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"@vprusso" ], "date": "2026-10-15", "found_at_samples": 400, "survived_samples": 400, "tool": "research/kit/surrogate.lightest_logical", "seeds": [ 1 ] } }, "Z": { "value": 59, "confidence": "upper_bound", "witness": [ 2, 9, 13, 22, 23, 24, 28, 33, 37, 40, 47, 67, 68, 69, 73, 87, 96, 99, 100, 104, 107, 111, 115, 129, 139, 147, 149, 162, 190, 192, 204, 209, 212, 237, 240, 258, 260, 268, 271, 273, 297, 321, 335, 358, 361, 390, 392, 410, 418, 423, 435, 446, 447, 457, 466, 473, 479, 481, 496 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-10-15", "found_at_samples": 400, "survived_samples": 400, "tool": "research/kit/surrogate.lightest_logical", "seeds": [ 2 ] } } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized bicycle at m=257, a prime with ord_2(m)=16, so the nontrivial cyclotomic cosets of 2 all have size 16 and the reachable divisor degrees are the subset sums of the coset sizes. The divisor g is a product of the minimal polynomials of 2 cyclotomic cosets of size 16 times x+1, of degree 33, which fixes k = 2 deg g = 66 by construction. The pair (a,b) was drawn from the ideal (g) by information-set decoding over sparse supports, keeping weight 8 in each block, which is what gives row weight 16 rather than the 18 of codes/514-66-63.json. Both weights are even, so x+1 divides the gcd; m is prime, so the only block logical this forces has weight m and is far above the claim. H_X = [circ(a) | circ(b)] and H_Z = [circ(b)^T | circ(a)^T] on n = 2m = 514 qubits at uniform row weight 16, with a = [8, 59, 123, 129, 153, 180, 189, 218] and b = [32, 56, 78, 92, 170, 184, 206, 230].", "references": [], "date": "2026-10-15", "notes": "", "model": "Claude Opus 5" }, "family": "generalized-bicycle" }