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 "distance": {
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  "X": {
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    "date": "2026-09-24",
    "found_at_samples": 1,
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    "tool": "norm-word lift of a Z_87 quotient logical (exact algebra)",
    "seeds": [
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 "provenance": {
  "authors": [
   "@vprusso"
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  "construction": "Cyclic generalized-bicycle code on the ring x^174 - 1 with a(x) = x^23 + x^51 + x^63 + x^130 + x^157 + x^165, b(x) = x^13 + x^21 + x^22 + x^39 + x^45 + x^55 + x^98 + x^104 + x^110 + x^167; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T].",
  "origin": "submission",
  "novelty": "known_parameters",
  "model": "Claude Opus 5",
  "date": "2026-09-23",
  "notes": "Found by a randomized sweep over sparse polynomial pairs, screened against the live board before any expensive work. Checked for single-block logicals via the ideal generated by (x^m - 1)/gcd(a, x^m - 1) before the distance was believed."
 },
 "family": "generalized-bicycle"
}