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 "distance": {
  "d": 38,
  "X": {
   "value": 38,
   "confidence": "upper_bound",
   "witness": [
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   "witness_provenance": {
    "found_by": [
     "@vprusso"
    ],
    "date": "2026-09-23",
    "found_at_samples": 20000000,
    "seeds": [
     2101
    ],
    "tool": "GPU deep kernel (full basis, pair depth 8)",
    "survived_samples": 183000000
   }
  },
  "Z": {
   "value": 38,
   "confidence": "upper_bound",
   "witness": [
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   "witness_provenance": {
    "found_by": [
     "@vprusso"
    ],
    "date": "2026-09-23",
    "found_at_samples": 5000000,
    "seeds": [
     13000006607
    ],
    "tool": "GPU sketch k_sub 256 (recover), screen stage 3",
    "survived_samples": 183000000
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  }
 },
 "family": "generalized-bicycle",
 "provenance": {
  "authors": [
   "@vprusso"
  ],
  "origin": "submission",
  "novelty": "new_parameters",
  "model": "Claude Fable 5.1 (Claude Code)",
  "construction": "Cyclic (single-circulant-pair) generalized-bicycle code over Z_365 (research/cyclic_gb.py build_cyclic_gb): a(x) = 1 + x^25 + x^97 + x^237, b(x) = 1 + x^3 + x^138 + x^350; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T] with circ(v)[i, (i + j) mod 365] = v[j]. n = 2m = 730, k = 2 deg gcd(a, b, x^365 - 1) = 28, every check has weight 8. a and b were drawn as weight-4 multiples of a degree-13 divisor g of x^365 - 1 (g as a little-endian bit integer: 8479).",
  "references": [
   "arXiv:1212.6703",
   "arXiv:2111.03654"
  ],
  "date": "2026-09-23",
  "notes": "Found by a GPU random-information-set screen (deep kernel: full-basis RREF plus pair sums) over cyclic generalized-bicycle codes with weight-4 polynomials at n in [702, 1000]; see the research note for the ladder. Lightest logicals: X 38, Z 38; deep-kernel GPU passes (full basis, pair depth 8): X 38 at 20,000,000 trials (seed 2101); Z 40 at 20,000,000 trials (seed 2101); X 38 at 100,000,000 trials (seed 2102); Z 38 at 100,000,000 trials (seed 2102); board fast pass 40 at 8,000,000 trials. Every operator re-verified with verify/gf2.py. Distance is a witness-backed upper bound. Novelty: no isomorphic code found by a nauty canonical-form check against the board and the 2BGA, GB, BB, QECDB, and codetables data (submitter claim). Generator spec: {\"family\": \"cyclic-gb\", \"m\": 365, \"g_int\": 8479, \"deg_g\": 13, \"a\": [0, 25, 97, 237], \"b\": [0, 3, 138, 350]}"
 }
}