Subsequent Events (Details Narrative) 1 - Yorkville [Member]	Feb. 02, 2024 USD ($) Days $ / shares	Sep. 06, 2024 USD ($)
Other Promissory Notes [Member]
Subsequent Event [Line Items]
Debt instrument, face amount	$ 2,877,319
Debt instrument discount as a percentage of face value	20.00%
Short term debt bearing fixed interest rate percentage	10.00%
Short term debt default interest rate percentage	18.00%
Loan conversion price \| $ / shares	$ 10
Debt instrument convertible threshold percentage of stock price trigger	90.00%
Debt Instrument consecutive trading days \| Days	10
Debt instrument conversion price per share floor price \| $ / shares	$ 2
Subsequent Event [Member]
Subsequent Event [Line Items]
Debt instrument, face amount	$ 2,500,000
Debt instrument discount as a percentage of face value	20.00%
Short term debt bearing fixed interest rate percentage	10.00%
Short term debt default interest rate percentage	18.00%
Loan conversion price \| $ / shares	$ 10
Debt instrument convertible threshold percentage of stock price trigger	90.00%
Debt Instrument consecutive trading days \| Days	10
Debt instrument conversion price per share floor price \| $ / shares	$ 2
Subsequent Event [Member] \| Second A&R YA Agreement [Member]
Subsequent Event [Line Items]
Debt instrument, face amount		$ 7,500,000
Subsequent Event [Member] \| Tranche One [Member] \| Second A&R YA Agreement [Member]
Subsequent Event [Line Items]
Debt instrument, face amount		2,500,000
Subsequent Event [Member] \| Tranche Two [Member] \| Second A&R YA Agreement [Member]
Subsequent Event [Line Items]
Debt instrument, face amount		2,500,000
Subsequent Event [Member] \| Tranche Three [Member] \| Second A&R YA Agreement [Member]
Subsequent Event [Line Items]
Debt instrument, face amount		$ 2,500,000
Subsequent Event [Member] \| Other Promissory Notes [Member]
Subsequent Event [Line Items]
Debt instrument, face amount	$ 2,877,319
Debt instrument discount as a percentage of face value	20.00%
Short term debt bearing fixed interest rate percentage	10.00%
Short term debt default interest rate percentage	18.00%
Loan conversion price \| $ / shares	$ 10
Debt instrument convertible threshold percentage of stock price trigger	90.00%
Debt Instrument consecutive trading days \| Days	10
Debt instrument conversion price per share floor price \| $ / shares	$ 2

Debt instrument conversion price per share floor price.

No definition available.

Name:	rzlv_DebtInstrumentConversionPricePerShareFloorPrice
Namespace Prefix:	rzlv_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	instant

- Definition

Debt instrument discount as a percentage of face value.

+ References

No definition available.

+ Details

Name:	rzlv_DebtInstrumentDiscountAsAPercentageOfFaceValue
Namespace Prefix:	rzlv_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

Short term debt default interest rate percentage.

+ References

No definition available.

+ Details

Name:	rzlv_ShortTermDebtDefaultInterestRatePercentage
Namespace Prefix:	rzlv_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

The price per share of the conversion feature embedded in the debt instrument.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1B
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1B

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 5
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-5

+ Details

Name:	us-gaap_DebtInstrumentConvertibleConversionPrice1
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	instant

- Definition

Threshold period of specified consecutive trading days within which common stock price to conversion price of convertible debt instrument must exceed threshold percentage for specified number of trading days to trigger conversion feature.

+ References

No definition available.

+ Details

Name:	us-gaap_DebtInstrumentConvertibleThresholdConsecutiveTradingDays1
Namespace Prefix:	us-gaap_
Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	duration

- Definition

Minimum percentage of common stock price to conversion price of convertible debt instruments to determine eligibility of conversion.

+ References

No definition available.

+ Details

Name:	us-gaap_DebtInstrumentConvertibleThresholdPercentageOfStockPriceTrigger
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
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
-Paragraph 8
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482949/835-30-55-8

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1B
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1B

Reference 3: http://www.xbrl.org/2003/role/exampleRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 55
-Paragraph 69B
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481568/470-20-55-69B

Reference 4: http://www.xbrl.org/2003/role/exampleRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 55
-Paragraph 69C
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481568/470-20-55-69C

Reference 5: http://www.xbrl.org/2003/role/disclosureRef
-Topic 835
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482900/835-30-50-1

Reference 6: http://www.xbrl.org/2003/role/disclosureRef
-Topic 835
-SubTopic 30
-Name Accounting Standards Codification
-Section 45
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482925/835-30-45-2

+ Details

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

- Definition

The portion of the carrying amount of short-term borrowings outstanding as of the balance sheet date which accrues interest at a set, unchanging rate.

+ References

No definition available.

+ Details

Name:	us-gaap_ShortTermDebtPercentageBearingFixedInterestRate
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
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
-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

- Details

Name:	us-gaap_RelatedPartyTransactionsByRelatedPartyAxis=rzlv_YorkvilleMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

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

- Details

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

- Details

Name:	us-gaap_TypeOfArrangementAxis=rzlv_SecondARYaAgreementMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	rzlv_TrancheAxis=rzlv_TrancheOneMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	rzlv_TrancheAxis=rzlv_TrancheTwoMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	rzlv_TrancheAxis=rzlv_TrancheThreeMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: