{
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 "name": "[[85,40,5]] check-deletion chain of codes/85-37-5.json",
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 "distance": {
  "d": 5,
  "X": {
   "value": 5,
   "confidence": "upper_bound",
   "witness": [
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  "Z": {
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 "provenance": {
  "authors": [
   "@mathysrennela"
  ],
  "construction": "Greedy check-deletion chain from board code codes/85-37-5.json (reconstructed from qecdb.org record 68e107e6). Deleted 3 X-checks [7, 8, 9] over 3 greedy steps, each priced by the check-deletion theorem (unpublished theorem by @mathysrennela, claim 12.1). k' = 37 + 3 = 40 exact by rank; the deleted X rows weigh 24, above the inherited d <= 5 tier (term 1), so the packaged witnesses are gate-confirmed weight-5 logicals on both sides.",
  "date": "2026-09-09",
  "notes": "Derived code, honest provenance: check-deletion child of its source entry codes/85-37-5.json (k 37 -> 40 at equal n, distance tier, and weight class; different check sets, not equivalent to the source under any code symmetry). Deleted 3 X-checks [7, 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embedded per-side X witnesses, the source's Z witness is inherited unchanged (term-1 of the check-deletion theorem, an unpublished theorem by @mathysrennela).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"
 }
}