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 "provenance": {
  "authors": [
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  "construction": "Cyclic generalized bicycle at m=215 = 5 x 43, with ord_2(m)=28, so x^215 - 1 factors over GF(2) into 11 cyclotomic cosets, 1 of size 1, 1 of size 4, 3 of size 14, 6 of size 28. The divisor g is assembled from coset minimal polynomials to degree 28, which fixes k = 2 deg g = 56 by construction, and (a,b) was drawn from the ideal (g) by information-set decoding over sparse supports, keeping weight 9 and weight 7 in the two blocks. At least one weight is odd, so x+1 does not divide the gcd. m is composite, so the quotient fold acts at t=5 and t=43; a fold over every equal-orbit partition of the qubits returns nothing lighter than 65, clear of the claim. H_X = [circ(a) | circ(b)] and H_Z = [circ(b)^T | circ(a)^T] on n = 2m = 430 qubits at uniform row weight 16, with a = [24, 43, 71, 76, 86, 107, 136, 154, 165] and b = [36, 43, 132, 182, 183, 209, 211].",
  "references": [],
  "date": "2026-10-15",
  "notes": "",
  "model": "Claude Opus 5"
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 "family": "generalized-bicycle"
}