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"confidence": "upper_bound", "witness": [ 4, 12, 37, 42, 46, 59, 65, 74, 76, 103, 107, 118, 122, 124, 128, 136, 138, 139, 156, 165, 171, 188, 193, 196, 217, 223, 228, 234, 237, 245, 263, 266, 273, 278, 281, 299, 303, 305, 312, 324, 332, 350, 368, 380, 383, 385, 388, 402 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-10-15", "found_at_samples": 400, "survived_samples": 400, "tool": "research/kit/surrogate.lightest_logical", "seeds": [ 1 ] } }, "Z": { "value": 48, "confidence": "upper_bound", "witness": [ 0, 32, 46, 49, 51, 54, 66, 84, 102, 110, 122, 129, 131, 135, 153, 156, 161, 168, 171, 189, 197, 200, 206, 211, 238, 241, 246, 263, 269, 278, 295, 296, 298, 306, 310, 312, 316, 327, 331, 358, 360, 369, 375, 388, 392, 397, 422, 430 ], "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=217 = 7 x 31, with ord_2(m)=15, so x^217 - 1 factors over GF(2) into 21 cyclotomic cosets, 1 of size 1, 2 of size 3, 6 of size 5, 12 of size 15. The divisor g is assembled from coset minimal polynomials to degree 26, which fixes k = 2 deg g = 52 by construction, and (a,b) was drawn from the ideal (g) by information-set decoding over sparse supports, keeping weight 9 and weight 9 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=7 and t=31; a fold over every equal-orbit partition of the qubits returns nothing lighter than 62, clear of the claim. H_X = [circ(a) | circ(b)] and H_Z = [circ(b)^T | circ(a)^T] on n = 2m = 434 qubits at uniform row weight 18, with a = [4, 51, 60, 123, 141, 146, 154, 185, 208] and b = [33, 69, 104, 133, 158, 184, 199, 209, 211].", "references": [], "date": "2026-10-15", "notes": "", "model": "Claude Opus 5" }, "family": "generalized-bicycle" }