{
  "schema_version": "1.0.0",
  "packet_id": "state-of-proof-maxwell-lemma2-exact-2026-10-06",
  "case_id": "2026-07-29-maxwell-conjecture",
  "status": "REPRODUCED_LOCAL",
  "scope": "Only the exact critical-point and Hessian classification of the displayed limiting polynomial in Lemma 2, conditional on manual transcription. No Maxwell counterexample disposition.",
  "primary_source": {
    "title": "The Maxwell Conjecture is False",
    "authors": "Philip Arathoon; Gavin Ball; Matthew D. Kvalheim",
    "url": "https://arxiv.org/pdf/2607.27197v1",
    "locator": "Lemma 2, printed pages 4-5 (PDF pages 4-5)",
    "sha256": "4178ddc5a4efcdc11726bea6d6d20785575c55564095dbf53bfaa6d26055a958",
    "source_bytes_in_packet": false
  },
  "replay": {
    "command": "python3 maxwell_lemma2_exact.py maxwell-conjecture-v1.pdf",
    "working_directory": "Directory containing the checker and a downloaded copy of the pinned primary-source PDF",
    "checker": {
      "path": "maxwell_lemma2_exact.py",
      "sha256": "2bd3cea509186905f98388b268d06706ec83369673158bcae0e6a8465adc528e",
      "runtime": "Python 3 standard library only; no package installation"
    },
    "captured_output": {
      "path": "maxwell_lemma2_exact_output.json",
      "sha256": "c69e360e4bbb6574bccd15c0a0f7a8111d7b44da575036a92cc8074ae6b00736"
    },
    "acceptance": "The checker rejects a PDF with a different SHA-256. With the locked PDF, it exits 0 and emits JSON with exactly 21 critical points, all nondegenerate, with inertia counts 10 (2 positive, 1 negative) and 11 (1 positive, 2 negative)."
  },
  "methods": {
    "source_transcription": "Manual transcription of the displayed polynomial, checked visually against the rendered primary-source pages",
    "finite_check": "Own exact rational/quadratic-field checker plus exhaustive cylindrical case split and Cartesian gradient/Hessian evaluation",
    "manuscript_code_executed": false,
    "third_party_code_executed": false,
    "specialist_review_recorded": false
  },
  "limits": [
    "The polynomial's derivation from the five-charge potential (MAX-G1) was not examined.",
    "Persistence of 21 plus 3 points, Morse perturbation, and global finiteness (MAX-G3 through MAX-G5) were not examined.",
    "This packet is a local finite calculation, not independent verification of the manuscript or proof of the headline theorem."
  ]
}