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Expenses and Other Non-Operating Income/(Expense), Net - Schedule of Other non-operating income (expense), net (Details) - USD ($)	6 Months Ended
	Jun. 30, 2025	Jun. 30, 2024
Expenses And Other Non Operating Income Expense Net [Line Items]
Total	$ 169,613	$ (98,818)

X

- Definition

Expenses and other non operating income expense net.

+ References

No definition available.

+ Details

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Namespace Prefix:	rzlv_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Amount of income (expense) related to nonoperating activities, classified as other.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 815
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 4A
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480434/815-10-50-4A

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 220
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Subparagraph (SX 210.5-03(9))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147483621/220-10-S99-2

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration