{
  "checked_at": "2026-08-29T00:00:00Z",
  "result": "passed",
  "lean": {
    "version": "4.30.0-rc2",
    "commit": "3dc1a088b6d2d8eafe25a7cd7ec7b58d731bd7cc",
    "clean_build": true,
    "verified_modules": [
      "Matrix4Research.Scheme49LowMemory",
      "Matrix4Research.CircuitLiveness",
      "Matrix4Research.WholeCircuitSchedule"
    ]
  },
  "exact_replay": {
    "python": "3.10.15",
    "verified": true,
    "rank": 49,
    "left_additions": 41,
    "right_additions": 41,
    "post_additions": 74,
    "total_additions": 156,
    "scalar_operations": 205,
    "brent_identities": 4096
  },
  "storage_peaks": {
    "left": { "public": 20, "reordered": 7 },
    "right": { "public": 19, "reordered": 6 },
    "post": { "public": 17, "reordered": 8 },
    "whole_dag": { "public": 80, "reordered": 38 }
  },
  "sha256": {
    "lean_certificates_archive": "8aab50ea9b0fb787211e10d637708b9412c5676fecdde1364598d468ede76755",
    "Scheme49LowMemory.lean": "6e3110f7fa84836c74d7e7e5b1e02f835d3115360267ac5e1e7f9f7e4a10c8e1",
    "CircuitLiveness.lean": "ffbf7c937d3e0662d0212e307345ce090894e5a3f9ccffc5bc4bafa47c1bbdb5",
    "WholeCircuitSchedule.lean": "644a53396fa3c63cb8b540f3ebf378a8c544e8ddf63d34bb83e0f94f0a70d838",
    "exact_verification_json": "b7be89a2c99ace9ca8b58aea0ebed9b58b4c6eb83731688ec7e0444bacbfe4ab",
    "whole_liveness_json": "140de32ceaff38dd39080204031e0927a02508c039f47b53a6c15b5c9c244c1d"
  },
  "limitations": [
    "The result concerns execution order for one fixed arithmetic DAG.",
    "It does not reduce arithmetic work or establish global schedule optimality.",
    "The storage model is scalar and excludes platform-specific memory effects."
  ]
}