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156 ], "Z": [ 17, 82, 124, 159 ] }, { "X": [ 16, 61, 105, 157 ], "Z": [ 16, 81, 123, 158 ] }, { "X": [ 17, 62, 106, 158 ], "Z": [ 15, 80, 122, 157 ] }, { "X": [ 18, 63, 107, 159 ], "Z": [ 14, 79, 121, 156 ] }, { "X": [ 19, 64, 108, 160 ], "Z": [ 13, 78, 120, 155 ] }, { "X": [ 20, 65, 109, 161 ], "Z": [ 12, 77, 119, 154 ] }, { "X": [ 21, 66, 110, 162 ], "Z": [ 11, 76, 118, 153 ] }, { "X": [ 22, 67, 111, 163 ], "Z": [ 10, 75, 117, 152 ] }, { "X": [ 23, 68, 112, 164 ], "Z": [ 9, 74, 116, 151 ] }, { "X": [ 24, 69, 113, 165 ], "Z": [ 8, 73, 115, 150 ] }, { "X": [ 25, 70, 114, 166 ], "Z": [ 7, 72, 114, 149 ] }, { "X": [ 26, 71, 115, 167 ], "Z": [ 6, 71, 113, 148 ] }, { "X": [ 27, 72, 116, 168 ], "Z": [ 5, 70, 112, 147 ] }, { "X": [ 28, 73, 117, 169 ], "Z": [ 4, 69, 111, 146 ] }, { "X": [ 29, 74, 118, 170 ], "Z": [ 3, 68, 110, 145 ] }, { "X": [ 30, 75, 119, 171 ], "Z": [ 2, 67, 109, 144 ] }, { "X": [ 31, 76, 120, 172 ], "Z": [ 1, 66, 108, 143 ] }, { "X": [ 32, 77, 121, 173 ], "Z": [ 0, 65, 107, 142 ] }, { "X": [ 33, 78, 122, 174 ], "Z": [ 46, 64, 106, 141 ] }, { "X": [ 34, 79, 123, 175 ], "Z": [ 45, 63, 105, 187 ] }, { "X": [ 35, 80, 124, 176 ], "Z": [ 44, 62, 104, 186 ] }, { "X": [ 36, 81, 125, 177 ], "Z": [ 43, 61, 103, 185 ] } ] }, "distance": { "d": 6, "P": { "value": 6, "confidence": "upper_bound", "witness": { "X": [ 11, 39, 100, 118 ], "Z": [ 11, 40, 100, 128 ] } } }, "provenance": { "construction": "Symplectic-halved CPM pair-partition code: Prop. 4 of arXiv:2609.30069. (J,L,P)=(3,8,47); the CSS parent on n_par=L*P=376 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 = [[5, 37, 39, 9, 3, 25, 8, 40], [17, 16, 35, 37, 34, 33, 33, 2], [10, 12, 15, 13, 8, 10, 42, 43]] and sigma(l) = l=0->6, l=1->3, l=2->4, l=3->1, l=4->2, l=5->7, l=6->0, l=7->5 (a fixed-point-free involution of the 8 block columns). The parent is folded under pi(l,t) = (sigma(l), -t) to this general stabilizer code S = (A | B) on 188 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 = 49 against the parent's 98. 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" }