XML 121 R106.htm IDEA: XBRL DOCUMENT
v3.25.2

Subsequent Events - Additional Information (Details) - USD ($) | Feb. 19, 2025 | Jan. 24, 2025 | Jan. 14, 2025 | Jan. 07, 2025 | Dec. 31, 2024 | Sep. 30, 2024 | Jun. 30, 2024 | Jun. 28, 2024 | Mar. 31, 2024 | Dec. 31, 2023
--- | --- | --- | --- | --- | --- | --- | --- | --- | --- | ---
Subsequent Event [Line Items] |  |  |  |  |  |  |  |  |  |
Shares Issuable Upon Exercise of Warrant |  |  |  |  | 767,697 |  |  |  |  | 16,151
Common stock, par value |  |  |  |  | $ 0.0001 | $ 0.0001 | $ 0.0001 |  | $ 0.0001 | $ 0.0001
Warrants exercisable price |  |  |  |  | $ 202.5 |  |  |  |  |
Private Placement with RTW |  |  |  |  |  |  |  |  |  |
Subsequent Event [Line Items] |  |  |  |  |  |  |  |  |  |
Shares Issuable Upon Exercise of Warrant |  |  |  |  |  |  |  | 90,407 |  |
Common Stock | Public Offering Warrants Issued in July 2024 |  |  |  |  |  |  |  |  |  |
Subsequent Event [Line Items] |  |  |  |  |  |  |  |  |  |
Shares Issuable Upon Exercise of Warrant |  |  |  |  | 753,108 |  |  |  |  |
Warrants exercisable price |  |  |  |  | $ 30 |  |  |  |  |
Subsequent Event | January 2025 Offering |  |  |  |  |  |  |  |  |  |
Subsequent Event [Line Items] |  |  |  |  |  |  |  |  |  |
Shares Issuable Upon Exercise of Warrant |  | 1,240,000 |  |  |  |  |  |  |  |
Subsequent Event | January 2025 Private Placement |  |  |  |  |  |  |  |  |  |
Subsequent Event [Line Items] |  |  |  |  |  |  |  |  |  |
Shares Issuable Upon Exercise of Warrant |  | 1,240,000 |  |  |  |  |  |  |  |
Purchase price per share |  | $ 6 |  |  |  |  |  |  |  |
Subsequent Event | January 2025 Offering and January 2025 Private Placement |  |  |  |  |  |  |  |  |  |
Subsequent Event [Line Items] |  |  |  |  |  |  |  |  |  |
Gross proceeds from offering |  | $ 7,400,000 |  |  |  |  |  |  |  |
Subsequent Event | February 2025 Offering |  |  |  |  |  |  |  |  |  |
Subsequent Event [Line Items] |  |  |  |  |  |  |  |  |  |
Shares Issuable Upon Exercise of Warrant | 1,800,000 |  |  |  |  |  |  |  |  |
Subsequent Event | February 2025 Private Placement |  |  |  |  |  |  |  |  |  |
Subsequent Event [Line Items] |  |  |  |  |  |  |  |  |  |
Shares Issuable Upon Exercise of Warrant | 1,800,000 |  |  |  |  |  |  |  |  |
Purchase price per share | $ 5.23 |  |  |  |  |  |  |  |  |
Subsequent Event | February 2025 Offering and February 2025 Private Placement |  |  |  |  |  |  |  |  |  |
Subsequent Event [Line Items] |  |  |  |  |  |  |  |  |  |
Gross proceeds from offering | $ 4,700,000 |  |  |  |  |  |  |  |  |
Subsequent Event | Leavitt Private Placement |  |  |  |  |  |  |  |  |  |
Subsequent Event [Line Items] |  |  |  |  |  |  |  |  |  |
Shares Issuable Upon Exercise of Warrant | 535,372 |  |  |  |  |  |  |  |  |
Aggregate purchase price | $ 1,400,000 |  |  |  |  |  |  |  |  |
Purchase price per share | $ 5.23 |  |  |  |  |  |  |  |  |
Subsequent Event | Common Stock |  |  |  |  |  |  |  |  |  |
Subsequent Event [Line Items] |  |  |  |  |  |  |  |  |  |
Percentage of diluted shares outstanding |  |  |  | 5.00% |  |  |  |  |  |
Aggregate net proceeds |  |  |  | $ 12,000,000 |  |  |  |  |  |
Subsequent Event | Common Stock | Private Placement with RTW |  |  |  |  |  |  |  |  |  |
Subsequent Event [Line Items] |  |  |  |  |  |  |  |  |  |
Number of shares sold per unit |  |  | 841,751 |  |  |  |  |  |  |
Common stock, par value |  |  | $ 0.0001 |  |  |  |  |  |  |
Aggregate purchase price |  |  | $ 2,500,000 |  |  |  |  |  |  |
Purchase price per share |  |  | $ 2.97 |  |  |  |  |  |  |
Subsequent Event | Common Stock | January 2025 Offering |  |  |  |  |  |  |  |  |  |
Subsequent Event [Line Items] |  |  |  |  |  |  |  |  |  |
Number of shares sold per unit |  | 1,240,000 |  |  |  |  |  |  |  |
Subsequent Event | Common Stock | January 2025 Offering and January 2025 Private Placement | Public Offering Warrants Issued in July 2024 |  |  |  |  |  |  |  |  |  |
Subsequent Event [Line Items] |  |  |  |  |  |  |  |  |  |
Warrants exercisable price |  | $ 6 |  |  |  |  |  |  |  |
Subsequent Event | Common Stock | February 2025 Offering |  |  |  |  |  |  |  |  |  |
Subsequent Event [Line Items] |  |  |  |  |  |  |  |  |  |
Number of shares sold per unit | 900,000 |  |  |  |  |  |  |  |  |
Subsequent Event | Common Stock | Leavitt Private Placement |  |  |  |  |  |  |  |  |  |
Subsequent Event [Line Items] |  |  |  |  |  |  |  |  |  |
Number of shares sold per unit | 267,686 |  |  |  |  |  |  |  |  |

X
- Definition Aggregate purchase price from offering. + References No definition available. + Details
Name: | alur_AggregatePurchasePriceFromOffering
Namespace Prefix: | alur_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration

X
- Definition Percentage of diluted shares outstanding. + References No definition available. + Details
Name: | alur_PercentageOfDilutedSharesOutstanding
Namespace Prefix: | alur_
Data Type: | dtr-types:percentItemType
Balance Type: | na
Period Type: | duration

X
- Definition Exercise price per share or per unit of warrants or rights outstanding. + 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_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1
Namespace Prefix: | us-gaap_
Data Type: | dtr-types:perShareItemType
Balance Type: | na
Period Type: | instant

X
- 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

X
- Definition Face amount or stated value per share of common stock. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -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
Name: | us-gaap_CommonStockParOrStatedValuePerShare
Namespace Prefix: | us-gaap_
Data Type: | dtr-types:perShareItemType
Balance Type: | na
Period Type: | instant

X
- Definition The cash inflow from the additional capital contribution to the entity. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Name Accounting Standards Codification -Section 45 -Paragraph 14 -Subparagraph (a) -SubTopic 10 -Topic 230 -Publisher FASB -URI https://asc.fasb.org/1943274/2147482740/230-10-45-14 + Details
Name: | us-gaap_ProceedsFromIssuanceOfCommonStock
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration

X
- Definition The cash inflow from the issuance of common stock, preferred stock, treasury stock, stock options, and other types of equity. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Name Accounting Standards Codification -Section 45 -Paragraph 14 -Subparagraph (a) -SubTopic 10 -Topic 230 -Publisher FASB -URI https://asc.fasb.org/1943274/2147482740/230-10-45-14 Reference 2: http://www.xbrl.org/2003/role/disclosureRef -Topic 946 -SubTopic 10 -Name Accounting Standards Codification -Section S99 -Paragraph 3 -Subparagraph (SX 210.6-03(i)(1)) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479886/946-10-S99-3 + Details
Name: | us-gaap_ProceedsFromIssuanceOrSaleOfEquity
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration

X
- Definition The number of shares issued or sold by the subsidiary or equity method investee per stock transaction. + References No definition available. + Details
Name: | us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction
Namespace Prefix: | us-gaap_
Data Type: | xbrli:sharesItemType
Balance Type: | na
Period Type: | duration

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

X
- 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 -Topic 830 -SubTopic 30 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Publisher FASB -URI https://asc.fasb.org/1943274/2147481674/830-30-50-2 Reference 2: http://www.xbrl.org/2003/role/disclosureRef -Topic 855 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Publisher FASB -URI https://asc.fasb.org/1943274/2147483399/855-10-50-2 + Details
Name: | us-gaap_SubsequentEventLineItems
Namespace Prefix: | us-gaap_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration

X
- Details
Name: | us-gaap_SubsidiarySaleOfStockAxis=alur_PrivatePlacementWithRTWMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

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

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

X
- Details
Name: | us-gaap_SubsequentEventTypeAxis=us-gaap_SubsequentEventMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_SubsidiarySaleOfStockAxis=alur_JanuaryTwoThousandTwentyFiveOfferingMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_SubsidiarySaleOfStockAxis=alur_JanuaryTwoThousandTwentyFivePrivatePlacementMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_SubsidiarySaleOfStockAxis=alur_JanuaryTwoThousandTwentyFiveOfferingAndPrivatePlacementMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_SubsidiarySaleOfStockAxis=alur_FebruaryTwoThousandTwentyFiveOfferingMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_SubsidiarySaleOfStockAxis=alur_FebruaryTwoThousandTwentyFivePrivatePlacementMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_SubsidiarySaleOfStockAxis=alur_FebruaryTwoThousandTwentyFiveOfferingAndPrivatePlacementMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_SubsidiarySaleOfStockAxis=alur_LeavittPrivatePlacementMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |