label="us-gaap_InvestmentOwnedPercentOfNetAssets"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_DcgMember" xlink:label="hzen_DcgMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentIncomeNet" xlink:label="us-gaap_InvestmentIncomeNet"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyDomain" xlink:label="us-gaap_RelatedPartyDomain"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxDisclosureTextBlock" xlink:label="us-gaap_IncomeTaxDisclosureTextBlock"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_AdditionalTrustExpensesPaidBySponsor" xlink:label="hzen_AdditionalTrustExpensesPaidBySponsor"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_VisaNetMember" xlink:label="hzen_VisaNetMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxDisclosureAbstract" xlink:label="us-gaap_IncomeTaxDisclosureAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_CommonStockValueSharesAuthorized" xlink:label="hzen_CommonStockValueSharesAuthorized"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems" xlink:label="us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateAdoptionDate" xlink:label="us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateAdoptionDate"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_TradingSymbol" xlink:label="dei_TradingSymbol"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:label="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventTypeAxis" xlink:label="us-gaap_SubsequentEventTypeAxis"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentCompanyFinancialHighlightsAbstract" xlink:label="us-gaap_InvestmentCompanyFinancialHighlightsAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityExTransitionPeriod" xlink:label="dei_EntityExTransitionPeriod"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsPayableCurrentAndNoncurrent" xlink:label="us-gaap_AccountsPayableCurrentAndNoncurrent"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentCompanyFinancialHighlightsTextBlock" xlink:label="us-gaap_InvestmentCompanyFinancialHighlightsTextBlock"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentCompanyInvestmentIncomeLossPerShare" xlink:label="us-gaap_InvestmentCompanyInvestmentIncomeLossPerShare"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentIncomeNetAbstract" xlink:label="us-gaap_InvestmentIncomeNetAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MaximumMember" xlink:label="srt_MaximumMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeAxis" xlink:label="srt_RangeAxis"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionAmountsOfTransaction" xlink:label="us-gaap_RelatedPartyTransactionAmountsOfTransaction"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentCompanyFinancialRatiosAbstract" xlink:label="us-gaap_InvestmentCompanyFinancialRatiosAbstract"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_InvestmentOwnedBalanceSharesHeldByCustodian" xlink:label="hzen_InvestmentOwnedBalanceSharesHeldByCustodian"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentCompanyExpenseRatioIncludingIncentiveFee" xlink:label="us-gaap_InvestmentCompanyExpenseRatioIncludingIncentiveFee"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionLineItems" xlink:label="us-gaap_RelatedPartyTransactionLineItems"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityRegistrantName" xlink:label="dei_EntityRegistrantName"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_InvestmentIncome" xlink:label="hzen_InvestmentIncome"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesHeldInEmployeeTrustShares" xlink:label="us-gaap_CommonStockSharesHeldInEmployeeTrustShares"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventsAbstract" xlink:label="us-gaap_SubsequentEventsAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentCompanyAbstract" xlink:label="us-gaap_InvestmentCompanyAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityCommonStockSharesOutstanding" xlink:label="dei_EntityCommonStockSharesOutstanding"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquityPeriodIncreaseDecrease" xlink:label="us-gaap_StockholdersEquityPeriodIncreaseDecrease"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_CommonStockHeldInEmployeeTrustUnderAuthorization" xlink:label="hzen_CommonStockHeldInEmployeeTrustUnderAuthorization"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventsDate" xlink:label="us-gaap_SubsequentEventsDate"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossOnInvestments" xlink:label="us-gaap_GainLossOnInvestments"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetAssetValuePerShare" xlink:label="us-gaap_NetAssetValuePerShare"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_SponsorMember" xlink:label="hzen_SponsorMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Assets" xlink:label="us-gaap_Assets"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementAbstract" xlink:label="us-gaap_IncomeStatementAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:label="us-gaap_FairValueOfFinancialInstrumentsPolicy"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_IndemnificationsDisclosureTextBlock" xlink:label="hzen_IndemnificationsDisclosureTextBlock"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_Security12gTitle" xlink:label="dei_Security12gTitle"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_CityAreaCode" xlink:label="dei_CityAreaCode"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_NetAssetsAbstract" xlink:label="hzen_NetAssetsAbstract"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_EthereumNetworkMember" xlink:label="hzen_EthereumNetworkMember"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_CryptoAssetNumberOfUnitsTransferred" xlink:label="hzen_CryptoAssetNumberOfUnitsTransferred"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentCompanyFinancialHighlightsRollForward" xlink:label="us-gaap_InvestmentCompanyFinancialHighlightsRollForward"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_SponsorParentMember" xlink:label="hzen_SponsorParentMember"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_CommonUnitsIssuedMinimumBasket" xlink:label="hzen_CommonUnitsIssuedMinimumBasket"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_CoinbaseincMember" xlink:label="hzen_CoinbaseincMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel1Member" xlink:label="us-gaap_FairValueInputsLevel1Member"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateAdopted" xlink:label="us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateAdopted"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_MinimumPercentageOfTaxPositions" xlink:label="hzen_MinimumPercentageOfTaxPositions"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesHeldInEmployeeTrust" xlink:label="us-gaap_CommonStockSharesHeldInEmployeeTrust"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityInteractiveDataCurrent" xlink:label="dei_EntityInteractiveDataCurrent"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLossAttributableToReportingEntityAbstract" xlink:label="us-gaap_NetIncomeLossAttributableToReportingEntityAbstract"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_InvestmentOwnedBalanceContractsDistributed" xlink:label="hzen_InvestmentOwnedBalanceContractsDistributed"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_InvestmentOwnedBalanceContractsNetRealizedLossGain" xlink:label="hzen_InvestmentOwnedBalanceContractsNetRealizedLossGain"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityTaxIdentificationNumber" xlink:label="dei_EntityTaxIdentificationNumber"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_HorizenFairValuePerShare" xlink:label="hzen_HorizenFairValuePerShare"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:label="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_LocalPhoneNumber" xlink:label="dei_LocalPhoneNumber"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_AccumulatedNetInvestmentLoss" xlink:label="hzen_AccumulatedNetInvestmentLoss"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountingPoliciesAbstract" xlink:label="us-gaap_AccountingPoliciesAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesAuthorizedUnlimited" xlink:label="us-gaap_CommonStockSharesAuthorizedUnlimited"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityEmergingGrowthCompany" xlink:label="dei_EntityEmergingGrowthCompany"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_ChiefExecutiveOfficerAndChiefFinancialOfficerMember" xlink:label="hzen_ChiefExecutiveOfficerAndChiefFinancialOfficerMember"/>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityIncorporationStateCountryCode_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Incorporation, State or Country Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_IncreaseDecreaseInNetAssetsFromOperationsAndCapitalShareTransactions_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Increase (decrease) in net assets from operations and capital share transactions.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_IncreaseDecreaseInNetAssetsFromOperationsAndCapitalShareTransactions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase Decrease in Net Assets from Operations and Capital Share Transactions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_IncreaseDecreaseInNetAssetsFromOperationsAndCapitalShareTransactions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total (decrease) increase in net assets from operations and capital share transactions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_IncreaseDecreaseInNetAssetsFromOperationsAndCapitalShareTransactions_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total decrease in net assets from operations and capital share transactions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Measurements, Recurring and Nonrecurring [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Fair Value Estimates</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCurrentReportingStatus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Current Reporting Status</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingExpensesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Expenses [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingExpensesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Expenses:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel2Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Inputs, Level 2 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel2Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Level 2</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentCompanyFinancialHighlightsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Per Share Data</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentCompanyFinancialHighlightsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment Company, Financial Highlights [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_CryptoAssetDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Crypto Asset [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalPeriodFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Fiscal Period Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityShellCompany_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Shell Company</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Segment Reporting</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Beginning of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">End of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Values</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Shares, Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares issued, no par value (unlimited Shares authorized)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentCompanyInvestmentIncomeLossFromOperationsPerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment Company, Investment Income (Loss) from Operations, Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentCompanyInvestmentIncomeLossFromOperationsPerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net decrease in net assets resulting from operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenueFromContractWithCustomerPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revenue from Contract with Customer [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenueFromContractWithCustomerPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Investment Transactions and Revenue Recognition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityFilerCategory_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Filer Category</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentOwnedBalanceContracts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment Owned, Balance, Contracts</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentOwnedBalanceContracts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Investment Owned, Balance, Contracts</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentOwnedBalanceContracts_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Investment Owned, Balance, Contracts</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentOwnedBalanceContracts_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Investment Owned, Balance, Contracts</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, at Federal Statutory Income Tax Rate, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">U.S. Federal income tax rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Event [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Additional Paid in Capital, Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Paid-in-capital</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentOwnedAccumulatedNetChangeInUnrecognizedUnrealizedAppreciationDepreciationNet_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Investment owned, accumulated net change in unrecognized unrealized appreciation (depreciation), net.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentOwnedAccumulatedNetChangeInUnrecognizedUnrealizedAppreciationDepreciationNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment Owned, Accumulated Net Change In Unrecognized Unrealized Appreciation (Depreciation), Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentOwnedAccumulatedNetChangeInUnrecognizedUnrealizedAppreciationDepreciationNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated net change in unrealized depreciation on investment in ZEN</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentOwnedAccumulatedNetChangeInUnrecognizedUnrealizedAppreciationDepreciationNet_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Accumulated net change in unrealized depreciation on investment in ZEN</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SignificantAccountingPoliciesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Significant Accounting Policies [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SignificantAccountingPoliciesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Significant Accounting Policies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Concentration Risk Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Concentration Risk</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentCompanyTotalReturn_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment Company, Total Return</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentCompanyTotalReturn_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total return</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_CryptoAssetsMiningNumberOfTransactionsPerSecond_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Crypto Assets Mining Number of Transactions Per Second</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_CryptoAssetsMiningNumberOfTransactionsPerSecond_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Crypto Assets Mining Number of Transactions Per Second</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_CryptoAssetsMiningNumberOfTransactionsPerSecond_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of transactions per second</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsForNewAccountingPronouncementsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounting Standards Update [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntitySmallBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Small Business</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentsOwnedNewContributions_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">ZEN contributed</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentsOwnedNewContributions_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Investments owned new contributions.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentsOwnedNewContributions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investments Owned New Contributions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentsOwnedNewContributions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">LTC contributed</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Organization, Consolidation and Presentation of Financial Statements [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AmendmentFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amendment Flag</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation at Federal Statutory Income Tax Rate, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Reserves for uncertain tax positions related to federal taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressPostalZipCode_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, Postal Zip Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingCodmProfitLossMeasureHowUsedDescription_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting, CODM, Profit (Loss) Measure, How Used, Description</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounting Standards Update and Change in Accounting Principle [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountingStandardsUpdate202308Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounting Standards Update 2023-08 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CryptoAssetNumberOfUnits_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Crypto Asset, Number of Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CryptoAssetNumberOfUnits_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Crypto Asset, Number of Units, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CryptoAssetNumberOfUnits_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressAddressLine1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, Address Line One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateImmaterialEffect_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Change in Accounting Principle, Accounting Standards Update, Immaterial Effect [true false]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_NumberOfIncidentalRightsDistributedInPaymentOfSponsorsFee_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Number of incidental rights distributed in payment of sponsors fee.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_NumberOfIncidentalRightsDistributedInPaymentOfSponsorsFee_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number of Incidental Rights Distributed in Payment of Sponsors Fee</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_NumberOfIncidentalRightsDistributedInPaymentOfSponsorsFee_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of Incidental Rights distributed</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByFairValueHierarchyLevelAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Hierarchy and NAV [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentCompanyInvestmentIncomeLossFromOperationsPerShareAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment Company, Investment Income (Loss) from Operations, Per Share [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentCompanyInvestmentIncomeLossFromOperationsPerShareAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net decrease in net assets from investment operations:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment Type [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentType_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByParent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsidiary, Ownership Percentage, Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByParent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Percentage of minority interest owned</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesPeriodIncreaseDecrease_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net increase in Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesPeriodIncreaseDecrease_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Shares, Period Increase (Decrease)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCentralIndexKey_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Central Index Key</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Event Type [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentInZenMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Investment in ZEN</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentInZenMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment in ZEN [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentInZenMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Investment in ZEN.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Par or Stated Value Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock, par value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TypeOfAdoptionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounting Standards Update [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingCostsAndExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Operating Costs and Expenses, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingCostsAndExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Costs and Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingCostsAndExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Sponsor's Fees</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Liabilities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_HorizenFoundationMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Horizen Foundation [Member</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_HorizenFoundationMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Horizen Foundation [Member</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_HorizenFoundationMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Horizen Foundation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_IndemnificationsDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Indemnifications Disclosure [Abstract].</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_IndemnificationsDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Indemnifications Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RealizedInvestmentGainsLosses_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net realized loss on investment in ZEN</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RealizedInvestmentGainsLosses_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Realized Investment Gains (Losses), Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RealizedInvestmentGainsLosses_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Realized Investment Gains (Losses)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RealizedInvestmentGainsLosses_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Net realized loss on investment in ZEN</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RealizedInvestmentGainsLosses_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Net realized loss on investment in ZEN</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_OwnershipDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Ownership [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CurrentFiscalYearEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Current Fiscal Year End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_AccumulatedNetRealizedGainOnInvestment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated net realized gain on investment in ZEN</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_AccumulatedNetRealizedGainOnInvestment_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Accumulated net realized gain on investment.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_AccumulatedNetRealizedGainOnInvestment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accumulated Net Realized Gain On Investment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentQuarterlyReport_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Quarterly Report</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressStateOrProvince_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, State or Province</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentCompanyInvestmentIncomeLossRatio_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment Company, Investment Income (Loss) Ratio</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentCompanyInvestmentIncomeLossRatio_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net investment loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RisksAndUncertaintiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Risks and Uncertainties [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, State and Local Income Taxes, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Reserves for uncertain tax positions related to state and local taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Subsequent Event</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Event [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxLiabilityNotRecognizedAmountOfUnrecognizedDeferredTaxLiabilityPolicyholdersSurplus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Liability Not Recognized, Amount of Unrecognized Deferred Tax Liability, Policyholders' Surplus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxLiabilityNotRecognizedAmountOfUnrecognizedDeferredTaxLiabilityPolicyholdersSurplus_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Liability for unrecognized tax amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SponsorFees_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sponsor Fees</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SponsorFees_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Sponsor's Fee, related party</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel3Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Inputs, Level 3 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel3Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Level 3</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentCompanyGainLossOnInvestmentPerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment Company, Gain (Loss) on Investment, Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentCompanyGainLossOnInvestmentPerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net realized and unrealized loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrealizedGainLossOnInvestments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Unrealized Gain (Loss) on Investments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrealizedGainLossOnInvestments_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Net change in unrealized appreciation/depreciation on investment in ZEN</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrealizedGainLossOnInvestments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net change in unrealized appreciation/depreciation on investment in ZEN</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Investment.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Investment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transactions [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentOwnedBalanceContractsNewContributions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">LTC contributed</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentOwnedBalanceContractsNewContributions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment Owned Balance Contracts New Contributions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentOwnedBalanceContractsNewContributions_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Investment Owned, Balance, Contracts New Contributions.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentOwnedBalanceContractsNewContributions_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">ZEN contributed</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_HorizenDAOMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Horizen DAO [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_HorizenDAOMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Horizen DAO [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_HorizenDAOMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Horizen DAO</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Events [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Subsequent Events</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transactions Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Related Parties</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_DCGMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">DCG</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_DCGMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">D C G [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_DCGMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">D C G.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressAddressLine2_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, Address Line Two</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueDisclosuresTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value of ZEN</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueDisclosuresTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Disclosures [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentOwnedAtFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Investment in ZEN</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentOwnedAtFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentOwnedAtFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Investment Owned, at Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentOwnedAtFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Investment Owned, at Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentOwnedAtFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Investment in ZEN, at fair value (cost $17,830 and $18,053 as of June 30, 2026 and December 31, 2025, respectively)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_NetRealizedAndUnrealizedGainLossAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net realized and unrealized loss from:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_NetRealizedAndUnrealizedGainLossAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Net Realized And Unrealized Gain Loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_NetRealizedAndUnrealizedGainLossAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Realized And Unrealized Gain Loss [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_NetRealizedAndUnrealizedGainLossAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Net realized and unrealized loss from:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentOwnedBalanceContractsNetChangeInUnrealizedDepreciationAppreciation_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Investment owned balance contracts net change in unrealized depreciation appreciation.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentOwnedBalanceContractsNetChangeInUnrealizedDepreciationAppreciation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment Owned Balance Contracts Net Change in Unrealized Depreciation Appreciation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentOwnedBalanceContractsNetChangeInUnrealizedDepreciationAppreciation_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net change in unrealized appreciation/depreciation on investment in ZEN</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingCodmIndividualTitleAndPositionOrGroupOrCommitteeNameExtensibleEnumeration_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting, CODM, Individual Title and Position or Group Name [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfInvestmentsLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule Of Investments [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfInvestmentsLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Investments [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related and Nonrelated Parties [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressCityOrTown_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, City or Town</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_Quantityofhorizen_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Quantity of ZEN</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_Quantityofhorizen_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Quantity Of Horizen</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_Quantityofhorizen_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Quantity of horizen.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_SecurityExchangeName_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Security Exchange Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentOwnedAtCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment Owned, Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentOwnedAtCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Investment at fair value cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentOwnedAtCost_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statistical Measurement [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentPeriodEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Period End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementsFairValueHierarchyDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Hierarchy and NAV [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfFinancialPositionAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Financial Position [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transaction, Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Related party sponsor fee percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Liabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Liabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Liabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_IncreaseInNetAssetsFromCapitalShareTransactionsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Increase in Net Assets From Capital Share Transactions.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_IncreaseInNetAssetsFromCapitalShareTransactionsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase In Net Assets From Capital Share Transactions [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_IncreaseInNetAssetsFromCapitalShareTransactionsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Decrease in net assets from capital share transactions:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityFileNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Securities Act File Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityFileNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity File Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CoverAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cover [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentTypeCategorizationMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investments [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfOperatingSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of operating segment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfOperatingSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number of Operating Segments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Event [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfInvestmentsTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Investments [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">New Accounting Pronouncements, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Recently Adopted/Issued Accounting Pronouncements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_OwnershipAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Ownership [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentTypeExtensibleEnumeration_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment, Type [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentHoldingsScheduleOfInvestmentsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment Holdings, Schedule of Investments [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentHoldingsScheduleOfInvestmentsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Changes in Quantity of ZEN and Respective Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Shares, Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares outstanding, no par value (unlimited Shares authorized)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Shares outstanding at end of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Shares outstanding at beginning of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_CommonShareEquivalentOfHorizen_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share represented as ZEN</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_CommonShareEquivalentOfHorizen_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Share Equivalent Of Horizen</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_CommonShareEquivalentOfHorizen_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Common share equivalent of horizen.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentTransitionReport_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Transition Report</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_NumberOfIncidentalRightsHeld_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Number of incidental rights held.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_NumberOfIncidentalRightsHeld_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number Of Incidental Rights Held</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_NumberOfIncidentalRightsHeld_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of incidental rights held</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfInvestmentsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Investments [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Value, New Issues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Shares issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityNoteDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityNoteDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Creations and Redemptions of Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net decrease in net assets resulting from operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_NonSponsorPaidExpensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Non Sponsor Paid Expenses [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_NonSponsorPaidExpensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Non Sponsor Paid Expenses [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_NonSponsorPaidExpensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Non Sponsor</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Assets:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentsOwnedDistributions_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">ZEN distributed for Sponsor's Fee, related party</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentsOwnedDistributions_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Investments owned distributions.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentsOwnedDistributions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investments Owned Distributions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentsOwnedDistributions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">LTC distributed for Sponsor's Fee, related party</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentsOwnedDistributions_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">LTC distributed for Sponsor's Fee, related party</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalYearFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Fiscal Year Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_CryptoAssetAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Crypto Asset [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_ChangeInSharesOutstandingAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Change in Shares outstanding:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_ChangeInSharesOutstandingAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Change In Shares Outstanding [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_ChangeInSharesOutstandingAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Change in shares outstanding.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Measurement, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value Measurement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueDisclosuresAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Disclosures [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentOwnedPercentOfNetAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment Owned, Net Assets, Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentOwnedPercentOfNetAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Percent of Net Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_DcgMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">DCG</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_DcgMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">DCG Member.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_DcgMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">DCG[Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentIncomeNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment Income, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentIncomeNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net investment loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentIncomeNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net investment loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentIncomeNet_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel">Net investment loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related and Nonrelated Parties [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income Taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_AdditionalTrustExpensesPaidBySponsor_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Additional trust expenses paid by sponsor.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_AdditionalTrustExpensesPaidBySponsor_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Additional Trust Expenses Paid By Sponsor</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_AdditionalTrustExpensesPaidBySponsor_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Additional trust expenses paid by sponsor</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_VisaNetMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">VisaNet [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_VisaNetMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">VisaNet [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_VisaNetMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">VisaNet</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Recurring and Nonrecurring [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_CommonStockValueSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock value, shares authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_CommonStockValueSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Common stock value shares authorized.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_CommonStockValueSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amount of shares approved for purchase</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">New Accounting Pronouncements or Change in Accounting Principle [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateAdoptionDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Change in Accounting Principle, Accounting Standards Update, Adoption Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_TradingSymbol_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Trading Symbol</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transaction [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Event Type [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentCompanyFinancialHighlightsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment Company, Financial Highlights [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityExTransitionPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Ex Transition Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableCurrentAndNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Accounts Payable, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableCurrentAndNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableCurrentAndNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Sponsor's Fee payable, related party</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentCompanyFinancialHighlightsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment Company, Financial Highlights [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentCompanyFinancialHighlightsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Financial Highlights Per Share Performance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentCompanyInvestmentIncomeLossPerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment Company, Investment Income (Loss), Per Share, Basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentCompanyInvestmentIncomeLossPerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net investment loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentIncomeNetAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment Income, Net [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentIncomeNetAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Investment income:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MaximumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Maximum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MaximumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Maximum [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statistical Measurement [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionAmountsOfTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transaction, Amounts of Transaction</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionAmountsOfTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Related party maximum transaction in a fiscal year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentCompanyFinancialRatiosAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment Company, Financial Ratios [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentCompanyFinancialRatiosAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Ratios to average net assets:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentOwnedBalanceSharesHeldByCustodian_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Investment owned, balance, shares held by custodian.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentOwnedBalanceSharesHeldByCustodian_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment Owned Balance Shares Held By Custodian</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentOwnedBalanceSharesHeldByCustodian_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Investment owned balance shares held by custodian</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentCompanyExpenseRatioIncludingIncentiveFee_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment Company, Expense Ratio, after Fee Waiver and Incentive Fee Deduction</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentCompanyExpenseRatioIncludingIncentiveFee_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentCompanyExpenseRatioIncludingIncentiveFee_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transaction [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityRegistrantName_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Registrant Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentIncome_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Investment Income.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentIncome_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment Income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentIncome_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Investment income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesHeldInEmployeeTrustShares_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Shares Held in Employee Trust, Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesHeldInEmployeeTrustShares_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares of the Trust, held by related parties</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesHeldInEmployeeTrustShares_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Amount of the Trust, held by related parties</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Events [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentCompanyAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment Company [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Common Stock, Shares Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityPeriodIncreaseDecrease_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stockholders' Equity, Period Increase (Decrease)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityPeriodIncreaseDecrease_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net increase in net assets resulting from capital share transactions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityPeriodIncreaseDecrease_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel">Net increase in net assets resulting from capital share transactions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_CommonStockHeldInEmployeeTrustUnderAuthorization_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Common stock held in employee trust under authorization.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_CommonStockHeldInEmployeeTrustUnderAuthorization_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock Held In Employee Trust Under Authorization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_CommonStockHeldInEmployeeTrustUnderAuthorization_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of shares purchased under authorization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventsDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Event, Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventsDate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Subsequent events date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnInvestments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Gain (Loss) on Investments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnInvestments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net realized and unrealized (loss) gain on investment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnInvestments_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net realized and unrealized loss on investment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetAssetValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Asset Value Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetAssetValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Principal Market NAV, beginning of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetAssetValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Principal Market NAV, end of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetAssetValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Principal Market NAV per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_SponsorMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Sponsor [Member].</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_SponsorMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sponsor [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_SponsorMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Sponsor</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Assets_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Assets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Assets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Statement [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueOfFinancialInstrumentsPolicy_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value of Financial Instruments, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueOfFinancialInstrumentsPolicy_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Principal Market and Fair Value Determination</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_IndemnificationsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Indemnifications Disclosure [Text Block].</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_IndemnificationsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Indemnifications Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_IndemnificationsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Indemnifications</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Shares, New Issues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_Security12gTitle_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Title of 12(g) Security</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CityAreaCode_lbl" xlink:role="http://www.xbrl.org/2003/role/label">City Area Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_NetAssetsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Net assets.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_NetAssetsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Assets [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_NetAssetsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net assets:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_EthereumNetworkMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Ethereum Network</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_EthereumNetworkMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Ethereum Network [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_EthereumNetworkMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Ethereum Network [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_CryptoAssetNumberOfUnitsTransferred_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Crypto Asset, Number of Units Transferred</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_CryptoAssetNumberOfUnitsTransferred_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Crypto asset, number of units transferred.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_CryptoAssetNumberOfUnitsTransferred_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of units transferred</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentCompanyFinancialHighlightsRollForward_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment Company, Financial Highlights [Roll Forward]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_SponsorParentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Sponsor's Parent [Member].</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_SponsorParentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sponsor Parent [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_SponsorParentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Sponsor's Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_CommonUnitsIssuedMinimumBasket_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Common units issued minimum basket.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_CommonUnitsIssuedMinimumBasket_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Units Issued Minimum Basket</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_CommonUnitsIssuedMinimumBasket_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common units issued, minimum basket</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_CoinbaseincMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">CoinbaseInc[Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_CoinbaseincMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Coinbase Inc</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_CoinbaseincMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Coinbase Inc Member</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel1Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Inputs, Level 1 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel1Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Level 1</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateAdopted_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Change in Accounting Principle, Accounting Standards Update, Adopted [true false]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_MinimumPercentageOfTaxPositions_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Minimum percentage of tax positions.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_MinimumPercentageOfTaxPositions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Minimum Percentage Of Tax Positions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_MinimumPercentageOfTaxPositions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Minimum percentage of tax positions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesHeldInEmployeeTrust_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Shares Held in Employee Trust</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesHeldInEmployeeTrust_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amount of the Trust, held by related parties</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityInteractiveDataCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Interactive Data Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLossAttributableToReportingEntityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Income (Loss), Including Portion Attributable to Noncontrolling Interest [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLossAttributableToReportingEntityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Decrease in net assets from operations:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentOwnedBalanceContractsDistributed_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Investment owned, balance, contracts distributed.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentOwnedBalanceContractsDistributed_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment Owned Balance Contracts Distributed</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentOwnedBalanceContractsDistributed_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">LTC distributed for Sponsor's Fee, related party</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentOwnedBalanceContractsDistributed_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">ZEN distributed for Sponsor's Fee, related party</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentOwnedBalanceContractsNetRealizedLossGain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net realized loss on investment in ZEN</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentOwnedBalanceContractsNetRealizedLossGain_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Investment owned balance contracts net realized loss gain.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_InvestmentOwnedBalanceContractsNetRealizedLossGain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment Owned Balance Contracts Net Realized Loss Gain</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityTaxIdentificationNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Tax Identification Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_HorizenFairValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Horizen fair value per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_HorizenFairValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Horizen Fair Value Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_HorizenFairValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Horizen fair value per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Organization, Consolidation and Presentation of Financial Statements Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Organization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_LocalPhoneNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Local Phone Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_AccumulatedNetInvestmentLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Accumulated net investment loss.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_AccumulatedNetInvestmentLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accumulated Net Investment Loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_AccumulatedNetInvestmentLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated net investment loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_AccumulatedNetInvestmentLoss_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Accumulated net investment loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountingPoliciesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounting Policies [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesAuthorizedUnlimited_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Shares Authorized, Unlimited [Fixed List]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesAuthorizedUnlimited_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common shares authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityEmergingGrowthCompany_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Emerging Growth Company</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_ChiefExecutiveOfficerAndChiefFinancialOfficerMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Chief Executive Officer and Chief Financial Officer [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="hzen_ChiefExecutiveOfficerAndChiefFinancialOfficerMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Chief executive officer and chief financial officer.</link:label>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityIncorporationStateCountryCode" xlink:to="dei_EntityIncorporationStateCountryCode_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_IncreaseDecreaseInNetAssetsFromOperationsAndCapitalShareTransactions" xlink:to="hzen_IncreaseDecreaseInNetAssetsFromOperationsAndCapitalShareTransactions_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock" xlink:to="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquityAbstract" xlink:to="us-gaap_EquityAbstract_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityCurrentReportingStatus" xlink:to="dei_EntityCurrentReportingStatus_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingExpensesAbstract" xlink:to="us-gaap_OperatingExpensesAbstract_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueInputsLevel2Member" xlink:to="us-gaap_FairValueInputsLevel2Member_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InvestmentCompanyFinancialHighlightsTableTextBlock" xlink:to="us-gaap_InvestmentCompanyFinancialHighlightsTableTextBlock_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_CryptoAssetDomain" xlink:to="srt_CryptoAssetDomain_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_DocumentFiscalPeriodFocus" xlink:to="dei_DocumentFiscalPeriodFocus_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityShellCompany" xlink:to="dei_EntityShellCompany_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:to="us-gaap_SegmentReportingPolicyPolicyTextBlock_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetsNet" xlink:to="us-gaap_AssetsNet_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockSharesIssued" xlink:to="us-gaap_CommonStockSharesIssued_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementTable" xlink:to="us-gaap_StatementTable_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InvestmentCompanyInvestmentIncomeLossFromOperationsPerShare" xlink:to="us-gaap_InvestmentCompanyInvestmentIncomeLossFromOperationsPerShare_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_StatementLineItems_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RevenueFromContractWithCustomerPolicyTextBlock" xlink:to="us-gaap_RevenueFromContractWithCustomerPolicyTextBlock_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityFilerCategory" xlink:to="dei_EntityFilerCategory_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InvestmentOwnedBalanceContracts" xlink:to="us-gaap_InvestmentOwnedBalanceContracts_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate" xlink:to="us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventLineItems" xlink:to="us-gaap_SubsequentEventLineItems_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AdditionalPaidInCapitalCommonStock" xlink:to="us-gaap_AdditionalPaidInCapitalCommonStock_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_InvestmentOwnedAccumulatedNetChangeInUnrecognizedUnrealizedAppreciationDepreciationNet" xlink:to="hzen_InvestmentOwnedAccumulatedNetChangeInUnrecognizedUnrealizedAppreciationDepreciationNet_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SignificantAccountingPoliciesTextBlock" xlink:to="us-gaap_SignificantAccountingPoliciesTextBlock_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConcentrationRiskDisclosureTextBlock" xlink:to="us-gaap_ConcentrationRiskDisclosureTextBlock_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InvestmentCompanyTotalReturn" xlink:to="us-gaap_InvestmentCompanyTotalReturn_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_CryptoAssetsMiningNumberOfTransactionsPerSecond" xlink:to="hzen_CryptoAssetsMiningNumberOfTransactionsPerSecond_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AdjustmentsForNewAccountingPronouncementsAxis" xlink:to="us-gaap_AdjustmentsForNewAccountingPronouncementsAxis_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntitySmallBusiness" xlink:to="dei_EntitySmallBusiness_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_InvestmentsOwnedNewContributions" xlink:to="hzen_InvestmentsOwnedNewContributions_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:to="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_AmendmentFlag" xlink:to="dei_AmendmentFlag_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate" xlink:to="us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityAddressPostalZipCode" xlink:to="dei_EntityAddressPostalZipCode_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SegmentReportingCodmProfitLossMeasureHowUsedDescription" xlink:to="us-gaap_SegmentReportingCodmProfitLossMeasureHowUsedDescription_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleTable" xlink:to="us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleTable_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountingStandardsUpdate202308Member" xlink:to="us-gaap_AccountingStandardsUpdate202308Member_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CryptoAssetNumberOfUnits" xlink:to="us-gaap_CryptoAssetNumberOfUnits_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityAddressAddressLine1" xlink:to="dei_EntityAddressAddressLine1_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateImmaterialEffect" xlink:to="us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateImmaterialEffect_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_NumberOfIncidentalRightsDistributedInPaymentOfSponsorsFee" xlink:to="hzen_NumberOfIncidentalRightsDistributedInPaymentOfSponsorsFee_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:to="us-gaap_FairValueByFairValueHierarchyLevelAxis_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InvestmentCompanyInvestmentIncomeLossFromOperationsPerShareAbstract" xlink:to="us-gaap_InvestmentCompanyInvestmentIncomeLossFromOperationsPerShareAbstract_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InvestmentTypeAxis" xlink:to="us-gaap_InvestmentTypeAxis_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_DocumentType" xlink:to="dei_DocumentType_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:to="us-gaap_MinorityInterestOwnershipPercentageByParent_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodSharesPeriodIncreaseDecrease" xlink:to="us-gaap_StockIssuedDuringPeriodSharesPeriodIncreaseDecrease_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityCentralIndexKey" xlink:to="dei_EntityCentralIndexKey_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventTypeDomain" xlink:to="us-gaap_SubsequentEventTypeDomain_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_InvestmentInZenMember" xlink:to="hzen_InvestmentInZenMember_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockParOrStatedValuePerShare" xlink:to="us-gaap_CommonStockParOrStatedValuePerShare_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TypeOfAdoptionMember" xlink:to="us-gaap_TypeOfAdoptionMember_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingCostsAndExpenses" xlink:to="us-gaap_OperatingCostsAndExpenses_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesAbstract" xlink:to="us-gaap_LiabilitiesAbstract_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_HorizenFoundationMember" xlink:to="hzen_HorizenFoundationMember_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_IndemnificationsDisclosureAbstract" xlink:to="hzen_IndemnificationsDisclosureAbstract_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RealizedInvestmentGainsLosses" xlink:to="us-gaap_RealizedInvestmentGainsLosses_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_OwnershipDomain" xlink:to="srt_OwnershipDomain_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_CurrentFiscalYearEndDate" xlink:to="dei_CurrentFiscalYearEndDate_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_AccumulatedNetRealizedGainOnInvestment" xlink:to="hzen_AccumulatedNetRealizedGainOnInvestment_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_DocumentQuarterlyReport" xlink:to="dei_DocumentQuarterlyReport_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityAddressStateOrProvince" xlink:to="dei_EntityAddressStateOrProvince_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InvestmentCompanyInvestmentIncomeLossRatio" xlink:to="us-gaap_InvestmentCompanyInvestmentIncomeLossRatio_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RisksAndUncertaintiesAbstract" xlink:to="us-gaap_RisksAndUncertaintiesAbstract_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes" xlink:to="us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventMember" xlink:to="us-gaap_SubsequentEventMember_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DeferredTaxLiabilityNotRecognizedAmountOfUnrecognizedDeferredTaxLiabilityPolicyholdersSurplus" xlink:to="us-gaap_DeferredTaxLiabilityNotRecognizedAmountOfUnrecognizedDeferredTaxLiabilityPolicyholdersSurplus_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SponsorFees" xlink:to="us-gaap_SponsorFees_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueInputsLevel3Member" xlink:to="us-gaap_FairValueInputsLevel3Member_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InvestmentCompanyGainLossOnInvestmentPerShare" xlink:to="us-gaap_InvestmentCompanyGainLossOnInvestmentPerShare_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_UnrealizedGainLossOnInvestments" xlink:to="us-gaap_UnrealizedGainLossOnInvestments_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_InvestmentMember" xlink:to="hzen_InvestmentMember_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyTransactionsAbstract" xlink:to="us-gaap_RelatedPartyTransactionsAbstract_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_InvestmentOwnedBalanceContractsNewContributions" xlink:to="hzen_InvestmentOwnedBalanceContractsNewContributions_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_HorizenDAOMember" xlink:to="hzen_HorizenDAOMember_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventsTextBlock" xlink:to="us-gaap_SubsequentEventsTextBlock_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:to="us-gaap_RelatedPartyTransactionsDisclosureTextBlock_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_DCGMember" xlink:to="hzen_DCGMember_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityAddressAddressLine2" xlink:to="dei_EntityAddressAddressLine2_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueDisclosuresTextBlock" xlink:to="us-gaap_FairValueDisclosuresTextBlock_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InvestmentOwnedAtFairValue" xlink:to="us-gaap_InvestmentOwnedAtFairValue_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_NetRealizedAndUnrealizedGainLossAbstract" xlink:to="hzen_NetRealizedAndUnrealizedGainLossAbstract_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_InvestmentOwnedBalanceContractsNetChangeInUnrealizedDepreciationAppreciation" xlink:to="hzen_InvestmentOwnedBalanceContractsNetChangeInUnrealizedDepreciationAppreciation_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SegmentReportingCodmIndividualTitleAndPositionOrGroupOrCommitteeNameExtensibleEnumeration" xlink:to="us-gaap_SegmentReportingCodmIndividualTitleAndPositionOrGroupOrCommitteeNameExtensibleEnumeration_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfInvestmentsLineItems" xlink:to="us-gaap_ScheduleOfInvestmentsLineItems_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:to="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityAddressCityOrTown" xlink:to="dei_EntityAddressCityOrTown_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_Quantityofhorizen" xlink:to="hzen_Quantityofhorizen_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_SecurityExchangeName" xlink:to="dei_SecurityExchangeName_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InvestmentOwnedAtCost" xlink:to="us-gaap_InvestmentOwnedAtCost_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_RangeMember" xlink:to="srt_RangeMember_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_DocumentPeriodEndDate" xlink:to="dei_DocumentPeriodEndDate_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:to="us-gaap_FairValueMeasurementsFairValueHierarchyDomain_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementOfFinancialPositionAbstract" xlink:to="us-gaap_StatementOfFinancialPositionAbstract_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyTransactionRate" xlink:to="us-gaap_RelatedPartyTransactionRate_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Liabilities" xlink:to="us-gaap_Liabilities_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_IncreaseInNetAssetsFromCapitalShareTransactionsAbstract" xlink:to="hzen_IncreaseInNetAssetsFromCapitalShareTransactionsAbstract_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityFileNumber" xlink:to="dei_EntityFileNumber_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_CoverAbstract" xlink:to="dei_CoverAbstract_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InvestmentTypeCategorizationMember" xlink:to="us-gaap_InvestmentTypeCategorizationMember_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NumberOfOperatingSegments" xlink:to="us-gaap_NumberOfOperatingSegments_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventTable" xlink:to="us-gaap_SubsequentEventTable_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfInvestmentsTable" xlink:to="us-gaap_ScheduleOfInvestmentsTable_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:to="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_OwnershipAxis" xlink:to="srt_OwnershipAxis_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InvestmentTypeExtensibleEnumeration" xlink:to="us-gaap_InvestmentTypeExtensibleEnumeration_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InvestmentHoldingsScheduleOfInvestmentsTableTextBlock" xlink:to="us-gaap_InvestmentHoldingsScheduleOfInvestmentsTableTextBlock_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockSharesOutstanding" xlink:to="us-gaap_CommonStockSharesOutstanding_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_CommonShareEquivalentOfHorizen" xlink:to="hzen_CommonShareEquivalentOfHorizen_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_DocumentTransitionReport" xlink:to="dei_DocumentTransitionReport_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_NumberOfIncidentalRightsHeld" xlink:to="hzen_NumberOfIncidentalRightsHeld_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfInvestmentsAbstract" xlink:to="us-gaap_ScheduleOfInvestmentsAbstract_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:to="us-gaap_StockIssuedDuringPeriodValueNewIssues_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:to="us-gaap_StockholdersEquityNoteDisclosureTextBlock_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetIncomeLoss" xlink:to="us-gaap_NetIncomeLoss_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_NonSponsorPaidExpensesMember" xlink:to="hzen_NonSponsorPaidExpensesMember_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetsAbstract" xlink:to="us-gaap_AssetsAbstract_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_InvestmentsOwnedDistributions" xlink:to="hzen_InvestmentsOwnedDistributions_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_DocumentFiscalYearFocus" xlink:to="dei_DocumentFiscalYearFocus_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_CryptoAssetAxis" xlink:to="srt_CryptoAssetAxis_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_ChangeInSharesOutstandingAbstract" xlink:to="hzen_ChangeInSharesOutstandingAbstract_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xlink:to="us-gaap_FairValueMeasurementPolicyPolicyTextBlock_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueDisclosuresAbstract" xlink:to="us-gaap_FairValueDisclosuresAbstract_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InvestmentOwnedPercentOfNetAssets" xlink:to="us-gaap_InvestmentOwnedPercentOfNetAssets_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_DcgMember" xlink:to="hzen_DcgMember_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InvestmentIncomeNet" xlink:to="us-gaap_InvestmentIncomeNet_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyDomain" xlink:to="us-gaap_RelatedPartyDomain_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeTaxDisclosureTextBlock" xlink:to="us-gaap_IncomeTaxDisclosureTextBlock_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_AdditionalTrustExpensesPaidBySponsor" xlink:to="hzen_AdditionalTrustExpensesPaidBySponsor_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_VisaNetMember" xlink:to="hzen_VisaNetMember_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeTaxDisclosureAbstract" xlink:to="us-gaap_IncomeTaxDisclosureAbstract_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:to="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_CommonStockValueSharesAuthorized" xlink:to="hzen_CommonStockValueSharesAuthorized_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems" xlink:to="us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateAdoptionDate" xlink:to="us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateAdoptionDate_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_TradingSymbol" xlink:to="dei_TradingSymbol_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:to="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventTypeAxis" xlink:to="us-gaap_SubsequentEventTypeAxis_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InvestmentCompanyFinancialHighlightsAbstract" xlink:to="us-gaap_InvestmentCompanyFinancialHighlightsAbstract_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityExTransitionPeriod" xlink:to="dei_EntityExTransitionPeriod_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsPayableCurrentAndNoncurrent" xlink:to="us-gaap_AccountsPayableCurrentAndNoncurrent_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InvestmentCompanyFinancialHighlightsTextBlock" xlink:to="us-gaap_InvestmentCompanyFinancialHighlightsTextBlock_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InvestmentCompanyInvestmentIncomeLossPerShare" xlink:to="us-gaap_InvestmentCompanyInvestmentIncomeLossPerShare_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InvestmentIncomeNetAbstract" xlink:to="us-gaap_InvestmentIncomeNetAbstract_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_MaximumMember" xlink:to="srt_MaximumMember_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_RangeAxis" xlink:to="srt_RangeAxis_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyTransactionAmountsOfTransaction" xlink:to="us-gaap_RelatedPartyTransactionAmountsOfTransaction_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InvestmentCompanyFinancialRatiosAbstract" xlink:to="us-gaap_InvestmentCompanyFinancialRatiosAbstract_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_InvestmentOwnedBalanceSharesHeldByCustodian" xlink:to="hzen_InvestmentOwnedBalanceSharesHeldByCustodian_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InvestmentCompanyExpenseRatioIncludingIncentiveFee" xlink:to="us-gaap_InvestmentCompanyExpenseRatioIncludingIncentiveFee_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="us-gaap_RelatedPartyTransactionLineItems_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityRegistrantName" xlink:to="dei_EntityRegistrantName_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_InvestmentIncome" xlink:to="hzen_InvestmentIncome_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockSharesHeldInEmployeeTrustShares" xlink:to="us-gaap_CommonStockSharesHeldInEmployeeTrustShares_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventsAbstract" xlink:to="us-gaap_SubsequentEventsAbstract_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InvestmentCompanyAbstract" xlink:to="us-gaap_InvestmentCompanyAbstract_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityCommonStockSharesOutstanding" xlink:to="dei_EntityCommonStockSharesOutstanding_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockholdersEquityPeriodIncreaseDecrease" xlink:to="us-gaap_StockholdersEquityPeriodIncreaseDecrease_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_CommonStockHeldInEmployeeTrustUnderAuthorization" xlink:to="hzen_CommonStockHeldInEmployeeTrustUnderAuthorization_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventsDate" xlink:to="us-gaap_SubsequentEventsDate_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GainLossOnInvestments" xlink:to="us-gaap_GainLossOnInvestments_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetAssetValuePerShare" xlink:to="us-gaap_NetAssetValuePerShare_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_SponsorMember" xlink:to="hzen_SponsorMember_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Assets" xlink:to="us-gaap_Assets_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeStatementAbstract" xlink:to="us-gaap_IncomeStatementAbstract_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:to="us-gaap_FairValueOfFinancialInstrumentsPolicy_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_IndemnificationsDisclosureTextBlock" xlink:to="hzen_IndemnificationsDisclosureTextBlock_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:to="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_Security12gTitle" xlink:to="dei_Security12gTitle_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_CityAreaCode" xlink:to="dei_CityAreaCode_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_NetAssetsAbstract" xlink:to="hzen_NetAssetsAbstract_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_EthereumNetworkMember" xlink:to="hzen_EthereumNetworkMember_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_CryptoAssetNumberOfUnitsTransferred" xlink:to="hzen_CryptoAssetNumberOfUnitsTransferred_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InvestmentCompanyFinancialHighlightsRollForward" xlink:to="us-gaap_InvestmentCompanyFinancialHighlightsRollForward_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_SponsorParentMember" xlink:to="hzen_SponsorParentMember_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_CommonUnitsIssuedMinimumBasket" xlink:to="hzen_CommonUnitsIssuedMinimumBasket_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_CoinbaseincMember" xlink:to="hzen_CoinbaseincMember_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueInputsLevel1Member" xlink:to="us-gaap_FairValueInputsLevel1Member_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateAdopted" xlink:to="us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateAdopted_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_MinimumPercentageOfTaxPositions" xlink:to="hzen_MinimumPercentageOfTaxPositions_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockSharesHeldInEmployeeTrust" xlink:to="us-gaap_CommonStockSharesHeldInEmployeeTrust_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityInteractiveDataCurrent" xlink:to="dei_EntityInteractiveDataCurrent_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetIncomeLossAttributableToReportingEntityAbstract" xlink:to="us-gaap_NetIncomeLossAttributableToReportingEntityAbstract_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_InvestmentOwnedBalanceContractsDistributed" xlink:to="hzen_InvestmentOwnedBalanceContractsDistributed_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_InvestmentOwnedBalanceContractsNetRealizedLossGain" xlink:to="hzen_InvestmentOwnedBalanceContractsNetRealizedLossGain_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityTaxIdentificationNumber" xlink:to="dei_EntityTaxIdentificationNumber_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_HorizenFairValuePerShare" xlink:to="hzen_HorizenFairValuePerShare_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:to="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_LocalPhoneNumber" xlink:to="dei_LocalPhoneNumber_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_AccumulatedNetInvestmentLoss" xlink:to="hzen_AccumulatedNetInvestmentLoss_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountingPoliciesAbstract" xlink:to="us-gaap_AccountingPoliciesAbstract_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockSharesAuthorizedUnlimited" xlink:to="us-gaap_CommonStockSharesAuthorizedUnlimited_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityEmergingGrowthCompany" xlink:to="dei_EntityEmergingGrowthCompany_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="hzen_ChiefExecutiveOfficerAndChiefFinancialOfficerMember" xlink:to="hzen_ChiefExecutiveOfficerAndChiefFinancialOfficerMember_lbl"/>
        </link:labelLink>
        <link:presentationLink xlink:role="http://grayscale.com/20260630/taxonomy/role/DocumentDocumentAndEntityInformation" xlink:title="presentationLink" xlink:type="extended">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_CoverAbstract" xlink:label="dei_CoverAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentType" xlink:label="dei_DocumentType"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_AmendmentFlag" xlink:label="dei_AmendmentFlag"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentPeriodEndDate" xlink:label="dei_DocumentPeriodEndDate"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentFiscalYearFocus" xlink:label="dei_DocumentFiscalYearFocus"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentFiscalPeriodFocus" xlink:label="dei_DocumentFiscalPeriodFocus"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_CurrentFiscalYearEndDate" xlink:label="dei_CurrentFiscalYearEndDate"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentQuarterlyReport" xlink:label="dei_DocumentQuarterlyReport"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentTransitionReport" xlink:label="dei_DocumentTransitionReport"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityCentralIndexKey" xlink:label="dei_EntityCentralIndexKey"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityFileNumber" xlink:label="dei_EntityFileNumber"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityRegistrantName" xlink:label="dei_EntityRegistrantName"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityIncorporationStateCountryCode" xlink:label="dei_EntityIncorporationStateCountryCode"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityTaxIdentificationNumber" xlink:label="dei_EntityTaxIdentificationNumber"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressAddressLine1" xlink:label="dei_EntityAddressAddressLine1"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressAddressLine2" xlink:label="dei_EntityAddressAddressLine2"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressCityOrTown" xlink:label="dei_EntityAddressCityOrTown"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressStateOrProvince" xlink:label="dei_EntityAddressStateOrProvince"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressPostalZipCode" xlink:label="dei_EntityAddressPostalZipCode"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_CityAreaCode" xlink:label="dei_CityAreaCode"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_LocalPhoneNumber" xlink:label="dei_LocalPhoneNumber"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_Security12gTitle" xlink:label="dei_Security12gTitle"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_TradingSymbol" xlink:label="dei_TradingSymbol"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_SecurityExchangeName" xlink:label="dei_SecurityExchangeName"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityCurrentReportingStatus" xlink:label="dei_EntityCurrentReportingStatus"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityInteractiveDataCurrent" xlink:label="dei_EntityInteractiveDataCurrent"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityFilerCategory" xlink:label="dei_EntityFilerCategory"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntitySmallBusiness" xlink:label="dei_EntitySmallBusiness"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityEmergingGrowthCompany" xlink:label="dei_EntityEmergingGrowthCompany"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityExTransitionPeriod" xlink:label="dei_EntityExTransitionPeriod"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityShellCompany" xlink:label="dei_EntityShellCompany"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityCommonStockSharesOutstanding" xlink:label="dei_EntityCommonStockSharesOutstanding"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_CoverAbstract" xlink:to="dei_DocumentType" order="49.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_CoverAbstract" xlink:to="dei_AmendmentFlag" order="50.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_CoverAbstract" xlink:to="dei_DocumentPeriodEndDate" order="51.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_CoverAbstract" xlink:to="dei_DocumentFiscalYearFocus" order="52.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_CoverAbstract" xlink:to="dei_DocumentFiscalPeriodFocus" order="53.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_CoverAbstract" xlink:to="dei_CurrentFiscalYearEndDate" order="54.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_CoverAbstract" xlink:to="dei_DocumentQuarterlyReport" order="55.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_CoverAbstract" xlink:to="dei_DocumentTransitionReport" order="56.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_CoverAbstract" xlink:to="dei_EntityCentralIndexKey" order="57.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_CoverAbstract" xlink:to="dei_EntityFileNumber" order="58.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_CoverAbstract" xlink:to="dei_EntityRegistrantName" order="59.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_CoverAbstract" xlink:to="dei_EntityIncorporationStateCountryCode" order="60.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_CoverAbstract" xlink:to="dei_EntityTaxIdentificationNumber" order="61.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_CoverAbstract" xlink:to="dei_EntityAddressAddressLine1" order="62.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_CoverAbstract" xlink:to="dei_EntityAddressAddressLine2" order="63.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_CoverAbstract" xlink:to="dei_EntityAddressCityOrTown" order="64.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_CoverAbstract" xlink:to="dei_EntityAddressStateOrProvince" order="65.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_CoverAbstract" xlink:to="dei_EntityAddressPostalZipCode" order="66.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_CoverAbstract" xlink:to="dei_CityAreaCode" order="67.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_CoverAbstract" xlink:to="dei_LocalPhoneNumber" order="68.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_CoverAbstract" xlink:to="dei_Security12gTitle" order="69.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_CoverAbstract" xlink:to="dei_TradingSymbol" order="70.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_CoverAbstract" xlink:to="dei_SecurityExchangeName" order="71.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_CoverAbstract" xlink:to="dei_EntityCurrentReportingStatus" order="72.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_CoverAbstract" xlink:to="dei_EntityInteractiveDataCurrent" order="73.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_CoverAbstract" xlink:to="dei_EntityFilerCategory" order="74.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_CoverAbstract" xlink:to="dei_EntitySmallBusiness" order="75.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_CoverAbstract" xlink:to="dei_EntityEmergingGrowthCompany" order="76.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_CoverAbstract" xlink:to="dei_EntityExTransitionPeriod" order="77.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_CoverAbstract" xlink:to="dei_EntityShellCompany" order="78.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_CoverAbstract" xlink:to="dei_EntityCommonStockSharesOutstanding" order="79.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
        </link:presentationLink>
        <link:presentationLink xlink:role="http://grayscale.com/20260630/taxonomy/role/StatementStatementsOfAssetsAndLiabilitiesUnaudited" xlink:title="presentationLink" xlink:type="extended">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementTable" xlink:label="us-gaap_StatementTable"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:label="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementLineItems" xlink:label="us-gaap_StatementLineItems"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsAbstract" xlink:label="us-gaap_AssetsAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesAbstract" xlink:label="us-gaap_LiabilitiesAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsPayableCurrentAndNoncurrent" xlink:label="us-gaap_AccountsPayableCurrentAndNoncurrent"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyDomain" xlink:label="us-gaap_RelatedPartyDomain"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementOfFinancialPositionAbstract" xlink:label="us-gaap_StatementOfFinancialPositionAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentOwnedAtFairValue" xlink:label="us-gaap_InvestmentOwnedAtFairValue"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_SponsorMember" xlink:label="hzen_SponsorMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Liabilities" xlink:label="us-gaap_Liabilities"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Assets" xlink:label="us-gaap_Assets"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsNet" xlink:label="us-gaap_AssetsNet"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdditionalPaidInCapitalCommonStock" xlink:label="us-gaap_AdditionalPaidInCapitalCommonStock"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_AccumulatedNetInvestmentLoss" xlink:label="hzen_AccumulatedNetInvestmentLoss"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_AccumulatedNetRealizedGainOnInvestment" xlink:label="hzen_AccumulatedNetRealizedGainOnInvestment"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_InvestmentOwnedAccumulatedNetChangeInUnrecognizedUnrealizedAppreciationDepreciationNet" xlink:label="hzen_InvestmentOwnedAccumulatedNetChangeInUnrecognizedUnrealizedAppreciationDepreciationNet"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesIssued" xlink:label="us-gaap_CommonStockSharesIssued"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesOutstanding" xlink:label="us-gaap_CommonStockSharesOutstanding"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetAssetValuePerShare" xlink:label="us-gaap_NetAssetValuePerShare"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_StatementTable" xlink:to="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_AssetsAbstract" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_LiabilitiesAbstract" xlink:to="us-gaap_AccountsPayableCurrentAndNoncurrent" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:to="us-gaap_RelatedPartyDomain" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_StatementOfFinancialPositionAbstract" xlink:to="us-gaap_StatementTable" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_AssetsAbstract" xlink:to="us-gaap_InvestmentOwnedAtFairValue" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_RelatedPartyDomain" xlink:to="hzen_SponsorMember" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_StatementTable" xlink:to="us-gaap_StatementLineItems" order="1" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_LiabilitiesAbstract" order="1" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_LiabilitiesAbstract" xlink:to="us-gaap_Liabilities" order="1" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/totalLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_AssetsAbstract" xlink:to="us-gaap_Assets" order="1" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/totalLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_AssetsNet" order="2" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/totalLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_AdditionalPaidInCapitalCommonStock" order="3" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_StatementLineItems" xlink:to="hzen_AccumulatedNetInvestmentLoss" order="4" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2009/role/negatedLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_StatementLineItems" xlink:to="hzen_AccumulatedNetRealizedGainOnInvestment" order="5" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_StatementLineItems" xlink:to="hzen_InvestmentOwnedAccumulatedNetChangeInUnrecognizedUnrealizedAppreciationDepreciationNet" order="6" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2009/role/negatedLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_CommonStockSharesIssued" order="7" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_CommonStockSharesOutstanding" order="8" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_NetAssetValuePerShare" order="9" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
        </link:presentationLink>
        <link:presentationLink xlink:role="http://grayscale.com/20260630/taxonomy/role/StatementStatementsOfAssetsAndLiabilitiesUnauditedParenthetical" xlink:title="presentationLink" xlink:type="extended">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementOfFinancialPositionAbstract" xlink:label="us-gaap_StatementOfFinancialPositionAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentOwnedAtCost" xlink:label="us-gaap_InvestmentOwnedAtCost"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockParOrStatedValuePerShare" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesAuthorizedUnlimited" xlink:label="us-gaap_CommonStockSharesAuthorizedUnlimited"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_StatementOfFinancialPositionAbstract" xlink:to="us-gaap_InvestmentOwnedAtCost" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_StatementOfFinancialPositionAbstract" xlink:to="us-gaap_CommonStockParOrStatedValuePerShare" order="1" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_StatementOfFinancialPositionAbstract" xlink:to="us-gaap_CommonStockSharesAuthorizedUnlimited" order="2" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
        </link:presentationLink>
        <link:presentationLink xlink:role="http://grayscale.com/20260630/taxonomy/role/StatementSchedulesOfInvestmentUnaudited" xlink:title="presentationLink" xlink:type="extended">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeAxis" xlink:label="us-gaap_InvestmentTypeAxis"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeCategorizationMember" xlink:label="us-gaap_InvestmentTypeCategorizationMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfInvestmentsLineItems" xlink:label="us-gaap_ScheduleOfInvestmentsLineItems"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_Quantityofhorizen" xlink:label="hzen_Quantityofhorizen"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_InvestmentInZenMember" xlink:label="hzen_InvestmentInZenMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfInvestmentsTable" xlink:label="us-gaap_ScheduleOfInvestmentsTable"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfInvestmentsAbstract" xlink:label="us-gaap_ScheduleOfInvestmentsAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeExtensibleEnumeration" xlink:label="us-gaap_InvestmentTypeExtensibleEnumeration"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_InvestmentMember" xlink:label="hzen_InvestmentMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentOwnedAtCost" xlink:label="us-gaap_InvestmentOwnedAtCost"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentOwnedAtFairValue" xlink:label="us-gaap_InvestmentOwnedAtFairValue"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentOwnedPercentOfNetAssets" xlink:label="us-gaap_InvestmentOwnedPercentOfNetAssets"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_InvestmentTypeAxis" xlink:to="us-gaap_InvestmentTypeCategorizationMember" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_ScheduleOfInvestmentsLineItems" xlink:to="hzen_Quantityofhorizen" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_InvestmentTypeCategorizationMember" xlink:to="hzen_InvestmentInZenMember" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_ScheduleOfInvestmentsTable" xlink:to="us-gaap_InvestmentTypeAxis" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_ScheduleOfInvestmentsAbstract" xlink:to="us-gaap_ScheduleOfInvestmentsTable" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_ScheduleOfInvestmentsLineItems" xlink:to="us-gaap_InvestmentTypeExtensibleEnumeration" order="1" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_InvestmentTypeCategorizationMember" xlink:to="hzen_InvestmentMember" order="1" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_ScheduleOfInvestmentsTable" xlink:to="us-gaap_ScheduleOfInvestmentsLineItems" order="1" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_ScheduleOfInvestmentsLineItems" xlink:to="us-gaap_InvestmentOwnedAtCost" order="2" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/verboseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_ScheduleOfInvestmentsLineItems" xlink:to="us-gaap_InvestmentOwnedAtFairValue" order="3" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_ScheduleOfInvestmentsLineItems" xlink:to="us-gaap_InvestmentOwnedPercentOfNetAssets" order="4" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
        </link:presentationLink>
        <link:presentationLink xlink:role="http://grayscale.com/20260630/taxonomy/role/StatementStatementsOfOperationsUnaudited" xlink:title="presentationLink" xlink:type="extended">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingExpensesAbstract" xlink:label="us-gaap_OperatingExpensesAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SponsorFees" xlink:label="us-gaap_SponsorFees"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_NetRealizedAndUnrealizedGainLossAbstract" xlink:label="hzen_NetRealizedAndUnrealizedGainLossAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealizedInvestmentGainsLosses" xlink:label="us-gaap_RealizedInvestmentGainsLosses"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentIncomeNetAbstract" xlink:label="us-gaap_InvestmentIncomeNetAbstract"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_InvestmentIncome" xlink:label="hzen_InvestmentIncome"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementAbstract" xlink:label="us-gaap_IncomeStatementAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnrealizedGainLossOnInvestments" xlink:label="us-gaap_UnrealizedGainLossOnInvestments"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentIncomeNet" xlink:label="us-gaap_InvestmentIncomeNet"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossOnInvestments" xlink:label="us-gaap_GainLossOnInvestments"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLoss" xlink:label="us-gaap_NetIncomeLoss"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_OperatingExpensesAbstract" xlink:to="us-gaap_SponsorFees" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="hzen_NetRealizedAndUnrealizedGainLossAbstract" xlink:to="us-gaap_RealizedInvestmentGainsLosses" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_InvestmentIncomeNetAbstract" xlink:to="hzen_InvestmentIncome" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_IncomeStatementAbstract" xlink:to="us-gaap_InvestmentIncomeNetAbstract" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="hzen_NetRealizedAndUnrealizedGainLossAbstract" xlink:to="us-gaap_UnrealizedGainLossOnInvestments" order="1" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_IncomeStatementAbstract" xlink:to="us-gaap_OperatingExpensesAbstract" order="1" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_IncomeStatementAbstract" xlink:to="us-gaap_InvestmentIncomeNet" order="2" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/totalLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_IncomeStatementAbstract" xlink:to="hzen_NetRealizedAndUnrealizedGainLossAbstract" order="3" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/verboseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_IncomeStatementAbstract" xlink:to="us-gaap_GainLossOnInvestments" order="4" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/totalLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_IncomeStatementAbstract" xlink:to="us-gaap_NetIncomeLoss" order="5" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/totalLabel"/>
        </link:presentationLink>
        <link:presentationLink xlink:role="http://grayscale.com/20260630/taxonomy/role/StatementStatementsOfChangesInNetAssetsUnaudited" xlink:title="presentationLink" xlink:type="extended">
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_IncreaseInNetAssetsFromCapitalShareTransactionsAbstract" xlink:label="hzen_IncreaseInNetAssetsFromCapitalShareTransactionsAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_ChangeInSharesOutstandingAbstract" xlink:label="hzen_ChangeInSharesOutstandingAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesOutstanding" xlink:label="us-gaap_CommonStockSharesOutstanding"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentCompanyAbstract" xlink:label="us-gaap_InvestmentCompanyAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLossAttributableToReportingEntityAbstract" xlink:label="us-gaap_NetIncomeLossAttributableToReportingEntityAbstract"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_NetAssetsAbstract" xlink:label="hzen_NetAssetsAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsNet" xlink:label="us-gaap_AssetsNet"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentIncomeNet" xlink:label="us-gaap_InvestmentIncomeNet"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquityPeriodIncreaseDecrease" xlink:label="us-gaap_StockholdersEquityPeriodIncreaseDecrease"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsNet" xlink:label="us-gaap_AssetsNet_1"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealizedInvestmentGainsLosses" xlink:label="us-gaap_RealizedInvestmentGainsLosses"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_IncreaseDecreaseInNetAssetsFromOperationsAndCapitalShareTransactions" xlink:label="hzen_IncreaseDecreaseInNetAssetsFromOperationsAndCapitalShareTransactions"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodSharesPeriodIncreaseDecrease" xlink:label="us-gaap_StockIssuedDuringPeriodSharesPeriodIncreaseDecrease"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnrealizedGainLossOnInvestments" xlink:label="us-gaap_UnrealizedGainLossOnInvestments"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesOutstanding" xlink:label="us-gaap_CommonStockSharesOutstanding_3"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLoss" xlink:label="us-gaap_NetIncomeLoss"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="hzen_IncreaseInNetAssetsFromCapitalShareTransactionsAbstract" xlink:to="us-gaap_StockIssuedDuringPeriodValueNewIssues" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="hzen_ChangeInSharesOutstandingAbstract" xlink:to="us-gaap_CommonStockSharesOutstanding" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/periodStartLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_InvestmentCompanyAbstract" xlink:to="us-gaap_NetIncomeLossAttributableToReportingEntityAbstract" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="hzen_NetAssetsAbstract" xlink:to="us-gaap_AssetsNet" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/periodStartLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_NetIncomeLossAttributableToReportingEntityAbstract" xlink:to="us-gaap_InvestmentIncomeNet" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="hzen_IncreaseInNetAssetsFromCapitalShareTransactionsAbstract" xlink:to="us-gaap_StockholdersEquityPeriodIncreaseDecrease" order="1" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/totalLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="hzen_ChangeInSharesOutstandingAbstract" xlink:to="us-gaap_StockIssuedDuringPeriodSharesNewIssues" order="1" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="hzen_NetAssetsAbstract" xlink:to="us-gaap_AssetsNet_1" order="1" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/periodEndLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_NetIncomeLossAttributableToReportingEntityAbstract" xlink:to="us-gaap_RealizedInvestmentGainsLosses" order="1" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/verboseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="hzen_IncreaseInNetAssetsFromCapitalShareTransactionsAbstract" xlink:to="hzen_IncreaseDecreaseInNetAssetsFromOperationsAndCapitalShareTransactions" order="2" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/totalLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="hzen_ChangeInSharesOutstandingAbstract" xlink:to="us-gaap_StockIssuedDuringPeriodSharesPeriodIncreaseDecrease" order="2" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_NetIncomeLossAttributableToReportingEntityAbstract" xlink:to="us-gaap_UnrealizedGainLossOnInvestments" order="2" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="hzen_ChangeInSharesOutstandingAbstract" xlink:to="us-gaap_CommonStockSharesOutstanding_3" order="3" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/periodEndLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_NetIncomeLossAttributableToReportingEntityAbstract" xlink:to="us-gaap_NetIncomeLoss" order="3" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/totalLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_NetIncomeLossAttributableToReportingEntityAbstract" xlink:to="hzen_IncreaseInNetAssetsFromCapitalShareTransactionsAbstract" order="4" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_NetIncomeLossAttributableToReportingEntityAbstract" xlink:to="hzen_NetAssetsAbstract" order="5" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_NetIncomeLossAttributableToReportingEntityAbstract" xlink:to="hzen_ChangeInSharesOutstandingAbstract" order="6" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
        </link:presentationLink>
        <link:presentationLink xlink:role="http://grayscale.com/20260630/taxonomy/role/DisclosureOrganization" xlink:title="presentationLink" xlink:type="extended">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:label="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:label="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:to="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
        </link:presentationLink>
        <link:presentationLink xlink:role="http://grayscale.com/20260630/taxonomy/role/DisclosureSummaryOfSignificantAccountingPolicies" xlink:title="presentationLink" xlink:type="extended">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountingPoliciesAbstract" xlink:label="us-gaap_AccountingPoliciesAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SignificantAccountingPoliciesTextBlock" xlink:label="us-gaap_SignificantAccountingPoliciesTextBlock"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_AccountingPoliciesAbstract" xlink:to="us-gaap_SignificantAccountingPoliciesTextBlock" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
        </link:presentationLink>
        <link:presentationLink xlink:role="http://grayscale.com/20260630/taxonomy/role/DisclosureFairValueOfZen1" xlink:title="presentationLink" xlink:type="extended">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueDisclosuresAbstract" xlink:label="us-gaap_FairValueDisclosuresAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueDisclosuresTextBlock" xlink:label="us-gaap_FairValueDisclosuresTextBlock"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_FairValueDisclosuresAbstract" xlink:to="us-gaap_FairValueDisclosuresTextBlock" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
        </link:presentationLink>
        <link:presentationLink xlink:role="http://grayscale.com/20260630/taxonomy/role/DisclosureCreationsAndRedemptionsOfShares" xlink:title="presentationLink" xlink:type="extended">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityAbstract" xlink:label="us-gaap_EquityAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:label="us-gaap_StockholdersEquityNoteDisclosureTextBlock"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_EquityAbstract" xlink:to="us-gaap_StockholdersEquityNoteDisclosureTextBlock" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
        </link:presentationLink>
        <link:presentationLink xlink:role="http://grayscale.com/20260630/taxonomy/role/DisclosureIncomeTaxes1" xlink:title="presentationLink" xlink:type="extended">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxDisclosureAbstract" xlink:label="us-gaap_IncomeTaxDisclosureAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxDisclosureTextBlock" xlink:label="us-gaap_IncomeTaxDisclosureTextBlock"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_IncomeTaxDisclosureAbstract" xlink:to="us-gaap_IncomeTaxDisclosureTextBlock" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
        </link:presentationLink>
        <link:presentationLink xlink:role="http://grayscale.com/20260630/taxonomy/role/DisclosureRelatedParties" xlink:title="presentationLink" xlink:type="extended">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionsAbstract" xlink:label="us-gaap_RelatedPartyTransactionsAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:label="us-gaap_RelatedPartyTransactionsDisclosureTextBlock"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_RelatedPartyTransactionsAbstract" xlink:to="us-gaap_RelatedPartyTransactionsDisclosureTextBlock" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
        </link:presentationLink>
        <link:presentationLink xlink:role="http://grayscale.com/20260630/taxonomy/role/DisclosureConcentrationRisk" xlink:title="presentationLink" xlink:type="extended">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RisksAndUncertaintiesAbstract" xlink:label="us-gaap_RisksAndUncertaintiesAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskDisclosureTextBlock" xlink:label="us-gaap_ConcentrationRiskDisclosureTextBlock"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_RisksAndUncertaintiesAbstract" xlink:to="us-gaap_ConcentrationRiskDisclosureTextBlock" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
        </link:presentationLink>
        <link:presentationLink xlink:role="http://grayscale.com/20260630/taxonomy/role/DisclosureFinancialHighlightsPerSharePerformance" xlink:title="presentationLink" xlink:type="extended">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentCompanyFinancialHighlightsAbstract" xlink:label="us-gaap_InvestmentCompanyFinancialHighlightsAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentCompanyFinancialHighlightsTextBlock" xlink:label="us-gaap_InvestmentCompanyFinancialHighlightsTextBlock"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_InvestmentCompanyFinancialHighlightsAbstract" xlink:to="us-gaap_InvestmentCompanyFinancialHighlightsTextBlock" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
        </link:presentationLink>
        <link:presentationLink xlink:role="http://grayscale.com/20260630/taxonomy/role/DisclosureIndemnifications" xlink:title="presentationLink" xlink:type="extended">
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_IndemnificationsDisclosureAbstract" xlink:label="hzen_IndemnificationsDisclosureAbstract"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_IndemnificationsDisclosureTextBlock" xlink:label="hzen_IndemnificationsDisclosureTextBlock"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="hzen_IndemnificationsDisclosureAbstract" xlink:to="hzen_IndemnificationsDisclosureTextBlock" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
        </link:presentationLink>
        <link:presentationLink xlink:role="http://grayscale.com/20260630/taxonomy/role/DisclosureSubsequentEvents" xlink:title="presentationLink" xlink:type="extended">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventsAbstract" xlink:label="us-gaap_SubsequentEventsAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventsTextBlock" xlink:label="us-gaap_SubsequentEventsTextBlock"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_SubsequentEventsAbstract" xlink:to="us-gaap_SubsequentEventsTextBlock" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
        </link:presentationLink>
        <link:presentationLink xlink:role="http://grayscale.com/20260630/taxonomy/role/DisclosureSummaryOfSignificantAccountingPoliciesPolicies" xlink:title="presentationLink" xlink:type="extended">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountingPoliciesAbstract" xlink:label="us-gaap_AccountingPoliciesAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:label="us-gaap_FairValueOfFinancialInstrumentsPolicy"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenueFromContractWithCustomerPolicyTextBlock" xlink:label="us-gaap_RevenueFromContractWithCustomerPolicyTextBlock"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xlink:label="us-gaap_FairValueMeasurementPolicyPolicyTextBlock"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:label="us-gaap_SegmentReportingPolicyPolicyTextBlock"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_AccountingPoliciesAbstract" xlink:to="us-gaap_FairValueOfFinancialInstrumentsPolicy" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_AccountingPoliciesAbstract" xlink:to="us-gaap_RevenueFromContractWithCustomerPolicyTextBlock" order="1" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_AccountingPoliciesAbstract" xlink:to="us-gaap_FairValueMeasurementPolicyPolicyTextBlock" order="2" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_AccountingPoliciesAbstract" xlink:to="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" order="3" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_AccountingPoliciesAbstract" xlink:to="us-gaap_SegmentReportingPolicyPolicyTextBlock" order="4" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
        </link:presentationLink>
        <link:presentationLink xlink:role="http://grayscale.com/20260630/taxonomy/role/DisclosureSummaryOfSignificantAccountingPoliciesTables" xlink:title="presentationLink" xlink:type="extended">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountingPoliciesAbstract" xlink:label="us-gaap_AccountingPoliciesAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_AccountingPoliciesAbstract" xlink:to="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
        </link:presentationLink>
        <link:presentationLink xlink:role="http://grayscale.com/20260630/taxonomy/role/DisclosureFairValueOfZenTables" xlink:title="presentationLink" xlink:type="extended">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueDisclosuresAbstract" xlink:label="us-gaap_FairValueDisclosuresAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentHoldingsScheduleOfInvestmentsTableTextBlock" xlink:label="us-gaap_InvestmentHoldingsScheduleOfInvestmentsTableTextBlock"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_FairValueDisclosuresAbstract" xlink:to="us-gaap_InvestmentHoldingsScheduleOfInvestmentsTableTextBlock" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
        </link:presentationLink>
        <link:presentationLink xlink:role="http://grayscale.com/20260630/taxonomy/role/DisclosureFinancialHighlightsPerSharePerformanceTables" xlink:title="presentationLink" xlink:type="extended">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentCompanyFinancialHighlightsAbstract" xlink:label="us-gaap_InvestmentCompanyFinancialHighlightsAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentCompanyFinancialHighlightsTableTextBlock" xlink:label="us-gaap_InvestmentCompanyFinancialHighlightsTableTextBlock"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_InvestmentCompanyFinancialHighlightsAbstract" xlink:to="us-gaap_InvestmentCompanyFinancialHighlightsTableTextBlock" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
        </link:presentationLink>
        <link:presentationLink xlink:role="http://grayscale.com/20260630/taxonomy/role/DisclosureOrganizationAdditionalInformationDetail" xlink:title="presentationLink" xlink:type="extended">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:label="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_CommonUnitsIssuedMinimumBasket" xlink:label="hzen_CommonUnitsIssuedMinimumBasket"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:to="hzen_CommonUnitsIssuedMinimumBasket" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
        </link:presentationLink>
        <link:presentationLink xlink:role="http://grayscale.com/20260630/taxonomy/role/DisclosureSummaryOfSignificantAccountingPoliciesSummaryOfFairValueEstimatesDetail" xlink:title="presentationLink" xlink:type="extended">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:label="us-gaap_FairValueByFairValueHierarchyLevelAxis"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:label="us-gaap_FairValueMeasurementsFairValueHierarchyDomain"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentOwnedAtFairValue" xlink:label="us-gaap_InvestmentOwnedAtFairValue"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel1Member" xlink:label="us-gaap_FairValueInputsLevel1Member"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountingPoliciesAbstract" xlink:label="us-gaap_AccountingPoliciesAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeExtensibleEnumeration" xlink:label="us-gaap_InvestmentTypeExtensibleEnumeration"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel2Member" xlink:label="us-gaap_FairValueInputsLevel2Member"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel3Member" xlink:label="us-gaap_FairValueInputsLevel3Member"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:to="us-gaap_FairValueMeasurementsFairValueHierarchyDomain" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="us-gaap_InvestmentOwnedAtFairValue" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/verboseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:to="us-gaap_FairValueInputsLevel1Member" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:to="us-gaap_FairValueByFairValueHierarchyLevelAxis" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_AccountingPoliciesAbstract" xlink:to="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="us-gaap_InvestmentTypeExtensibleEnumeration" order="1" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:to="us-gaap_FairValueInputsLevel2Member" order="1" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:to="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" order="1" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:to="us-gaap_FairValueInputsLevel3Member" order="2" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
        </link:presentationLink>
        <link:presentationLink xlink:role="http://grayscale.com/20260630/taxonomy/role/DisclosureSummaryOfSignificantAccountingPoliciesAdditionalInformationDetails" xlink:title="presentationLink" xlink:type="extended">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdjustmentsForNewAccountingPronouncementsAxis" xlink:label="us-gaap_AdjustmentsForNewAccountingPronouncementsAxis"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TypeOfAdoptionMember" xlink:label="us-gaap_TypeOfAdoptionMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleTable" xlink:label="us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleTable"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountingStandardsUpdate202308Member" xlink:label="us-gaap_AccountingStandardsUpdate202308Member"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems" xlink:label="us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateAdopted" xlink:label="us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateAdopted"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountingPoliciesAbstract" xlink:label="us-gaap_AccountingPoliciesAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateAdoptionDate" xlink:label="us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateAdoptionDate"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateImmaterialEffect" xlink:label="us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateImmaterialEffect"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NumberOfOperatingSegments" xlink:label="us-gaap_NumberOfOperatingSegments"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingCodmIndividualTitleAndPositionOrGroupOrCommitteeNameExtensibleEnumeration" xlink:label="us-gaap_SegmentReportingCodmIndividualTitleAndPositionOrGroupOrCommitteeNameExtensibleEnumeration"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingCodmProfitLossMeasureHowUsedDescription" xlink:label="us-gaap_SegmentReportingCodmProfitLossMeasureHowUsedDescription"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_AdjustmentsForNewAccountingPronouncementsAxis" xlink:to="us-gaap_TypeOfAdoptionMember" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleTable" xlink:to="us-gaap_AdjustmentsForNewAccountingPronouncementsAxis" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_TypeOfAdoptionMember" xlink:to="us-gaap_AccountingStandardsUpdate202308Member" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems" xlink:to="us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateAdopted" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_AccountingPoliciesAbstract" xlink:to="us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleTable" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleTable" xlink:to="us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems" order="1" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems" xlink:to="us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateAdoptionDate" order="1" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems" xlink:to="us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateImmaterialEffect" order="2" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems" xlink:to="us-gaap_NumberOfOperatingSegments" order="3" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems" xlink:to="us-gaap_SegmentReportingCodmIndividualTitleAndPositionOrGroupOrCommitteeNameExtensibleEnumeration" order="4" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems" xlink:to="us-gaap_SegmentReportingCodmProfitLossMeasureHowUsedDescription" order="5" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
        </link:presentationLink>
        <link:presentationLink xlink:role="http://grayscale.com/20260630/taxonomy/role/DisclosureFairValueOfZenAdditionalInformationDetail" xlink:title="presentationLink" xlink:type="extended">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueDisclosuresAbstract" xlink:label="us-gaap_FairValueDisclosuresAbstract"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_InvestmentOwnedBalanceSharesHeldByCustodian" xlink:label="hzen_InvestmentOwnedBalanceSharesHeldByCustodian"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_HorizenFairValuePerShare" xlink:label="hzen_HorizenFairValuePerShare"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_FairValueDisclosuresAbstract" xlink:to="hzen_InvestmentOwnedBalanceSharesHeldByCustodian" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_FairValueDisclosuresAbstract" xlink:to="hzen_HorizenFairValuePerShare" order="1" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
        </link:presentationLink>
        <link:presentationLink xlink:role="http://grayscale.com/20260630/taxonomy/role/DisclosureFairValueOfZenSummaryOfChangesInQuantityOfZenAndRespectiveFairValueDetail" xlink:title="presentationLink" xlink:type="extended">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeExtensibleEnumeration" xlink:label="us-gaap_InvestmentTypeExtensibleEnumeration"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueDisclosuresAbstract" xlink:label="us-gaap_FairValueDisclosuresAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentOwnedBalanceContracts" xlink:label="us-gaap_InvestmentOwnedBalanceContracts"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_InvestmentOwnedBalanceContractsNewContributions" xlink:label="hzen_InvestmentOwnedBalanceContractsNewContributions"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_InvestmentOwnedBalanceContractsDistributed" xlink:label="hzen_InvestmentOwnedBalanceContractsDistributed"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_InvestmentOwnedBalanceContractsNetChangeInUnrealizedDepreciationAppreciation" xlink:label="hzen_InvestmentOwnedBalanceContractsNetChangeInUnrealizedDepreciationAppreciation"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_InvestmentOwnedBalanceContractsNetRealizedLossGain" xlink:label="hzen_InvestmentOwnedBalanceContractsNetRealizedLossGain"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentOwnedBalanceContracts" xlink:label="us-gaap_InvestmentOwnedBalanceContracts_6"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentOwnedAtFairValue" xlink:label="us-gaap_InvestmentOwnedAtFairValue"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_InvestmentsOwnedNewContributions" xlink:label="hzen_InvestmentsOwnedNewContributions"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_InvestmentsOwnedDistributions" xlink:label="hzen_InvestmentsOwnedDistributions"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnrealizedGainLossOnInvestments" xlink:label="us-gaap_UnrealizedGainLossOnInvestments"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealizedInvestmentGainsLosses" xlink:label="us-gaap_RealizedInvestmentGainsLosses"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentOwnedAtFairValue" xlink:label="us-gaap_InvestmentOwnedAtFairValue_12"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="us-gaap_InvestmentTypeExtensibleEnumeration" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_FairValueDisclosuresAbstract" xlink:to="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:to="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="us-gaap_InvestmentOwnedBalanceContracts" order="1" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/periodStartLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="hzen_InvestmentOwnedBalanceContractsNewContributions" order="2" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/verboseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="hzen_InvestmentOwnedBalanceContractsDistributed" order="3" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="hzen_InvestmentOwnedBalanceContractsNetChangeInUnrealizedDepreciationAppreciation" order="4" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="hzen_InvestmentOwnedBalanceContractsNetRealizedLossGain" order="5" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="us-gaap_InvestmentOwnedBalanceContracts_6" order="6" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/periodEndLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="us-gaap_InvestmentOwnedAtFairValue" order="7" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/periodStartLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="hzen_InvestmentsOwnedNewContributions" order="8" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/verboseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="hzen_InvestmentsOwnedDistributions" order="9" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/verboseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="us-gaap_UnrealizedGainLossOnInvestments" order="10" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/verboseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="us-gaap_RealizedInvestmentGainsLosses" order="11" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="us-gaap_InvestmentOwnedAtFairValue_12" order="12" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/periodEndLabel"/>
        </link:presentationLink>
        <link:presentationLink xlink:role="http://grayscale.com/20260630/taxonomy/role/DisclosureCreationsAndRedemptionsOfSharesAdditionalInformationDetail" xlink:title="presentationLink" xlink:type="extended">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityAbstract" xlink:label="us-gaap_EquityAbstract"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_CommonShareEquivalentOfHorizen" xlink:label="hzen_CommonShareEquivalentOfHorizen"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_EquityAbstract" xlink:to="hzen_CommonShareEquivalentOfHorizen" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
        </link:presentationLink>
        <link:presentationLink xlink:role="http://grayscale.com/20260630/taxonomy/role/DisclosureIncomeTaxesAdditionalInformationDetail" xlink:title="presentationLink" xlink:type="extended">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxDisclosureAbstract" xlink:label="us-gaap_IncomeTaxDisclosureAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_MinimumPercentageOfTaxPositions" xlink:label="hzen_MinimumPercentageOfTaxPositions"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxLiabilityNotRecognizedAmountOfUnrecognizedDeferredTaxLiabilityPolicyholdersSurplus" xlink:label="us-gaap_DeferredTaxLiabilityNotRecognizedAmountOfUnrecognizedDeferredTaxLiabilityPolicyholdersSurplus"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate" xlink:label="us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes" xlink:label="us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_IncomeTaxDisclosureAbstract" xlink:to="us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_IncomeTaxDisclosureAbstract" xlink:to="hzen_MinimumPercentageOfTaxPositions" order="1" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_IncomeTaxDisclosureAbstract" xlink:to="us-gaap_DeferredTaxLiabilityNotRecognizedAmountOfUnrecognizedDeferredTaxLiabilityPolicyholdersSurplus" order="2" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_IncomeTaxDisclosureAbstract" xlink:to="us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate" order="3" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_IncomeTaxDisclosureAbstract" xlink:to="us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes" order="4" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
        </link:presentationLink>
        <link:presentationLink xlink:role="http://grayscale.com/20260630/taxonomy/role/DisclosureRelatedPartiesAdditionalInformationDetail" xlink:title="presentationLink" xlink:type="extended">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_OwnershipDomain" xlink:label="srt_OwnershipDomain"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_CoinbaseincMember" xlink:label="hzen_CoinbaseincMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionsAbstract" xlink:label="us-gaap_RelatedPartyTransactionsAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:label="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:label="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyDomain" xlink:label="us-gaap_RelatedPartyDomain"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_OwnershipAxis" xlink:label="srt_OwnershipAxis"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_SponsorParentMember" xlink:label="hzen_SponsorParentMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionLineItems" xlink:label="us-gaap_RelatedPartyTransactionLineItems"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesHeldInEmployeeTrustShares" xlink:label="us-gaap_CommonStockSharesHeldInEmployeeTrustShares"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_SponsorMember" xlink:label="hzen_SponsorMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByParent"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_NonSponsorPaidExpensesMember" xlink:label="hzen_NonSponsorPaidExpensesMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeAxis" xlink:label="srt_RangeAxis"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeMember" xlink:label="srt_RangeMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionRate" xlink:label="us-gaap_RelatedPartyTransactionRate"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_DcgMember" xlink:label="hzen_DcgMember"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_NumberOfIncidentalRightsHeld" xlink:label="hzen_NumberOfIncidentalRightsHeld"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_DCGMember" xlink:label="hzen_DCGMember"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_NumberOfIncidentalRightsDistributedInPaymentOfSponsorsFee" xlink:label="hzen_NumberOfIncidentalRightsDistributedInPaymentOfSponsorsFee"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionAmountsOfTransaction" xlink:label="us-gaap_RelatedPartyTransactionAmountsOfTransaction"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MaximumMember" xlink:label="srt_MaximumMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingCostsAndExpenses" xlink:label="us-gaap_OperatingCostsAndExpenses"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsPayableCurrentAndNoncurrent" xlink:label="us-gaap_AccountsPayableCurrentAndNoncurrent"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_AdditionalTrustExpensesPaidBySponsor" xlink:label="hzen_AdditionalTrustExpensesPaidBySponsor"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_CommonStockValueSharesAuthorized" xlink:label="hzen_CommonStockValueSharesAuthorized"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesHeldInEmployeeTrust" xlink:label="us-gaap_CommonStockSharesHeldInEmployeeTrust"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_CommonStockHeldInEmployeeTrustUnderAuthorization" xlink:label="hzen_CommonStockHeldInEmployeeTrustUnderAuthorization"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="srt_OwnershipDomain" xlink:to="hzen_CoinbaseincMember" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_RelatedPartyTransactionsAbstract" xlink:to="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:to="us-gaap_RelatedPartyDomain" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="srt_OwnershipAxis" xlink:to="srt_OwnershipDomain" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_RelatedPartyDomain" xlink:to="hzen_SponsorParentMember" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:to="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="us-gaap_CommonStockSharesHeldInEmployeeTrustShares" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_RelatedPartyDomain" xlink:to="hzen_SponsorMember" order="1" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:to="srt_OwnershipAxis" order="1" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="us-gaap_MinorityInterestOwnershipPercentageByParent" order="1" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_RelatedPartyDomain" xlink:to="hzen_NonSponsorPaidExpensesMember" order="2" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:to="srt_RangeAxis" order="2" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="srt_RangeAxis" xlink:to="srt_RangeMember" order="2.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="us-gaap_RelatedPartyTransactionRate" order="2" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_RelatedPartyDomain" xlink:to="hzen_DcgMember" order="3" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:to="us-gaap_RelatedPartyTransactionLineItems" order="3" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="hzen_NumberOfIncidentalRightsHeld" order="3" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_RelatedPartyDomain" xlink:to="hzen_DCGMember" order="4" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="hzen_NumberOfIncidentalRightsDistributedInPaymentOfSponsorsFee" order="4" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="us-gaap_RelatedPartyTransactionAmountsOfTransaction" order="5" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="srt_RangeMember" xlink:to="srt_MaximumMember" order="6.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="us-gaap_OperatingCostsAndExpenses" order="6" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="us-gaap_AccountsPayableCurrentAndNoncurrent" order="7" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="hzen_AdditionalTrustExpensesPaidBySponsor" order="8" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="hzen_CommonStockValueSharesAuthorized" order="9" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="us-gaap_CommonStockSharesHeldInEmployeeTrust" order="10" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="hzen_CommonStockHeldInEmployeeTrustUnderAuthorization" order="11" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
        </link:presentationLink>
        <link:presentationLink xlink:role="http://grayscale.com/20260630/taxonomy/role/DisclosureFinancialHighlightsPerSharePerformanceSummaryOfPerShareDataDetail" xlink:title="presentationLink" xlink:type="extended">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentCompanyInvestmentIncomeLossFromOperationsPerShareAbstract" xlink:label="us-gaap_InvestmentCompanyInvestmentIncomeLossFromOperationsPerShareAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentCompanyInvestmentIncomeLossPerShare" xlink:label="us-gaap_InvestmentCompanyInvestmentIncomeLossPerShare"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentCompanyFinancialHighlightsAbstract" xlink:label="us-gaap_InvestmentCompanyFinancialHighlightsAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentCompanyFinancialHighlightsRollForward" xlink:label="us-gaap_InvestmentCompanyFinancialHighlightsRollForward"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentCompanyFinancialRatiosAbstract" xlink:label="us-gaap_InvestmentCompanyFinancialRatiosAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentCompanyInvestmentIncomeLossRatio" xlink:label="us-gaap_InvestmentCompanyInvestmentIncomeLossRatio"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetAssetValuePerShare" xlink:label="us-gaap_NetAssetValuePerShare"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentCompanyGainLossOnInvestmentPerShare" xlink:label="us-gaap_InvestmentCompanyGainLossOnInvestmentPerShare"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentCompanyExpenseRatioIncludingIncentiveFee" xlink:label="us-gaap_InvestmentCompanyExpenseRatioIncludingIncentiveFee"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentCompanyInvestmentIncomeLossFromOperationsPerShare" xlink:label="us-gaap_InvestmentCompanyInvestmentIncomeLossFromOperationsPerShare"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetAssetValuePerShare" xlink:label="us-gaap_NetAssetValuePerShare_2"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentCompanyTotalReturn" xlink:label="us-gaap_InvestmentCompanyTotalReturn"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_InvestmentCompanyInvestmentIncomeLossFromOperationsPerShareAbstract" xlink:to="us-gaap_InvestmentCompanyInvestmentIncomeLossPerShare" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_InvestmentCompanyFinancialHighlightsAbstract" xlink:to="us-gaap_InvestmentCompanyFinancialHighlightsRollForward" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_InvestmentCompanyFinancialRatiosAbstract" xlink:to="us-gaap_InvestmentCompanyInvestmentIncomeLossRatio" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_InvestmentCompanyFinancialHighlightsRollForward" xlink:to="us-gaap_NetAssetValuePerShare" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/periodStartLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_InvestmentCompanyInvestmentIncomeLossFromOperationsPerShareAbstract" xlink:to="us-gaap_InvestmentCompanyGainLossOnInvestmentPerShare" order="1" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_InvestmentCompanyFinancialRatiosAbstract" xlink:to="us-gaap_InvestmentCompanyExpenseRatioIncludingIncentiveFee" order="1" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2009/role/negatedLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_InvestmentCompanyFinancialHighlightsRollForward" xlink:to="us-gaap_InvestmentCompanyInvestmentIncomeLossFromOperationsPerShareAbstract" order="1" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_InvestmentCompanyInvestmentIncomeLossFromOperationsPerShareAbstract" xlink:to="us-gaap_InvestmentCompanyInvestmentIncomeLossFromOperationsPerShare" order="2" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/totalLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_InvestmentCompanyFinancialHighlightsRollForward" xlink:to="us-gaap_NetAssetValuePerShare_2" order="2" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/periodEndLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_InvestmentCompanyFinancialHighlightsRollForward" xlink:to="us-gaap_InvestmentCompanyTotalReturn" order="3" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_InvestmentCompanyFinancialHighlightsRollForward" xlink:to="us-gaap_InvestmentCompanyFinancialRatiosAbstract" order="4" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
        </link:presentationLink>
        <link:presentationLink xlink:role="http://grayscale.com/20260630/taxonomy/role/DisclosureSubsequentEventsAdditionalInformationDetail" xlink:title="presentationLink" xlink:type="extended">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_CryptoAssetDomain" xlink:label="srt_CryptoAssetDomain"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_HorizenDAOMember" xlink:label="hzen_HorizenDAOMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventLineItems" xlink:label="us-gaap_SubsequentEventLineItems"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventsDate" xlink:label="us-gaap_SubsequentEventsDate"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventTypeDomain" xlink:label="us-gaap_SubsequentEventTypeDomain"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventMember" xlink:label="us-gaap_SubsequentEventMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventTable" xlink:label="us-gaap_SubsequentEventTable"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventTypeAxis" xlink:label="us-gaap_SubsequentEventTypeAxis"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_CryptoAssetAxis" xlink:label="srt_CryptoAssetAxis"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventsAbstract" xlink:label="us-gaap_SubsequentEventsAbstract"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_HorizenFoundationMember" xlink:label="hzen_HorizenFoundationMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CryptoAssetNumberOfUnits" xlink:label="us-gaap_CryptoAssetNumberOfUnits"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_EthereumNetworkMember" xlink:label="hzen_EthereumNetworkMember"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_CryptoAssetNumberOfUnitsTransferred" xlink:label="hzen_CryptoAssetNumberOfUnitsTransferred"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_VisaNetMember" xlink:label="hzen_VisaNetMember"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_CryptoAssetsMiningNumberOfTransactionsPerSecond" xlink:label="hzen_CryptoAssetsMiningNumberOfTransactionsPerSecond"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="srt_CryptoAssetDomain" xlink:to="hzen_HorizenDAOMember" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_SubsequentEventLineItems" xlink:to="us-gaap_SubsequentEventsDate" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_SubsequentEventTypeDomain" xlink:to="us-gaap_SubsequentEventMember" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_SubsequentEventTable" xlink:to="us-gaap_SubsequentEventTypeAxis" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="srt_CryptoAssetAxis" xlink:to="srt_CryptoAssetDomain" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_SubsequentEventTypeAxis" xlink:to="us-gaap_SubsequentEventTypeDomain" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_SubsequentEventsAbstract" xlink:to="us-gaap_SubsequentEventTable" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="srt_CryptoAssetDomain" xlink:to="hzen_HorizenFoundationMember" order="1" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_SubsequentEventLineItems" xlink:to="us-gaap_CryptoAssetNumberOfUnits" order="1" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_SubsequentEventTable" xlink:to="srt_CryptoAssetAxis" order="1" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="srt_CryptoAssetDomain" xlink:to="hzen_EthereumNetworkMember" order="2" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_SubsequentEventLineItems" xlink:to="hzen_CryptoAssetNumberOfUnitsTransferred" order="2" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_SubsequentEventTable" xlink:to="us-gaap_SubsequentEventLineItems" order="2" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="srt_CryptoAssetDomain" xlink:to="hzen_VisaNetMember" order="3" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="us-gaap_SubsequentEventLineItems" xlink:to="hzen_CryptoAssetsMiningNumberOfTransactionsPerSecond" order="3" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
        </link:presentationLink>
        <link:definitionLink xlink:type="extended" xlink:role="http://grayscale.com/20260630/taxonomy/role/StatementStatementsOfAssetsAndLiabilitiesUnaudited">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementLineItems" xlink:label="us-gaap_StatementLineItems"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementTable" xlink:label="us-gaap_StatementTable"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:label="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsAbstract" xlink:label="us-gaap_AssetsAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesAbstract" xlink:label="us-gaap_LiabilitiesAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsPayableCurrentAndNoncurrent" xlink:label="us-gaap_AccountsPayableCurrentAndNoncurrent"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyDomain" xlink:label="us-gaap_RelatedPartyDomain"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyDomain" xlink:label="us-gaap_RelatedPartyDomain_default"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentOwnedAtFairValue" xlink:label="us-gaap_InvestmentOwnedAtFairValue"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_SponsorMember" xlink:label="hzen_SponsorMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Liabilities" xlink:label="us-gaap_Liabilities"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Assets" xlink:label="us-gaap_Assets"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsNet" xlink:label="us-gaap_AssetsNet"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdditionalPaidInCapitalCommonStock" xlink:label="us-gaap_AdditionalPaidInCapitalCommonStock"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_AccumulatedNetInvestmentLoss" xlink:label="hzen_AccumulatedNetInvestmentLoss"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_AccumulatedNetRealizedGainOnInvestment" xlink:label="hzen_AccumulatedNetRealizedGainOnInvestment"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_InvestmentOwnedAccumulatedNetChangeInUnrecognizedUnrealizedAppreciationDepreciationNet" xlink:label="hzen_InvestmentOwnedAccumulatedNetChangeInUnrecognizedUnrealizedAppreciationDepreciationNet"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesIssued" xlink:label="us-gaap_CommonStockSharesIssued"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesOutstanding" xlink:label="us-gaap_CommonStockSharesOutstanding"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetAssetValuePerShare" xlink:label="us-gaap_NetAssetValuePerShare"/>
          <link:definitionArc xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_StatementTable" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="us-gaap_StatementTable" xlink:to="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_AssetsAbstract" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_LiabilitiesAbstract" xlink:to="us-gaap_AccountsPayableCurrentAndNoncurrent" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:to="us-gaap_RelatedPartyDomain" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:to="us-gaap_RelatedPartyDomain_default" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_AssetsAbstract" xlink:to="us-gaap_InvestmentOwnedAtFairValue" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_RelatedPartyDomain" xlink:to="hzen_SponsorMember" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="1" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_LiabilitiesAbstract" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="1" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_LiabilitiesAbstract" xlink:to="us-gaap_Liabilities" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="1" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_AssetsAbstract" xlink:to="us-gaap_Assets" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="2" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_AssetsNet" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="3" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_AdditionalPaidInCapitalCommonStock" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="4" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems" xlink:to="hzen_AccumulatedNetInvestmentLoss" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="5" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems" xlink:to="hzen_AccumulatedNetRealizedGainOnInvestment" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="6" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems" xlink:to="hzen_InvestmentOwnedAccumulatedNetChangeInUnrecognizedUnrealizedAppreciationDepreciationNet" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="7" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_CommonStockSharesIssued" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="8" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_CommonStockSharesOutstanding" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="9" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_NetAssetValuePerShare" priority="2" use="optional"/>
        </link:definitionLink>
        <link:definitionLink xlink:type="extended" xlink:role="http://grayscale.com/20260630/taxonomy/role/StatementSchedulesOfInvestmentUnaudited">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfInvestmentsLineItems" xlink:label="us-gaap_ScheduleOfInvestmentsLineItems"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfInvestmentsTable" xlink:label="us-gaap_ScheduleOfInvestmentsTable"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeAxis" xlink:label="us-gaap_InvestmentTypeAxis"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeCategorizationMember" xlink:label="us-gaap_InvestmentTypeCategorizationMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeCategorizationMember" xlink:label="us-gaap_InvestmentTypeCategorizationMember_default"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_Quantityofhorizen" xlink:label="hzen_Quantityofhorizen"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_InvestmentInZenMember" xlink:label="hzen_InvestmentInZenMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeExtensibleEnumeration" xlink:label="us-gaap_InvestmentTypeExtensibleEnumeration"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_InvestmentMember" xlink:label="hzen_InvestmentMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentOwnedAtCost" xlink:label="us-gaap_InvestmentOwnedAtCost"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentOwnedAtFairValue" xlink:label="us-gaap_InvestmentOwnedAtFairValue"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentOwnedPercentOfNetAssets" xlink:label="us-gaap_InvestmentOwnedPercentOfNetAssets"/>
          <link:definitionArc xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="us-gaap_ScheduleOfInvestmentsLineItems" xlink:to="us-gaap_ScheduleOfInvestmentsTable" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="us-gaap_InvestmentTypeAxis" xlink:to="us-gaap_InvestmentTypeCategorizationMember" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="us-gaap_InvestmentTypeAxis" xlink:to="us-gaap_InvestmentTypeCategorizationMember_default" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ScheduleOfInvestmentsLineItems" xlink:to="hzen_Quantityofhorizen" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_InvestmentTypeCategorizationMember" xlink:to="hzen_InvestmentInZenMember" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="us-gaap_ScheduleOfInvestmentsTable" xlink:to="us-gaap_InvestmentTypeAxis" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="1" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ScheduleOfInvestmentsLineItems" xlink:to="us-gaap_InvestmentTypeExtensibleEnumeration" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="1" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_InvestmentTypeCategorizationMember" xlink:to="hzen_InvestmentMember" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="2" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ScheduleOfInvestmentsLineItems" xlink:to="us-gaap_InvestmentOwnedAtCost" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="3" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ScheduleOfInvestmentsLineItems" xlink:to="us-gaap_InvestmentOwnedAtFairValue" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="4" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ScheduleOfInvestmentsLineItems" xlink:to="us-gaap_InvestmentOwnedPercentOfNetAssets" priority="2" use="optional"/>
        </link:definitionLink>
        <link:definitionLink xlink:type="extended" xlink:role="http://grayscale.com/20260630/taxonomy/role/DisclosureSummaryOfSignificantAccountingPoliciesSummaryOfFairValueEstimatesDetail">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:label="us-gaap_FairValueByFairValueHierarchyLevelAxis"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:label="us-gaap_FairValueMeasurementsFairValueHierarchyDomain"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:label="us-gaap_FairValueMeasurementsFairValueHierarchyDomain_default"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentOwnedAtFairValue" xlink:label="us-gaap_InvestmentOwnedAtFairValue"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel1Member" xlink:label="us-gaap_FairValueInputsLevel1Member"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeExtensibleEnumeration" xlink:label="us-gaap_InvestmentTypeExtensibleEnumeration"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel2Member" xlink:label="us-gaap_FairValueInputsLevel2Member"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel3Member" xlink:label="us-gaap_FairValueInputsLevel3Member"/>
          <link:definitionArc xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:to="us-gaap_FairValueMeasurementsFairValueHierarchyDomain" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:to="us-gaap_FairValueMeasurementsFairValueHierarchyDomain_default" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="us-gaap_InvestmentOwnedAtFairValue" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:to="us-gaap_FairValueInputsLevel1Member" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:to="us-gaap_FairValueByFairValueHierarchyLevelAxis" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="1" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="us-gaap_InvestmentTypeExtensibleEnumeration" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="1" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:to="us-gaap_FairValueInputsLevel2Member" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="2" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:to="us-gaap_FairValueInputsLevel3Member" priority="2" use="optional"/>
        </link:definitionLink>
        <link:definitionLink xlink:type="extended" xlink:role="http://grayscale.com/20260630/taxonomy/role/DisclosureSummaryOfSignificantAccountingPoliciesAdditionalInformationDetails">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems" xlink:label="us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleTable" xlink:label="us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleTable"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdjustmentsForNewAccountingPronouncementsAxis" xlink:label="us-gaap_AdjustmentsForNewAccountingPronouncementsAxis"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TypeOfAdoptionMember" xlink:label="us-gaap_TypeOfAdoptionMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TypeOfAdoptionMember" xlink:label="us-gaap_TypeOfAdoptionMember_default"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountingStandardsUpdate202308Member" xlink:label="us-gaap_AccountingStandardsUpdate202308Member"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateAdopted" xlink:label="us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateAdopted"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateAdoptionDate" xlink:label="us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateAdoptionDate"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateImmaterialEffect" xlink:label="us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateImmaterialEffect"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NumberOfOperatingSegments" xlink:label="us-gaap_NumberOfOperatingSegments"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingCodmIndividualTitleAndPositionOrGroupOrCommitteeNameExtensibleEnumeration" xlink:label="us-gaap_SegmentReportingCodmIndividualTitleAndPositionOrGroupOrCommitteeNameExtensibleEnumeration"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingCodmProfitLossMeasureHowUsedDescription" xlink:label="us-gaap_SegmentReportingCodmProfitLossMeasureHowUsedDescription"/>
          <link:definitionArc xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems" xlink:to="us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleTable" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="us-gaap_AdjustmentsForNewAccountingPronouncementsAxis" xlink:to="us-gaap_TypeOfAdoptionMember" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="us-gaap_AdjustmentsForNewAccountingPronouncementsAxis" xlink:to="us-gaap_TypeOfAdoptionMember_default" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleTable" xlink:to="us-gaap_AdjustmentsForNewAccountingPronouncementsAxis" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_TypeOfAdoptionMember" xlink:to="us-gaap_AccountingStandardsUpdate202308Member" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems" xlink:to="us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateAdopted" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="1" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems" xlink:to="us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateAdoptionDate" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="2" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems" xlink:to="us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateImmaterialEffect" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="3" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems" xlink:to="us-gaap_NumberOfOperatingSegments" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="4" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems" xlink:to="us-gaap_SegmentReportingCodmIndividualTitleAndPositionOrGroupOrCommitteeNameExtensibleEnumeration" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="5" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems" xlink:to="us-gaap_SegmentReportingCodmProfitLossMeasureHowUsedDescription" priority="2" use="optional"/>
        </link:definitionLink>
        <link:definitionLink xlink:type="extended" xlink:role="http://grayscale.com/20260630/taxonomy/role/DisclosureFairValueOfZenSummaryOfChangesInQuantityOfZenAndRespectiveFairValueDetail">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeExtensibleEnumeration" xlink:label="us-gaap_InvestmentTypeExtensibleEnumeration"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentOwnedBalanceContracts" xlink:label="us-gaap_InvestmentOwnedBalanceContracts"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_InvestmentOwnedBalanceContractsNewContributions" xlink:label="hzen_InvestmentOwnedBalanceContractsNewContributions"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_InvestmentOwnedBalanceContractsDistributed" xlink:label="hzen_InvestmentOwnedBalanceContractsDistributed"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_InvestmentOwnedBalanceContractsNetChangeInUnrealizedDepreciationAppreciation" xlink:label="hzen_InvestmentOwnedBalanceContractsNetChangeInUnrealizedDepreciationAppreciation"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_InvestmentOwnedBalanceContractsNetRealizedLossGain" xlink:label="hzen_InvestmentOwnedBalanceContractsNetRealizedLossGain"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentOwnedAtFairValue" xlink:label="us-gaap_InvestmentOwnedAtFairValue"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_InvestmentsOwnedNewContributions" xlink:label="hzen_InvestmentsOwnedNewContributions"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_InvestmentsOwnedDistributions" xlink:label="hzen_InvestmentsOwnedDistributions"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnrealizedGainLossOnInvestments" xlink:label="us-gaap_UnrealizedGainLossOnInvestments"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealizedInvestmentGainsLosses" xlink:label="us-gaap_RealizedInvestmentGainsLosses"/>
          <link:definitionArc xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="us-gaap_InvestmentTypeExtensibleEnumeration" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="1" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="us-gaap_InvestmentOwnedBalanceContracts" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="2" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="hzen_InvestmentOwnedBalanceContractsNewContributions" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="3" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="hzen_InvestmentOwnedBalanceContractsDistributed" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="4" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="hzen_InvestmentOwnedBalanceContractsNetChangeInUnrealizedDepreciationAppreciation" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="5" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="hzen_InvestmentOwnedBalanceContractsNetRealizedLossGain" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="7" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="us-gaap_InvestmentOwnedAtFairValue" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="8" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="hzen_InvestmentsOwnedNewContributions" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="9" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="hzen_InvestmentsOwnedDistributions" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="10" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="us-gaap_UnrealizedGainLossOnInvestments" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="11" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="us-gaap_RealizedInvestmentGainsLosses" priority="2" use="optional"/>
        </link:definitionLink>
        <link:definitionLink xlink:type="extended" xlink:role="http://grayscale.com/20260630/taxonomy/role/DisclosureRelatedPartiesAdditionalInformationDetail">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionLineItems" xlink:label="us-gaap_RelatedPartyTransactionLineItems"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:label="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_OwnershipDomain" xlink:label="srt_OwnershipDomain"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_CoinbaseincMember" xlink:label="hzen_CoinbaseincMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:label="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyDomain" xlink:label="us-gaap_RelatedPartyDomain"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeMember" xlink:label="srt_RangeMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MaximumMember" xlink:label="srt_MaximumMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_OwnershipAxis" xlink:label="srt_OwnershipAxis"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_OwnershipDomain" xlink:label="srt_OwnershipDomain_default"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_SponsorParentMember" xlink:label="hzen_SponsorParentMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeAxis" xlink:label="srt_RangeAxis"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeMember" xlink:label="srt_RangeMember_default"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesHeldInEmployeeTrustShares" xlink:label="us-gaap_CommonStockSharesHeldInEmployeeTrustShares"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_SponsorMember" xlink:label="hzen_SponsorMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByParent"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_NonSponsorPaidExpensesMember" xlink:label="hzen_NonSponsorPaidExpensesMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionRate" xlink:label="us-gaap_RelatedPartyTransactionRate"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_DcgMember" xlink:label="hzen_DcgMember"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_NumberOfIncidentalRightsHeld" xlink:label="hzen_NumberOfIncidentalRightsHeld"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_DCGMember" xlink:label="hzen_DCGMember"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_NumberOfIncidentalRightsDistributedInPaymentOfSponsorsFee" xlink:label="hzen_NumberOfIncidentalRightsDistributedInPaymentOfSponsorsFee"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionAmountsOfTransaction" xlink:label="us-gaap_RelatedPartyTransactionAmountsOfTransaction"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingCostsAndExpenses" xlink:label="us-gaap_OperatingCostsAndExpenses"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsPayableCurrentAndNoncurrent" xlink:label="us-gaap_AccountsPayableCurrentAndNoncurrent"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_AdditionalTrustExpensesPaidBySponsor" xlink:label="hzen_AdditionalTrustExpensesPaidBySponsor"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_CommonStockValueSharesAuthorized" xlink:label="hzen_CommonStockValueSharesAuthorized"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesHeldInEmployeeTrust" xlink:label="us-gaap_CommonStockSharesHeldInEmployeeTrust"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_CommonStockHeldInEmployeeTrustUnderAuthorization" xlink:label="hzen_CommonStockHeldInEmployeeTrustUnderAuthorization"/>
          <link:definitionArc xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_OwnershipDomain" xlink:to="hzen_CoinbaseincMember" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:to="us-gaap_RelatedPartyDomain" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_RangeMember" xlink:to="srt_MaximumMember" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="srt_OwnershipAxis" xlink:to="srt_OwnershipDomain" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="srt_OwnershipAxis" xlink:to="srt_OwnershipDomain_default" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_RelatedPartyDomain" xlink:to="hzen_SponsorParentMember" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:to="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="srt_RangeAxis" xlink:to="srt_RangeMember" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="srt_RangeAxis" xlink:to="srt_RangeMember_default" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="us-gaap_CommonStockSharesHeldInEmployeeTrustShares" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="1" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_RelatedPartyDomain" xlink:to="hzen_SponsorMember" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="1" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:to="srt_OwnershipAxis" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="1" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="us-gaap_MinorityInterestOwnershipPercentageByParent" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="2" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_RelatedPartyDomain" xlink:to="hzen_NonSponsorPaidExpensesMember" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="2" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:to="srt_RangeAxis" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="2" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="us-gaap_RelatedPartyTransactionRate" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="3" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_RelatedPartyDomain" xlink:to="hzen_DcgMember" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="3" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="hzen_NumberOfIncidentalRightsHeld" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="4" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_RelatedPartyDomain" xlink:to="hzen_DCGMember" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="4" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="hzen_NumberOfIncidentalRightsDistributedInPaymentOfSponsorsFee" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="5" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="us-gaap_RelatedPartyTransactionAmountsOfTransaction" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="6" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="us-gaap_OperatingCostsAndExpenses" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="7" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="us-gaap_AccountsPayableCurrentAndNoncurrent" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="8" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="hzen_AdditionalTrustExpensesPaidBySponsor" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="9" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="hzen_CommonStockValueSharesAuthorized" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="10" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="us-gaap_CommonStockSharesHeldInEmployeeTrust" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="11" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="hzen_CommonStockHeldInEmployeeTrustUnderAuthorization" priority="2" use="optional"/>
        </link:definitionLink>
        <link:definitionLink xlink:type="extended" xlink:role="http://grayscale.com/20260630/taxonomy/role/DisclosureSubsequentEventsAdditionalInformationDetail">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventLineItems" xlink:label="us-gaap_SubsequentEventLineItems"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventTable" xlink:label="us-gaap_SubsequentEventTable"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_CryptoAssetDomain" xlink:label="srt_CryptoAssetDomain"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_HorizenDAOMember" xlink:label="hzen_HorizenDAOMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventsDate" xlink:label="us-gaap_SubsequentEventsDate"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventTypeDomain" xlink:label="us-gaap_SubsequentEventTypeDomain"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventMember" xlink:label="us-gaap_SubsequentEventMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventTypeAxis" xlink:label="us-gaap_SubsequentEventTypeAxis"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_CryptoAssetAxis" xlink:label="srt_CryptoAssetAxis"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_CryptoAssetDomain" xlink:label="srt_CryptoAssetDomain_default"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventTypeDomain" xlink:label="us-gaap_SubsequentEventTypeDomain_default"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_HorizenFoundationMember" xlink:label="hzen_HorizenFoundationMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CryptoAssetNumberOfUnits" xlink:label="us-gaap_CryptoAssetNumberOfUnits"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_EthereumNetworkMember" xlink:label="hzen_EthereumNetworkMember"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_CryptoAssetNumberOfUnitsTransferred" xlink:label="hzen_CryptoAssetNumberOfUnitsTransferred"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_VisaNetMember" xlink:label="hzen_VisaNetMember"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_CryptoAssetsMiningNumberOfTransactionsPerSecond" xlink:label="hzen_CryptoAssetsMiningNumberOfTransactionsPerSecond"/>
          <link:definitionArc xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="us-gaap_SubsequentEventLineItems" xlink:to="us-gaap_SubsequentEventTable" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_CryptoAssetDomain" xlink:to="hzen_HorizenDAOMember" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_SubsequentEventLineItems" xlink:to="us-gaap_SubsequentEventsDate" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_SubsequentEventTypeDomain" xlink:to="us-gaap_SubsequentEventMember" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="us-gaap_SubsequentEventTable" xlink:to="us-gaap_SubsequentEventTypeAxis" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="srt_CryptoAssetAxis" xlink:to="srt_CryptoAssetDomain" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="srt_CryptoAssetAxis" xlink:to="srt_CryptoAssetDomain_default" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="us-gaap_SubsequentEventTypeAxis" xlink:to="us-gaap_SubsequentEventTypeDomain" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="us-gaap_SubsequentEventTypeAxis" xlink:to="us-gaap_SubsequentEventTypeDomain_default" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="1" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_CryptoAssetDomain" xlink:to="hzen_HorizenFoundationMember" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="1" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_SubsequentEventLineItems" xlink:to="us-gaap_CryptoAssetNumberOfUnits" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="1" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="us-gaap_SubsequentEventTable" xlink:to="srt_CryptoAssetAxis" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="2" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_CryptoAssetDomain" xlink:to="hzen_EthereumNetworkMember" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="2" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_SubsequentEventLineItems" xlink:to="hzen_CryptoAssetNumberOfUnitsTransferred" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="3" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_CryptoAssetDomain" xlink:to="hzen_VisaNetMember" priority="2" use="optional"/>
          <link:definitionArc xlink:type="arc" order="3" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_SubsequentEventLineItems" xlink:to="hzen_CryptoAssetsMiningNumberOfTransactionsPerSecond" priority="2" use="optional"/>
        </link:definitionLink>
        <link:definitionLink xlink:type="extended" xlink:role="http://fasb.org/srt/role/srt-eedm/ExtensibleEnumerationLists">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_TitleOfIndividualWithRelationshipToEntityDomain" xlink:label="srt_TitleOfIndividualWithRelationshipToEntityDomain"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_ChiefExecutiveOfficerAndChiefFinancialOfficerMember" xlink:label="hzen_ChiefExecutiveOfficerAndChiefFinancialOfficerMember"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_TitleOfIndividualWithRelationshipToEntityDomain" xlink:to="hzen_ChiefExecutiveOfficerAndChiefFinancialOfficerMember" priority="2" use="optional"/>
        </link:definitionLink>
        <link:definitionLink xlink:type="extended" xlink:role="http://fasb.org/us-gaap/role/eedm/ExtensibleEnumerationLists">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeCategorizationMember" xlink:label="us-gaap_InvestmentTypeCategorizationMember"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_InvestmentInZenMember" xlink:label="hzen_InvestmentInZenMember"/>
          <link:definitionArc xlink:type="arc" order="0" xbrldt:closed="false" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_InvestmentTypeCategorizationMember" xlink:to="hzen_InvestmentInZenMember" priority="2" use="optional"/>
        </link:definitionLink>
        <link:calculationLink xlink:type="extended" xlink:role="http://grayscale.com/20260630/taxonomy/role/StatementStatementsOfAssetsAndLiabilitiesUnaudited">
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_AssetsNet" xlink:to="us-gaap_Assets" order="0" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_Liabilities" xlink:to="us-gaap_AccountsPayableCurrentAndNoncurrent" order="0" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_InvestmentOwnedAtFairValue" order="0" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_AssetsNet" xlink:to="us-gaap_Liabilities" order="1" weight="-1" use="optional"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsNet" xlink:label="us-gaap_AssetsNet"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Assets" xlink:label="us-gaap_Assets"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Liabilities" xlink:label="us-gaap_Liabilities"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsPayableCurrentAndNoncurrent" xlink:label="us-gaap_AccountsPayableCurrentAndNoncurrent"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentOwnedAtFairValue" xlink:label="us-gaap_InvestmentOwnedAtFairValue"/>
        </link:calculationLink>
        <link:calculationLink xlink:type="extended" xlink:role="http://grayscale.com/20260630/taxonomy/role/StatementStatementsOfAssetsAndLiabilitiesUnaudited2">
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_AssetsNet" xlink:to="hzen_AccumulatedNetInvestmentLoss" order="0" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_AssetsNet" xlink:to="us-gaap_AdditionalPaidInCapitalCommonStock" order="2" weight="-1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_AssetsNet" xlink:to="hzen_InvestmentOwnedAccumulatedNetChangeInUnrecognizedUnrealizedAppreciationDepreciationNet" order="3" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_AssetsNet" xlink:to="hzen_AccumulatedNetRealizedGainOnInvestment" order="4" weight="-1" use="optional"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsNet" xlink:label="us-gaap_AssetsNet"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_AccumulatedNetInvestmentLoss" xlink:label="hzen_AccumulatedNetInvestmentLoss"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdditionalPaidInCapitalCommonStock" xlink:label="us-gaap_AdditionalPaidInCapitalCommonStock"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_InvestmentOwnedAccumulatedNetChangeInUnrecognizedUnrealizedAppreciationDepreciationNet" xlink:label="hzen_InvestmentOwnedAccumulatedNetChangeInUnrecognizedUnrealizedAppreciationDepreciationNet"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_AccumulatedNetRealizedGainOnInvestment" xlink:label="hzen_AccumulatedNetRealizedGainOnInvestment"/>
        </link:calculationLink>
        <link:calculationLink xlink:type="extended" xlink:role="http://grayscale.com/20260630/taxonomy/role/StatementStatementsOfOperationsUnaudited">
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_NetIncomeLoss" xlink:to="us-gaap_InvestmentIncomeNet" order="0" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_InvestmentIncomeNet" xlink:to="hzen_InvestmentIncome" order="0" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_GainLossOnInvestments" xlink:to="us-gaap_RealizedInvestmentGainsLosses" order="0" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_NetIncomeLoss" xlink:to="us-gaap_GainLossOnInvestments" order="1" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_InvestmentIncomeNet" xlink:to="us-gaap_SponsorFees" order="1" weight="-1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_GainLossOnInvestments" xlink:to="us-gaap_UnrealizedGainLossOnInvestments" order="1" weight="1" use="optional"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLoss" xlink:label="us-gaap_NetIncomeLoss"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentIncomeNet" xlink:label="us-gaap_InvestmentIncomeNet"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_InvestmentIncome" xlink:label="hzen_InvestmentIncome"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossOnInvestments" xlink:label="us-gaap_GainLossOnInvestments"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealizedInvestmentGainsLosses" xlink:label="us-gaap_RealizedInvestmentGainsLosses"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SponsorFees" xlink:label="us-gaap_SponsorFees"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnrealizedGainLossOnInvestments" xlink:label="us-gaap_UnrealizedGainLossOnInvestments"/>
        </link:calculationLink>
        <link:calculationLink xlink:type="extended" xlink:role="http://grayscale.com/20260630/taxonomy/role/StatementStatementsOfChangesInNetAssetsUnaudited">
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="hzen_IncreaseDecreaseInNetAssetsFromOperationsAndCapitalShareTransactions" xlink:to="us-gaap_NetIncomeLoss" order="0" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_NetIncomeLoss" xlink:to="us-gaap_InvestmentIncomeNet" order="0" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_StockholdersEquityPeriodIncreaseDecrease" xlink:to="us-gaap_StockIssuedDuringPeriodValueNewIssues" order="0" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="hzen_IncreaseDecreaseInNetAssetsFromOperationsAndCapitalShareTransactions" xlink:to="us-gaap_StockholdersEquityPeriodIncreaseDecrease" order="1" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_NetIncomeLoss" xlink:to="us-gaap_RealizedInvestmentGainsLosses" order="1" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_NetIncomeLoss" xlink:to="us-gaap_UnrealizedGainLossOnInvestments" order="2" weight="1" use="optional"/>
          <link:loc xlink:type="locator" xlink:href="hzen-20260630.xsd#hzen_IncreaseDecreaseInNetAssetsFromOperationsAndCapitalShareTransactions" xlink:label="hzen_IncreaseDecreaseInNetAssetsFromOperationsAndCapitalShareTransactions"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLoss" xlink:label="us-gaap_NetIncomeLoss"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentIncomeNet" xlink:label="us-gaap_InvestmentIncomeNet"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquityPeriodIncreaseDecrease" xlink:label="us-gaap_StockholdersEquityPeriodIncreaseDecrease"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealizedInvestmentGainsLosses" xlink:label="us-gaap_RealizedInvestmentGainsLosses"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnrealizedGainLossOnInvestments" xlink:label="us-gaap_UnrealizedGainLossOnInvestments"/>
        </link:calculationLink>
        <link:calculationLink xlink:type="extended" xlink:role="http://grayscale.com/20260630/taxonomy/role/DisclosureFinancialHighlightsPerSharePerformanceSummaryOfPerShareDataDetail">
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_InvestmentCompanyInvestmentIncomeLossFromOperationsPerShare" xlink:to="us-gaap_InvestmentCompanyGainLossOnInvestmentPerShare" order="0" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_InvestmentCompanyInvestmentIncomeLossFromOperationsPerShare" xlink:to="us-gaap_InvestmentCompanyInvestmentIncomeLossPerShare" order="1" weight="1" use="optional"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentCompanyInvestmentIncomeLossFromOperationsPerShare" xlink:label="us-gaap_InvestmentCompanyInvestmentIncomeLossFromOperationsPerShare"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentCompanyGainLossOnInvestmentPerShare" xlink:label="us-gaap_InvestmentCompanyGainLossOnInvestmentPerShare"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentCompanyInvestmentIncomeLossPerShare" xlink:label="us-gaap_InvestmentCompanyInvestmentIncomeLossPerShare"/>
        </link:calculationLink>
      </link:linkbase>
    </xsd:appinfo>
  </xsd:annotation>
  <xsd:element id="hzen_CommonUnitsIssuedMinimumBasket" name="CommonUnitsIssuedMinimumBasket" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="hzen_NumberOfIncidentalRightsHeld" name="NumberOfIncidentalRightsHeld" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="hzen_Quantityofhorizen" name="Quantityofhorizen" type="xbrli:decimalItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="hzen_DCGMember" name="DCGMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="hzen_AccumulatedNetRealizedGainOnInvestment" name="AccumulatedNetRealizedGainOnInvestment" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="hzen_CommonStockValueSharesAuthorized" name="CommonStockValueSharesAuthorized" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="hzen_InvestmentOwnedBalanceSharesHeldByCustodian" name="InvestmentOwnedBalanceSharesHeldByCustodian" type="xbrli:decimalItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="hzen_NumberOfIncidentalRightsDistributedInPaymentOfSponsorsFee" name="NumberOfIncidentalRightsDistributedInPaymentOfSponsorsFee" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="hzen_HorizenFairValuePerShare" name="HorizenFairValuePerShare" type="dtr-types:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="hzen_CommonShareEquivalentOfHorizen" name="CommonShareEquivalentOfHorizen" type="xbrli:decimalItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="hzen_ChangeInSharesOutstandingAbstract" name="ChangeInSharesOutstandingAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="hzen_VisaNetMember" name="VisaNetMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="hzen_InvestmentOwnedBalanceContractsNetRealizedLossGain" name="InvestmentOwnedBalanceContractsNetRealizedLossGain" type="xbrli:decimalItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="hzen_CoinbaseincMember" name="CoinbaseincMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="hzen_MinimumPercentageOfTaxPositions" name="MinimumPercentageOfTaxPositions" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="hzen_AdditionalTrustExpensesPaidBySponsor" name="AdditionalTrustExpensesPaidBySponsor" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="hzen_CryptoAssetsMiningNumberOfTransactionsPerSecond" name="CryptoAssetsMiningNumberOfTransactionsPerSecond" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="hzen_NonSponsorPaidExpensesMember" name="NonSponsorPaidExpensesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="hzen_NetRealizedAndUnrealizedGainLossAbstract" name="NetRealizedAndUnrealizedGainLossAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="hzen_InvestmentInZenMember" name="InvestmentInZenMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="hzen_SponsorMember" name="SponsorMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="hzen_IncreaseInNetAssetsFromCapitalShareTransactionsAbstract" name="IncreaseInNetAssetsFromCapitalShareTransactionsAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="hzen_HorizenFoundationMember" name="HorizenFoundationMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="hzen_InvestmentOwnedAccumulatedNetChangeInUnrecognizedUnrealizedAppreciationDepreciationNet" name="InvestmentOwnedAccumulatedNetChangeInUnrecognizedUnrealizedAppreciationDepreciationNet" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="hzen_InvestmentMember" name="InvestmentMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="hzen_CryptoAssetNumberOfUnitsTransferred" name="CryptoAssetNumberOfUnitsTransferred" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="hzen_ChiefExecutiveOfficerAndChiefFinancialOfficerMember" name="ChiefExecutiveOfficerAndChiefFinancialOfficerMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="hzen_CommonStockHeldInEmployeeTrustUnderAuthorization" name="CommonStockHeldInEmployeeTrustUnderAuthorization" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="hzen_IndemnificationsDisclosureAbstract" name="IndemnificationsDisclosureAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="hzen_HorizenDAOMember" name="HorizenDAOMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="hzen_SponsorParentMember" name="SponsorParentMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="hzen_NetAssetsAbstract" name="NetAssetsAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="hzen_InvestmentsOwnedNewContributions" name="InvestmentsOwnedNewContributions" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="hzen_InvestmentsOwnedDistributions" name="InvestmentsOwnedDistributions" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="hzen_DcgMember" name="DcgMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="hzen_AccumulatedNetInvestmentLoss" name="AccumulatedNetInvestmentLoss" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="hzen_InvestmentOwnedBalanceContractsNewContributions" name="InvestmentOwnedBalanceContractsNewContributions" type="xbrli:decimalItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="hzen_InvestmentOwnedBalanceContractsNetChangeInUnrealizedDepreciationAppreciation" name="InvestmentOwnedBalanceContractsNetChangeInUnrealizedDepreciationAppreciation" type="xbrli:decimalItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="hzen_IndemnificationsDisclosureTextBlock" name="IndemnificationsDisclosureTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="hzen_InvestmentIncome" name="InvestmentIncome" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="hzen_InvestmentOwnedBalanceContractsDistributed" name="InvestmentOwnedBalanceContractsDistributed" type="xbrli:decimalItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="hzen_IncreaseDecreaseInNetAssetsFromOperationsAndCapitalShareTransactions" name="IncreaseDecreaseInNetAssetsFromOperationsAndCapitalShareTransactions" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="hzen_EthereumNetworkMember" name="EthereumNetworkMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
</xsd:schema>
