{
  "passed": true,
  "checks": [
    {
      "name": "Exact balanced Gaussian/modulation dilation and sixteen mixed derivatives",
      "passed": true,
      "scope": "Actual substituted family, both scaling factors, full chain identities and a wrong-spatial-dilation negative control; the Schwartz model supplements the compact-support proof."
    },
    {
      "name": "Both off-diagonal Schur exponents and low-frequency separation",
      "passed": true,
      "trials": 2772,
      "scope": "Dimensions 1–6 and shells 0–24; exact exponent arithmetic, both triangular regions and separation constant 3/8. The written proof treats all shells."
    },
    {
      "name": "Actual finite shell operator matrices and failure without overlap control",
      "passed": true,
      "models": [
        {
          "shell_count": 12,
          "near_norm": 6.33016836837044,
          "far_entry_sum": 0.33138275146484375
        },
        {
          "shell_count": 32,
          "near_norm": 6.882000500133065,
          "far_entry_sum": 0.33333333147068817
        },
        {
          "shell_count": 64,
          "near_norm": 6.968447340288168,
          "far_entry_sum": 0.3333333333333333
        }
      ],
      "scope": "Banded matrix norm and summable far matrix; twelve coincident identity pieces have norm twelve despite each having norm one."
    }
  ],
  "source_sha256": "e1cc8c0ead16146183259b4631e0d732e8e9e761792d8e9b4d0010dbc43bf0dc",
  "script_sha256": "ef8b8f5bec896ba9ec92cb29ad394cb3f38e0dfafae3714bcdacb7098c10046d",
  "general_proof_certified_by_finite_checks": false
}