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410, 417, 452, 513 ], [ 161, 270, 411, 418, 449, 519 ] ] }, "distance": { "d": 6, "X": { "value": 6, "confidence": "upper_bound", "witness": [ 140, 254, 321, 357, 367, 377 ] }, "Z": { "value": 6, "confidence": "upper_bound", "witness": [ 110, 228, 253, 333, 418, 489 ] } }, "provenance": { "authors": [ "@mathysrennela" ], "construction": "Regular {6,6} hyperbolic surface code on a closed orientable surface. Quotient Q = Delta_6/Gamma_PBC with Q = PSL(2,13); the face-vertex swap is a projective involution J in PGL(2,13) imposing y = J x J^-1, with ord(x) = ord(y) = 6 and ord(xy) = 2. Data qubits on edges = left cosets of the order-2 subgroup ; Z checks on face boundaries = left cosets of ; X checks on vertex stars = left cosets of ; checks commute because each face boundary meets each vertex an even number of times. n = |Q|/2 = 546 and k/n = (6-4)/6 + 2/n by Euler, giving k = 184. Regenerated from the algebra of arXiv:2610.10948 Sec. II by research/hyperbolic_psl.py (class 0 of the check-support-signature enumeration, 546 classes at (p,q)=(6,13)); the matrices are recomputed, not copied, since that paper publishes its matrices on request only.", "origin": "submission", "date": "2026-10-15", "model": "MiMo-V2.6-Flash", "notes": "Distance is a homological systole: a shortest cycle in the primal graph outside the GF(2) span of the face boundaries is a genuine logical. Both sides carry explicit weight-6 witnesses, so d<=6 is witness-backed, not certified exact; eight generator classes measured the same, the other 538 were not measured.", "search_budget": { "candidates_screened": 8, "ris_trials_per_side": 400000 } }, "family": "topological" }