XML 66 R52.htm IDEA: XBRL DOCUMENT
v3.24.4

Significant Accounting Policies - Summary of common stock reflected in the balance sheets are reconciled (Details) - Armada Acquisition Corp I [Member] - USD ($) |  |  |  | 1 Months Ended | 3 Months Ended | 9 Months Ended | 12 Months Ended
--- | --- | --- | --- | --- | --- | --- | ---
Feb. 15, 2024 | Feb. 09, 2024 | Aug. 02, 2023 | Aug. 31, 2023 | Mar. 31, 2024 | Dec. 31, 2023 | Jun. 30, 2024 | Sep. 30, 2023 | Sep. 30, 2022
Gross Proceeds |  |  |  |  |  |  |  |  | $ 150,000,000
Proceeds allocated to Public Warrants |  |  |  |  |  |  |  |  | (11,700,000)
Issuance costs related to common stock |  |  |  |  |  |  |  |  | (3,261,589)
Remeasurement of carrying value to redemption value | $ 10,384,496 | $ 10,384,496 |  |  |  | $ 467,884 |  | $ 3,943,038 | 14,961,589
Subsequent remeasurement of carrying value to redemption value – Trust interest income (excluding the amount that can be withdrawn from Trust Account for taxes) |  |  |  |  |  |  |  |  | 548,862
Common stock subject to possible redemption |  |  |  |  | $ 15,747,446 | $ 25,784,690 | $ 16,040,786 | 25,316,806 | 150,548,862
Redemptions |  |  |  |  | (10,384,496) |  | (10,384,496) | $ (129,175,094) | $ (129,175,094)
As filed [Member] |  |  |  |  |  |  |  |  |
Remeasurement of carrying value to redemption value |  |  | $ 12,095,215 | $ 12,095,215 | $ 347,252 |  | $ 1,108,476 |  |

X
- Definition Amount of issuance costs for temporary equity. + References No definition available. + Details
Name: | rzlv_TemporaryEquityIssuanceCosts
Namespace Prefix: | rzlv_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration

X
- Definition Temporary equity stock redeemed during the period value. + References No definition available. + Details
Name: | rzlv_TemporaryEquityStockRedeemedDuringThePeriodValue
Namespace Prefix: | rzlv_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration

X
- Definition Temporary equity subsequent accretion to redemption value. + References No definition available. + Details
Name: | rzlv_TemporaryEquitySubsequentAccretionToRedemptionValue
Namespace Prefix: | rzlv_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | duration

X
- Definition The cash inflow from issuance of rights to purchase common shares at predetermined price (usually issued together with corporate debt). + 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_ProceedsFromIssuanceOfWarrants
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration

X
- Definition Value of accretion of temporary equity to its redemption value during the period. + References No definition available. + Details
Name: | us-gaap_TemporaryEquityAccretionToRedemptionValue
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | duration

X
- Definition Carrying amount, attributable to parent, of an entity's issued and outstanding stock which is not included within permanent equity. Temporary equity is a security with redemption features that are outside the control of the issuer, is not classified as an asset or liability in conformity with GAAP, and is not mandatorily redeemable. Includes any type of security that is redeemable at a fixed or determinable price or on a fixed or determinable date or dates, is redeemable at the option of the holder, or has conditions for redemption which are not solely within the control of the issuer. Includes stock with a put option held by an ESOP and stock redeemable by a holder only in the event of a change in control of the issuer. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 944 -SubTopic 210 -Name Accounting Standards Codification -Section S99 -Paragraph 1 -Subparagraph (SX 210.7-03(a)(23)(a)(1)) -Publisher FASB -URI https://asc.fasb.org/1943274/2147478777/944-210-S99-1 Reference 2: http://www.xbrl.org/2003/role/disclosureRef -Topic 718 -SubTopic 10 -Name Accounting Standards Codification -Section S99 -Paragraph 1 -Subparagraph (SAB Topic 14.E.Q2) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479830/718-10-S99-1 Reference 3: http://www.xbrl.org/2003/role/disclosureRef -Topic 470 -SubTopic 10 -Name Accounting Standards Codification -Section S99 -Paragraph 1A -Subparagraph (SX 210.13-01(a)(4)(i)) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480097/470-10-S99-1A Reference 4: http://www.xbrl.org/2003/role/disclosureRef -Topic 470 -SubTopic 10 -Name Accounting Standards Codification -Section S99 -Paragraph 1A -Subparagraph (SX 210.13-01(a)(4)(iv)) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480097/470-10-S99-1A Reference 5: http://www.xbrl.org/2003/role/disclosureRef -Topic 470 -SubTopic 10 -Name Accounting Standards Codification -Section S99 -Paragraph 1A -Subparagraph (SX 210.13-01(a)(5)) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480097/470-10-S99-1A Reference 6: http://www.xbrl.org/2003/role/disclosureRef -Topic 470 -SubTopic 10 -Name Accounting Standards Codification -Section S99 -Paragraph 1B -Subparagraph (SX 210.13-02(a)(4)(i)) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480097/470-10-S99-1B Reference 7: http://www.xbrl.org/2003/role/disclosureRef -Topic 470 -SubTopic 10 -Name Accounting Standards Codification -Section S99 -Paragraph 1B -Subparagraph (SX 210.13-02(a)(4)(iv)) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480097/470-10-S99-1B Reference 8: http://www.xbrl.org/2003/role/disclosureRef -Topic 470 -SubTopic 10 -Name Accounting Standards Codification -Section S99 -Paragraph 1B -Subparagraph (SX 210.13-02(a)(5)) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480097/470-10-S99-1B + Details
Name: | us-gaap_TemporaryEquityCarryingAmountAttributableToParent
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | instant

X
- Definition Value of new stock classified as temporary equity issued during the period. + References No definition available. + Details
Name: | us-gaap_TemporaryEquityStockIssuedDuringPeriodValueNewIssues
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | duration

X
- Details
Name: | dei_LegalEntityAxis=rzlv_ArmadaAcquisitionCorpIMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | srt_RestatementAxis=srt_ScenarioPreviouslyReportedMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |