{
      "tool_id": "art-215-reg-z-appendix-j-apr",
      "tool_version": "1.0.0",
      "display_name": "Reg Z Appendix J APR Solver",
      "mcp_name": "compute_reg_z_appendix_j_apr",
      "mandate_type": "compliance_mandate",
      "wave": 37,
      "gpu": false,
      "url": "https://ainumbers.co/chaingraph/art-215-reg-z-appendix-j-apr.html",
      "description": "Reg Z Appendix J actuarial APR solver. Newton-Raphson iteration over the general actuarial equation (12 CFR 1026 Appendix J). Handles regular and irregular payment schedules with odd-days fractional first period. Pure ECMA-262 arithmetic, no floating-point built-ins beyond basic operations. APR accuracy, TRID disclosure, and QM spread test input.",
      "input_schema_ref": "chaingraph/art-215-reg-z-appendix-j-apr.html#manifest",
      "consumes": [
        "art-332-build-amortization-schedule"
      ],
      "feeds": [
        "art-217-trid-apr-accuracy"
      ],
      "status": "live",
      "conformance_fixtures": true,
      "compute_capability": "server",
      "compute_images": [{"system":"sha256-source","image_id":"sha256:429bfe0fa27879e429bbd5129f57243ebc99b4e6dc016f0ffebacd35acdd9219","valid_from":"2026-07-10"},{"system":"risc0","image_id":"sha256:a1a0bc89b5b1febaeda3519f6dbade0fa5ac16beeb143c4e1b01689573567bc6","valid_from":"2026-07-04"}],
      "export_capability": [
        "json"
      ],
      "compute_proof_ready": "ready",
      "compute_proof": {
        "type": "ZkVmReceipt",
        "system": "risc0",
        "receiptFormat": "groth16-bn254",
        "imageId": "sha256:a1a0bc89b5b1febaeda3519f6dbade0fa5ac16beeb143c4e1b01689573567bc6",
        "seal": "KfOnIoS3IENQlKAeHS/hr60QMxwhrT1J3V4iYEEQxWwSuVLQhIOjIOcxZdo/vXFogdGfTpHU6MNiYwmGmjhq4hMwft1RGmNd8eab0AW+44nHBmV4+2E8zCjBrEom2rTDJ42UYkBKgTUo9kVbgZlgNNFYsJTSbwytuG1XVhvFZ80Dtxb+7GGJS9VnRgXK+OLWVD6/Tv4zLKtazmEN+SShQgNwGY/Lv9sTbnup4Ur9N6uMxxLyp/UPRTS492ZI77XFIBugd50XkxUDSz6v+BN0Jme0X7U5lCANWSMBiVd0LqgoXIBbVjxNt03Rg9br6zkpxdOo/sHOKHIWeNtxuLWKZQ==",
        "journal": {
          "chaingraph_version": "0.4.0",
          "kernel_digest": "sha256:429bfe0fa27879e429bbd5129f57243ebc99b4e6dc016f0ffebacd35acdd9219",
          "output": {
            "advance_total": 6000,
            "apr_pct": 11.9961,
            "converged": true,
            "finance_charge": 778.32,
            "iterations": 3,
            "note": "APR computed via Appendix J actuarial method. Odd-days fraction included when advances/payments supplied with fractional periods_from_consummation. Input APOR separately for QM spread test.",
            "num_payments": 24,
            "payment_total": 6778.32,
            "periodic_rate": 0.009997,
            "periods_per_year": 12,
            "regulatory_basis": "Reg Z Appendix J, 12 CFR 1026 Appendix J (general actuarial equation)"
          }
        }
      }
    }