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"X": [ 14, 61, 124, 186, 194, 247 ], "Z": [ 24, 61, 113, 152, 223, 265 ] } ] }, "distance": { "d": 6, "P": { "value": 6, "confidence": "upper_bound", "witness": { "X": [ 45, 99, 165, 201 ], "Z": [ 1, 99, 165, 208 ] } } }, "provenance": { "construction": "Symplectic-halved CPM pair-partition code: Prop. 4 of arXiv:2609.30069. (J,L,P)=(3,12,47); the CSS parent on n_par=L*P=564 qubits has block (i,l) = C(E[i][l]) over Z_47 in H_X and D[j][l] = -E[j][sigma(l)] mod 47 in H_Z, with E = [[22, 32, 36, 19, 23, 36, 28, 34, 25, 20, 41, 18], [44, 11, 2, 18, 34, 8, 23, 43, 36, 37, 32, 4], [32, 32, 16, 1, 40, 34, 34, 23, 13, 29, 18, 10]] and sigma(l) = l=0->7, l=1->8, l=2->10, l=3->11, l=4->5, l=5->4, l=6->9, l=7->0, l=8->1, l=9->6, l=10->2, l=11->3 (a fixed-point-free involution of the 12 block columns). The parent is folded under pi(l,t) = (sigma(l), -t) to this general stabilizer code S = (A | B) on 282 qubits; k = n - rank S.", "notes": "Fold of a halving-constrained draw; the CSS parent is the symplectic double and is submitted as its own entry. The exponent array solves the pair-partition equations E[i][u]-E[i][v] = -(E[j][sigma(u)]-E[j][sigma(v)]) in a null space of dimension 12 and was hill-climbed inside it, so the CSS condition and the halving identity cannot be broken by a move. k = 143 against the parent's 286. Equivalence to an existing entry was checked by the trusted gate (exact-duplicate and WL-equivalent both null). Literature novelty unverified. Distance is a witness-backed upper bound, not an exact certificate.", "authors": [ "@MathysRennela" ], "references": [ "arXiv:2609.30069", "arXiv:2607.14091" ], "date": "2026-10-01", "model": "Space Bunny Alpha 1.0" }, "family": "pair-partition-cpm" }