Debt instrument, additional principal amount for conversion into common stock.

No definition available.

Name:	alur_DebtInstrumentAdditionalPrincipalAmountForConversionIntoCommonStock
Namespace Prefix:	alur_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Debt instrument, floor conversion price per share.

+ References

No definition available.

+ Details

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Namespace Prefix:	alur_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	duration

- Definition

Face amount or stated value per share of common stock.

+ References

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-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(29))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	instant

- Definition

The number of shares issued in exchange for the original debt being converted in a noncash (or part noncash) transaction. "Part noncash" refers to that portion of the transaction not resulting in cash receipts or payments in the period.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 50
-Paragraph 3
-Publisher FASB
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+ Details

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

- Definition

Face (par) amount of debt instrument at time of issuance.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 835
-SubTopic 30
-Name Accounting Standards Codification
-Section 55
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+ Details

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

- Definition

Detail information of subsequent event by type. User is expected to use existing line items from elsewhere in the taxonomy as the primary line items for this disclosure, which is further associated with dimension and member elements pertaining to a subsequent event.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
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-SubTopic 30
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-Publisher FASB
-URI https://asc.fasb.org/1943274/2147483399/855-10-50-2

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Details

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Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=alur_RtwConvertibleNotesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=alur_SecondAmendmentToNotePurchaseAgreementMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

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Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_RangeAxis=srt_MaximumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_StatementEquityComponentsAxis=us-gaap_CommonStockMember
Namespace Prefix:
Data Type:	na
Balance Type:
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Subsequent Events - Additional Information (Details) - USD ($) $ / shares in Units, $ in Millions	Apr. 15, 2026	Nov. 04, 2025	Apr. 16, 2025	Apr. 15, 2025	Mar. 31, 2026	Dec. 31, 2025	Apr. 14, 2024
Subsequent Event [Line Items]
Par value common stock					$ 0.0001	$ 0.0001
Note Purchase Agreement \| RTW Convertible Notes
Subsequent Event [Line Items]
Principal amount							$ 48.0
Second Amendment to Note Purchase Agreement \| RTW Convertible Notes
Subsequent Event [Line Items]
Principal amount		$ 5.0	$ 5.0	$ 5.0
Shares issued upon conversion of convertible notes				1,492,539
Debt instrument, additional principal amount for conversion into common stock				$ 5.0
Floor conversion price per share				$ 3.35
Second Amendment to Note Purchase Agreement \| RTW Convertible Notes \| Subsequent Events
Subsequent Event [Line Items]
Debt instrument, additional principal amount for conversion into common stock	$ 1.0
Second Amendment to Note Purchase Agreement \| RTW Convertible Notes \| Maximum \| Subsequent Events
Subsequent Event [Line Items]
Debt instrument, additional principal amount for conversion into common stock	$ 12.0
Second Amendment to Note Purchase Agreement \| RTW Convertible Notes \| Common Stock
Subsequent Event [Line Items]
Shares issued upon conversion of convertible notes		1,492,539	1,492,539