Aggregate purchase price from offering.

No definition available.

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Namespace Prefix:	alur_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Percentage of outstanding common stock.

+ References

No definition available.

+ Details

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

- 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

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Period Type:	duration

- Definition

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

+ References

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+ Details

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Balance Type:	credit
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.

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+ Details

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Period Type:	duration

- Definition

The number of shares issued or sold by the subsidiary or equity method investee per stock transaction.

+ References

No definition available.

+ Details

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Balance Type:	na
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- Definition

Per share amount received by subsidiary or equity investee for each share of common stock issued or sold in the stock transaction.

+ References

No definition available.

+ Details

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- Details

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Namespace Prefix:
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- Details

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- Details

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- Details

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- Details

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Related-party Transactions - Additional Information (Details) - USD ($) $ / shares in Units, $ in Millions	Nov. 12, 2025	Nov. 04, 2025	Apr. 16, 2025	Apr. 15, 2025	Jan. 14, 2025	Apr. 16, 2024	Aug. 01, 2023
Second Amendment to Note Purchase Agreement \| RTW Convertible Notes
Related Party Transaction [Line Items]
Principal amount		$ 5.0	$ 5.0	$ 5.0
Shares issued upon conversion of outstanding notes				1,492,539
Convertible Note Agreement with RTW
Related Party Transaction [Line Items]
Principal amount						$ 48.0
Percentage of Outstanding Common Stock						5.00%
Common Stock
Related Party Transaction [Line Items]
Sale of stock							$ 202.5
Common Stock \| Second Amendment to Note Purchase Agreement \| RTW Convertible Notes
Related Party Transaction [Line Items]
Shares issued upon conversion of outstanding notes		1,492,539	1,492,539
Common Stock \| November 2025 Private Placement with RTW
Related Party Transaction [Line Items]
Sale of stock	1,856,288
Sale of stock	$ 1.67
Aggregate purchase price	$ 3.1
Common Stock \| January 2025 Private Placement with RTW
Related Party Transaction [Line Items]
Sale of stock					841,751
Sale of stock					$ 2.97
Aggregate purchase price					$ 2.5