{
  "schema": "SAMPLING_POLAR_EXECUTION/1",
  "date": "2026-10-08",
  "python": "3.10.21",
  "commands": [
    "python3 verify_sampling_polar.py",
    "python3 -O verify_sampling_polar.py"
  ],
  "exit_codes": [
    0,
    0
  ],
  "cases": [
    "s=1/7",
    "s=1/2",
    "s=1/648000",
    "s=0 singular boundary"
  ],
  "logs_byte_identical": true,
  "canonical_sine_seed": "NOT EVALUATED",
  "external_hypotheses": "A-087 and A-343 NOT EXECUTED",
  "note": "Appendix A finite checks in Q(phi). Not a proof review, not a Lean check, and not an execution of the external symplectic statements.",
  "files": {
    "verify_sampling_polar.py": {
      "bytes": 5160,
      "sha256": "dc30795e4972514f34612c88adfd6604fb0817920977d0bf278d0d6719fe7fbe"
    },
    "python-normal.txt": {
      "bytes": 141,
      "sha256": "37a3c49d28a9854517a0bbc8c15ebbf85be9cd936f1ff0f30f173796d3fe1f39"
    },
    "python-optimized.txt": {
      "bytes": 141,
      "sha256": "37a3c49d28a9854517a0bbc8c15ebbf85be9cd936f1ff0f30f173796d3fe1f39"
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  }
}