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"found_by": [ "@vprusso" ], "date": "2026-10-16", "found_at_samples": 400, "survived_samples": 400, "tool": "research/kit/surrogate.lightest_logical", "seeds": [ 1 ] } }, "Z": { "value": 48, "confidence": "upper_bound", "witness": [ 9, 16, 17, 24, 25, 26, 32, 39, 48, 56, 67, 70, 110, 112, 130, 135, 146, 156, 158, 164, 172, 173, 181, 183, 201, 223, 225, 227, 244, 254, 259, 266, 306, 312, 317, 340, 344, 348, 351, 362, 389, 396, 406, 407, 415, 416, 417, 423 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-10-16", "found_at_samples": 400, "survived_samples": 400, "tool": "research/kit/surrogate.lightest_logical", "seeds": [ 2 ] } } }, "provenance": { "authors": [ "@vprusso" ], "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 29, which fixes k = 2 deg g = 58 by construction, and (a,b) was drawn from the ideal (g) by information-set decoding over sparse supports, keeping weight 10 and weight 10 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 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 20, with a = [31, 50, 73, 125, 136, 145, 162, 169, 176, 179] and b = [3, 11, 16, 18, 33, 41, 64, 124, 139, 160].", "references": [], "date": "2026-10-16", "notes": "", "model": "Claude Opus 5" }, "family": "generalized-bicycle" }