{
  "schema_version": 1,
  "claim_id": "EulerSignalBridge-FIR-2026-10-09",
  "repository": {
    "commit": "standalone script; no Git repository",
    "dirty": true
  },
  "command": "python verify_bridge.py",
  "environment": {
    "software": [
      "Python 3.12.14",
      "NumPy 2.3.5",
      "Matplotlib 3.10.8"
    ],
    "hardware": "Linux x86_64; CPU only"
  },
  "mathematics": {
    "assertion_tested": "FIR stencil equals finite binomial-coordinate transfer; successive affine transfers compose; prime residual coefficients are integral.",
    "coefficient_domain": "Python arbitrary-precision integers for all arithmetic checks; float64 only for illustrative frequency curves",
    "conventions": "Signed Euler EGF sech(t); a(n)=E_(2n); advance shift S a(n)=a(n+1); Delta=S-I.",
    "inputs": [
      "Signed Euler sequence through E_94",
      "deterministic alternating cubic integer signal",
      "affine transfer polynomial rows"
    ],
    "bounds": {
      "sample_count": 48,
      "transfer_M": [
        1,
        5
      ],
      "phase_s": "0 <= s < M",
      "difference_k": [
        0,
        6
      ],
      "composition_M_N": [
        1,
        3
      ],
      "composition_order": [
        0,
        4
      ],
      "primes": [
        2,
        3,
        5,
        7,
        11
      ]
    },
    "non_claims": [
      "No Fourier transform of the Euler sequence",
      "No universal Euler congruence follows from finite checks",
      "No novelty claim for the FIR or binomial identities",
      "No Lean build performed"
    ]
  },
  "randomness": {
    "used": false,
    "generator": "none",
    "seed": null
  },
  "run": {
    "started_at": "2026-10-09T01:58:32.687088+00:00",
    "runtime_seconds": 0.23854584200307727,
    "exit_status": 0
  },
  "outputs": [
    {
      "path": "exact_results.json",
      "sha256": "a5ae2204454aa4a1a2e1ab83415ba8a8a93cde6db6a0367833351902ad07dd6c"
    },
    {
      "path": "Komorebi_Euler_Signal_Bridge.png",
      "sha256": "c7b9e72a4c444f296831850f4ba97b58aae2860277ca091a5824c2803c95d0d4"
    }
  ],
  "checks": [
    "direct sample stencil versus independently expanded polynomial rows",
    "exact composition coefficient comparison",
    "small hand-computable Euler controls",
    "prime coefficient divisibility"
  ],
  "result": "PASS: 395 exact finite assertions plus initial-value controls.",
  "residual_risks": [
    "A version 1 manifest records limited execution provenance; the script hash is separately supplied.",
    "Full-branch valuation bounds require a separate mathematical argument."
  ]
}