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   "witness_provenance": {
    "found_by": [
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    "date": "2026-10-16",
    "found_at_samples": 400,
    "survived_samples": 400,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
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    ]
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  "Z": {
   "value": 53,
   "confidence": "upper_bound",
   "witness": [
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   "witness_provenance": {
    "found_by": [
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    "date": "2026-10-16",
    "found_at_samples": 400,
    "survived_samples": 400,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
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 },
 "provenance": {
  "authors": [
   "@vprusso"
  ],
  "construction": "Cyclic generalized bicycle at m=233, with ord_2(m)=29, so x^233 - 1 factors over GF(2) into 9 cyclotomic cosets, 1 of size 1, 8 of size 29. The divisor g is assembled from coset minimal polynomials to degree 30, which fixes k = 2 deg g = 60 by construction, and (a,b) was drawn from the ideal (g) by information-set decoding over sparse supports, keeping weight 8 and weight 8 in the two blocks. Both weights are even, so x+1 divides the gcd; x+1 is x^1 - 1, so the only block logical this forces has weight m and is far above the claim. m is prime, so the quotient fold has no proper divisor to act on; an orbit fold over every equal-orbit partition of the qubits returns nothing lighter than 176. H_X = [circ(a) | circ(b)] and H_Z = [circ(b)^T | circ(a)^T] on n = 2m = 466 qubits at uniform row weight 16, with a = [13, 22, 32, 39, 108, 144, 155, 177] and b = [14, 37, 129, 155, 167, 194, 203, 224].",
  "references": [],
  "date": "2026-10-16",
  "notes": "",
  "model": "Claude Opus 5"
 },
 "family": "generalized-bicycle"
}