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  ]
 },
 "distance": {
  "d": 12,
  "X": {
   "value": 12,
   "confidence": "upper_bound",
   "witness": [
    4,
    19,
    32,
    61,
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    107,
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   ]
  },
  "Z": {
   "value": 12,
   "confidence": "upper_bound",
   "witness": [
    1,
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    104,
    126,
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   ]
  }
 },
 "provenance": {
  "authors": [
   "@mathysrennela"
  ],
  "construction": "Greedy check-deletion chain from board code codes/192-40-12.json (GALA code of arXiv:2608.07431 Table S5; the paper certifies d = 12 exactly). Deleted 4 X-checks [0, 1, 8, 9] over 4 greedy steps, each priced by the check-deletion theorem (unpublished theorem by @mathysrennela, claim 12.1). k' = 40 + 4 = 43 exact by rank; the deleted X rows weigh exactly 12 and are the X-side witnesses (term 2); the Z witness was re-confirmed at weight 12 by the trusted gate.",
  "references": [
   "https://arxiv.org/abs/2608.07431"
  ],
  "date": "2026-09-09",
  "notes": "Derived code, honest provenance: check-deletion child of its source entry codes/192-40-12.json (k 40 -> 43 at equal n, distance tier, and weight class; different check sets, not equivalent to the source under any code symmetry). Deleted 4 X-checks [0, 1, 8, 9]; the deleted X rows are the embedded per-side X witnesses, the source's Z witness is inherited unchanged (term-1 of the check-deletion theorem, an unpublished theorem by @mathysrennela). Parameter novelty vs the literature unverified.",
  "origin": "submission",
  "model": "GLM 5.3 Flash",
  "novelty": "unknown"
 }
}