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"X": { "value": 4, "confidence": "upper_bound", "witness": [ 280, 281, 286, 287 ] }, "Z": { "value": 4, "confidence": "upper_bound", "witness": [ 280, 281, 286, 287 ] } }, "provenance": { "authors": [ "@MathysRennela" ], "construction": "Distance-amplified code: one tensor-product amplification step (central three-term truncation of the chain-complex tensor product, arXiv:2609.37231) with the [[6,4,2]] CSS amplifier -- H_X = H_Z = the all-ones row on 6 qubits, reduced form, so r_1 = r_2 = 1 -- applied to the board's [[52,26,2]] entry. The step is the operation the one-shot paper arXiv:2610.02137 uses to build its level map (App. A.2, Def 111: the local cones tensored with the repetition code), with the amplifier swapped: that paper takes k_A = d_A = 1, which preserves the distance exactly but leaves k unchanged (its Lemma 118, H_Q(Gamma) = H_Q(C)) and so cannot move a (n, k, d, w) frontier. Here d_A = 2, so n' = 6n + m_X + m_Z = 338, k' = 4k = 104, w' = 8. The X and Z witnesses are the base entry's stored witnesses tensored with the weight-2 [[6,4,2]] logical (weights 4 / 4), so the distance is derived, not searched: the logical-overlap criterion gives d' >= 2d and this witness gives d' <= 2d. Witness-backed upper bound, not an exact distance. Base provenance: 2BGA (arXiv:2306.16400) on SmallGroup(26,2), from github.com/QEC-pages/2BGA-codes @ 403d194c3f98f0cadc236aecbc4a8b6139ccf23c, abelian.zip, diswtabelian_wt6wtL2_order26_k26.txt, line 1. nonidentity supports a=[2], b=[2, 3, 4]. (family generalized-bicycle, 52-26-2). Distance confirmed at 100000 fresh-seed trials per side (seed 5000, gf2_fast, 10 threads): lightest logical found was 4 on both sides, i.e. the derived distance survives independent search. Packaging: Space Bunny Alpha 1.0.", "origin": "submission", "date": "2026-10-04", "model": "Space Bunny Alpha 1.0", "notes": "Constructed and packaged with the Space Bunny Alpha 1.0 model. Equivalence check, deliberate: qldpc submit's board dedup reported an exact fingerprint match against this entry's own slug, which is this document matching itself inside codes/ -- it is not present on the base branch. Checked, not equivalent: re-running verify/validate_candidate.py with the document held outside codes/, so the board is the base branch and excludes the candidate, returns exact_duplicate_of null and wl_equivalent_of null." }, "family": "distance-amplified", "locality": { "coordinates": [ [ 5.0, 6.0 ], [ 1.0, 6.0 ], [ 1.0, 5.0 ], [ 2.0, 4.0 ], [ 0.0, 6.0 ], [ 0.0, 5.0 ], [ 3.0, 5.0 ], [ 1.0, 5.0 ], [ 3.0, 6.0 ], [ 0.0, 5.0 ], [ 2.0, 5.0 ], [ 2.0, 5.0 ], [ 2.0, 10.0 ], [ 3.0, 7.0 ], [ 1.0, 10.0 ], [ 2.0, 7.0 ], [ 2.0, 9.0 ], [ 0.0, 8.0 ], [ 4.0, 8.0 ], [ 3.0, 6.0 ], [ 2.0, 8.0 ], [ 4.0, 7.0 ], [ 0.0, 9.0 ], [ 1.0, 8.0 ], [ 4.0, 12.0 ], [ 4.0, 12.0 ], [ 5.0, 10.0 ], [ 0.0, 11.0 ], [ 3.0, 11.0 ], [ 0.0, 11.0 ], [ 1.0, 10.0 ], [ 0.0, 10.0 ], [ 0.0, 10.0 ], [ 1.0, 11.0 ], [ 3.0, 12.0 ], [ 3.0, 12.0 ], [ 7.0, 11.0 ], [ 3.0, 9.0 ], [ 4.0, 6.0 ], [ 3.0, 10.0 ], [ 2.0, 11.0 ], [ 6.0, 11.0 ], [ 6.0, 7.0 ], [ 6.0, 10.0 ], [ 5.0, 9.0 ], [ 5.0, 12.0 ], [ 6.0, 12.0 ], [ 4.0, 8.0 ], [ 6.0, 9.0 ], [ 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