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 "distance": {
  "d": 34,
  "X": {
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   "confidence": "upper_bound",
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    "date": "2026-09-26",
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    "tool": "gate_changed.py RIS-fast (CI refuter, pair depth 8, budget cap 8M trials)",
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   }
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    "date": "2026-09-26",
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    "survived_samples": 300000000,
    "tool": "verify/ris_gpu.py recover mode, pair depth 0 (GPU RIS, CPU re-verified)",
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 },
 "provenance": {
  "authors": [
   "@vprusso"
  ],
  "construction": "Two-block group algebra (2BGA) code over the non-abelian metacyclic group C_3 semidirect_2 C_112 of order 336: H_X=[Lm(a)|Rm(b)], H_Z=[Rm(b)^T|Lm(a)^T] from the left and right regular representations, which commute for any group so the CSS condition holds without G abelian. Element (i,j) = x^i y^j indexed as i*112+j, with (i1,j1)(i2,j2) = (i1 + i2*2^j1 mod 3, j1+j2 mod 112). a = {0,9,122}, b = {0,13,249}. Construction of arXiv:2306.16400 applied past that paper's Table 1 range; the builder reproduces the board's [[540,12,28]] on C_9 semidirect C_30 exactly, including recovering that entry's unstated element index convention.",
  "origin": "submission",
  "date": "2026-09-07",
  "model": "Claude Opus 5"
 },
 "family": "2bga-coset"
}