Represents the deferred compensation arrangement, fixed interest rate.

No definition available.

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Namespace Prefix:	gyro_
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- Definition

The percentage of director fees that deferred.

+ References

No definition available.

+ Details

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- Definition

The cash outflow during the period from the payment for the Retention Bonus Plan.

+ References

No definition available.

+ Details

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Data Type:	xbrli:monetaryItemType
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Period Type:	duration

- Definition

Minimum amount of other commitment not otherwise specified in the taxonomy. Excludes commitments explicitly modeled in the taxonomy, including but not limited to, long-term and short-term purchase commitments, recorded and unrecorded purchase obligations, supply commitments, registration payment arrangements, leases, debt, product warranties, guarantees, environmental remediation obligations, and pensions.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 942
-SubTopic 235
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147477314/942-235-S99-2

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 235
-SubTopic 10
-Name Accounting Standards Codification
-Section S50
-Paragraph 4
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480738/235-10-S50-4

Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 235
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 3
-Subparagraph (SX 210.12-04(a))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480678/235-10-S99-3

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Number of shares authorized for issuance under share-based payment arrangement.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (a)(3)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

Maximum number of shares that may be issued in accordance with the plan as a proportion of outstanding capital stock.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 4
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-4

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Total number of shares issued during the period, including shares forfeited, as a result of Restricted Stock Awards.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-SubTopic 10
-Topic 505
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481112/505-10-50-2

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 505
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.3-04)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480008/505-10-S99-1

+ Details

Name:	us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Details

Name:	us-gaap_PlanNameAxis=gyro_StockPlanMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_PlanNameAxis=gyro_RightsOfferingMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_TitleOfIndividualAxis=srt_DirectorMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_OtherCommitmentsAxis=gyro_BonusPayableMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_TitleOfIndividualAxis=srt_ChiefExecutiveOfficerMember
Namespace Prefix:
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Period Type:

Note 12 - Commitments (Details Textual) - USD ($)			12 Months Ended
Note 12 - Commitments (Details Textual) - USD ($)	Nov. 14, 2023	Sep. 05, 2023	Dec. 31, 2025	Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020	Jan. 01, 2020
Other Commitment			$ 350,000	$ 439,000
Payment for Retention Bonus Plan			$ 0
Deferred Compensation, Arrangement Fixed Interest Rate									5.00%
Director Fees, Deferred, Percentage			100.00%	100.00%	100.00%	100.00%	100.00%	100.00%
Stock Plan [Member]
Stock Issued During Period, Shares, Restricted Stock Award, Gross	91,628
Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Shares Authorized	91,628
Share-Based Compensation Arrangement by Share-Based Payment Award, Percentage of Outstanding Stock Maximum	5.80%
Rights Offering [Member]
Share-Based Compensation Arrangement by Share-Based Payment Award, Percentage of Outstanding Stock Maximum				4.20%
Director [Member]
Stock Issued During Period, Shares, Restricted Stock Award, Gross		91,628
Bonus Payable [Member] \| Chief Executive Officer [Member]
Other Commitment			$ 125,000