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"confidence": "upper_bound", "witness": [ 92, 114, 129, 363, 468 ] } }, "provenance": { "authors": [ "@mathysrennela" ], "construction": "Regular {7,7} hyperbolic surface code on a closed orientable surface. Quotient Q = Delta_7/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) = 7 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 = (7-4)/7 + 2/n by Euler, giving k = 236. Class 28 of the 1638 check-support-signature classes at (p,q) = (7,13): same n, k and check weight as codes/546-236-4.json but a different periodic identification, which is the free choice the construction leaves open. Recomputed from the published algebra of arXiv:2610.10948 Sec. II with research/hyperbolic_psl.py; 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. Witness-backed upper bound d<=5, not certified exact. Four rungs agree (4000 + 2x400000 gf2_fast, 4000 numpy) and the matched-depth pair audit against codes/546-236-4.json returned credible: both claims held at 1000000 trials/side, seeds 51/52, pair depth 64. Equivalence checked, not equivalent: the WL-signature match to codes/546-236-4.json is a flag, not a verdict. This is class 28 of the 1638 check-support-signature classes at (p,q) = (7,13) while the filed entry is another class of the same family -- same n, k and check weight, different periodic identification. The matched-depth pair audit settled it by measurement: at 1000000 trials per side, seeds 51 and 52, pair depth 64, this class read d <= 5 and that entry read d <= 4 on every seed, and codes isomorphic up to a qubit relabelling have one distance, so they cannot be the same code.", "search_budget": { "candidates_screened": 29, "ris_trials_per_side": 1000000 } }, "family": "topological" }