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107, 148, 211 ], "Z": [ 12, 82, 137, 151, 226 ] }, { "X": [ 7, 86, 108, 149, 212 ], "Z": [ 11, 81, 136, 150, 225 ] }, { "X": [ 8, 87, 109, 150, 213 ], "Z": [ 10, 80, 135, 149, 224 ] }, { "X": [ 9, 88, 110, 151, 214 ], "Z": [ 9, 79, 134, 148, 223 ] }, { "X": [ 10, 89, 111, 152, 215 ], "Z": [ 8, 78, 133, 147, 222 ] }, { "X": [ 11, 90, 112, 153, 216 ], "Z": [ 7, 77, 132, 146, 221 ] }, { "X": [ 12, 91, 113, 154, 217 ], "Z": [ 6, 76, 131, 145, 220 ] }, { "X": [ 13, 92, 114, 155, 218 ], "Z": [ 5, 75, 130, 144, 219 ] }, { "X": [ 14, 93, 115, 156, 219 ], "Z": [ 4, 74, 129, 143, 218 ] }, { "X": [ 15, 47, 116, 157, 220 ], "Z": [ 3, 73, 128, 142, 217 ] } ] }, "distance": { "d": 8, "P": { "value": 8, "confidence": "upper_bound", "witness": { "X": [ 41, 48, 198 ], "Z": [ 2, 16, 24, 48, 103, 135, 198 ] } } }, "provenance": { "construction": "Symplectic-halved CPM pair-partition code: Prop. 4 of arXiv:2609.30069. (J,L,P)=(3,10,47); the CSS parent on n_par=L*P=470 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 = [[41, 37, 24, 43, 34, 33, 11, 27, 1, 31], [7, 23, 15, 30, 17, 13, 32, 0, 16, 26], [31, 46, 24, 30, 33, 14, 25, 2, 28, 0]] and sigma(l) = l=0->7, l=1->6, l=2->4, l=3->9, l=4->2, l=5->8, l=6->1, l=7->0, l=8->5, l=9->3 (a fixed-point-free involution of the 10 block columns). The parent is folded under pi(l,t) = (sigma(l), -t) to this general stabilizer code S = (A | B) on 235 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 = 96 against the parent's 192. 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" }