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Debt and other liabilities - Schedule of Convertible debt (Details) - USD ($)	Jun. 30, 2025	Jan. 23, 2025	Dec. 31, 2024
Convertible Debt [Line Items]
Discount on convertible debt under troubled debt restructuring		$ (3,000,000)
Short term convertible debt to related party	$ 108,047		$ 95,309

X

- Definition

Convertible debt.

+ References

No definition available.

+ Details

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Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Short term convertible debt payable to related party.

+ References

No definition available.

+ Details

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Namespace Prefix:	rzlv_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

X

- Definition

Amount, after accumulated amortization, of debt discount.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 835
-SubTopic 30
-Name Accounting Standards Codification
-Section 45
-Paragraph 1A
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482925/835-30-45-1A

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-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

Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef
-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 4: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1D
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1D

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