Capital Stock and Stockholders' Deficit - Summary of Warrants to Purchase Classes of Preferred Stock and Common Stock Outstanding (Details) - $ / shares	Dec. 31, 2025	Jan. 24, 2025	Dec. 31, 2024
Class of Warrant or Right [Line Items]
Warrants to purchase an aggregate shares	7,336,872		767,697
Weighted Average Exercise Price	$ 202.5
December 1, 2014 \| Common Stock
Class of Warrant or Right [Line Items]
Remaining Contractual Term (in years)			1 month 6 days
Warrants to purchase an aggregate shares			209
Weighted Average Exercise Price			$ 61
March 30, 2021 \| Common Stock
Class of Warrant or Right [Line Items]
Remaining Contractual Term (in years)	5 years 2 months 12 days		6 years 2 months 12 days
Warrants to purchase an aggregate shares	5,203		5,203
Weighted Average Exercise Price	$ 168.25		$ 168.25
September 15, 2022 \| Common Stock
Class of Warrant or Right [Line Items]
Remaining Contractual Term (in years)	6 years 8 months 12 days		7 years 8 months 12 days
Warrants to purchase an aggregate shares	1,810		1,810
Weighted Average Exercise Price	$ 303.5		$ 303.5
June 4, 2022 \| Common Stock
Class of Warrant or Right [Line Items]
Remaining Contractual Term (in years)	6 years 4 months 24 days		7 years 4 months 24 days
Warrants to purchase an aggregate shares	1,810		1,810
Weighted Average Exercise Price	$ 303.5		$ 303.5
January 17, 2017 \| Common Stock
Class of Warrant or Right [Line Items]
Remaining Contractual Term (in years)	1 year		2 years
Warrants to purchase an aggregate shares	2,934		2,934
Weighted Average Exercise Price	$ 0.5		$ 0.5
August 3, 2017 \| Common Stock
Class of Warrant or Right [Line Items]
Remaining Contractual Term (in years)	1 year 7 months 6 days		2 years 7 months 6 days
Warrants to purchase an aggregate shares	392		392
Weighted Average Exercise Price	$ 28.25		$ 28.25
September 8, 2017 \| Common Stock
Class of Warrant or Right [Line Items]
Remaining Contractual Term (in years)	1 year 8 months 12 days		2 years 8 months 12 days
Warrants to purchase an aggregate shares	1,151		1,151
Weighted Average Exercise Price	$ 26.25		$ 26.25
June 19, 2018 \| Common Stock
Class of Warrant or Right [Line Items]
Remaining Contractual Term (in years)	2 years 6 months		3 years 6 months
Warrants to purchase an aggregate shares	720		720
Weighted Average Exercise Price	$ 26.25		$ 26.25
June 25, 2019 \| Common Stock
Class of Warrant or Right [Line Items]
Remaining Contractual Term (in years)	3 years 6 months		4 years 6 months
Warrants to purchase an aggregate shares	360		360
Weighted Average Exercise Price	$ 26.25		$ 26.25
July 1, 2024 \| Common Stock
Class of Warrant or Right [Line Items]
Remaining Contractual Term (in years)	3 years 6 months		4 years 6 months
Warrants to purchase an aggregate shares	753,108		753,108
Weighted Average Exercise Price	$ 11.42	$ 30	$ 30
January 27, 2025 \| Common Stock
Class of Warrant or Right [Line Items]
Remaining Contractual Term (in years)	4 years 3 months 18 days
Warrants to purchase an aggregate shares	1,240,000
Weighted Average Exercise Price	$ 6
November 11, 2025 \| Common Stock
Class of Warrant or Right [Line Items]
Remaining Contractual Term (in years)	5 years
Warrants to purchase an aggregate shares	2,994,012
Weighted Average Exercise Price	$ 1.67
February 20, 2025 \| Common Stock
Class of Warrant or Right [Line Items]
Remaining Contractual Term (in years)	4 years 3 months 18 days
Warrants to purchase an aggregate shares	2,335,372
Weighted Average Exercise Price	$ 5.23

Exercise price per share or per unit of warrants or rights outstanding.

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 235
-SubTopic 10
-Name Accounting Standards Codification
-Section S50
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480738/235-10-S50-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 235
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.4-08(h)(4))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480678/235-10-S99-1

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 505
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481112/505-10-50-3

+ Details

Name:	us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	instant

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

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

- Definition

Number of securities into which the class of warrant or right may be converted. For example, but not limited to, 500,000 warrants may be converted into 1,000,000 shares.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 505
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481112/505-10-50-3

+ Details

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

- Definition

Period between issuance and expiration of outstanding warrant and right embodying unconditional obligation requiring redemption by transferring asset at specified or determinable date or upon event certain to occur, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (bbb)(2)(i)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-2

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (bbb)(2)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-2

Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (bbb)(1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-2

+ Details

Name:	us-gaap_WarrantsAndRightsOutstandingTerm
Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	instant

- Details

Name:	us-gaap_ClassOfWarrantOrRightAxis=alur_WarrantsIssuedAtDecember012014Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_StatementEquityComponentsAxis=us-gaap_CommonStockMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_ClassOfWarrantOrRightAxis=alur_WarrantsIssuedAtMarch302021Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_ClassOfWarrantOrRightAxis=alur_WarrantsIssuedAtSeptember152022Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_ClassOfWarrantOrRightAxis=alur_WarrantsIssuedAtJune042022Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_ClassOfWarrantOrRightAxis=alur_WarrantsIssuedAtJanuary172017Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_ClassOfWarrantOrRightAxis=alur_WarrantsIssuedAtAugust032017Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_ClassOfWarrantOrRightAxis=alur_WarrantsIssuedAtSeptember082017Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_ClassOfWarrantOrRightAxis=alur_WarrantsIssuedAtJune192018Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_ClassOfWarrantOrRightAxis=alur_WarrantsIssuedAtJune252019Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_ClassOfWarrantOrRightAxis=alur_WarrantsIssuedAtJuly012024Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_ClassOfWarrantOrRightAxis=alur_WarrantsIssuedAtJanuary272025Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_ClassOfWarrantOrRightAxis=alur_WarrantsIssuedAtNovember112025Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_ClassOfWarrantOrRightAxis=alur_WarrantsIssuedAtFebruary202025Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: