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Commitments - Summary of Commitments to Purchase Eligible Services and Offerings (Details) - Google [Member] | 12 Months Ended
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Dec. 31, 2024 USD ($)
Long-Term Purchase Commitment [Line Items] |  |
Commitment amount | $ 10,000,000 |
Commitment Period 1 [Member] |  |
Long-Term Purchase Commitment [Line Items] |  |
Commitment amount | 1,000,000 | [1]
Commitment Period 2 [Member] |  |
Long-Term Purchase Commitment [Line Items] |  |
Commitment amount | 3,000,000 | [2]
Commitment Period 3 [Member] |  |
Long-Term Purchase Commitment [Line Items] |  |
Commitment amount | $ 6,000,000 | [3]
[1] | The period starting on November 15, 2024 and continuing for 12 months.
[2] | The period starting at the end of Commitment Period 1 and continuing for 12 months.
[3] | The period starting at the end of Commitment Period 2 and continuing for 12 months.

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- Definition The minimum amount the entity agreed to spend under the long-term purchase commitment. + References No definition available. + Details
Name: | us-gaap_LongTermPurchaseCommitmentAmount
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | duration

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- Definition Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table. + References No definition available. + Details
Name: | us-gaap_LongTermPurchaseCommitmentLineItems
Namespace Prefix: | us-gaap_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration

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- Details
Name: | srt_CounterpartyNameAxis=rzlv_GoogleCloudEMEALtdMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

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- Details
Name: | us-gaap_LongTermPurchaseCommitmentByCategoryOfItemPurchasedAxis=rzlv_CommitmentPeriodOneMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

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- Details
Name: | us-gaap_LongTermPurchaseCommitmentByCategoryOfItemPurchasedAxis=rzlv_CommitmentPeriodTwoMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

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- Details
Name: | us-gaap_LongTermPurchaseCommitmentByCategoryOfItemPurchasedAxis=rzlv_CommitmentPeriodThreeMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |