{ "schema_version": "0.4", "name": "[[188,95,3]] symplectic-halved CPM pair-partition fold", "code_type": "stabilizer", "n": 188, "k": 95, "checks": { "S": [ { "X": [ 34, 57, 120, 145 ], "Z": [ 1, 65, 115, 161 ] }, { "X": [ 35, 58, 121, 146 ], "Z": [ 0, 64, 114, 160 ] }, { "X": [ 36, 59, 122, 147 ], "Z": [ 46, 63, 113, 159 ] }, { "X": [ 37, 60, 123, 148 ], "Z": [ 45, 62, 112, 158 ] }, { "X": [ 38, 61, 124, 149 ], "Z": [ 44, 61, 111, 157 ] }, { "X": [ 39, 62, 125, 150 ], "Z": [ 43, 60, 110, 156 ] }, { "X": [ 40, 63, 126, 151 ], "Z": [ 42, 59, 109, 155 ] }, { "X": [ 41, 64, 127, 152 ], "Z": [ 41, 58, 108, 154 ] }, { "X": [ 42, 65, 128, 153 ], "Z": [ 40, 57, 107, 153 ] }, { "X": [ 43, 66, 129, 154 ], "Z": [ 39, 56, 106, 152 ] }, { "X": [ 44, 67, 130, 155 ], "Z": [ 38, 55, 105, 151 ] }, { "X": [ 45, 68, 131, 156 ], "Z": [ 37, 54, 104, 150 ] }, { "X": [ 46, 69, 132, 157 ], "Z": [ 36, 53, 103, 149 ] }, { "X": [ 0, 70, 133, 158 ], "Z": [ 35, 52, 102, 148 ] }, { "X": [ 1, 71, 134, 159 ], "Z": 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185 ], "Z": [ 40, 80, 121, 149 ] }, { "X": [ 1, 60, 112, 186 ], "Z": [ 39, 79, 120, 148 ] }, { "X": [ 2, 61, 113, 187 ], "Z": [ 38, 78, 119, 147 ] }, { "X": [ 3, 62, 114, 141 ], "Z": [ 37, 77, 118, 146 ] }, { "X": [ 4, 63, 115, 142 ], "Z": [ 36, 76, 117, 145 ] }, { "X": [ 5, 64, 116, 143 ], "Z": [ 35, 75, 116, 144 ] }, { "X": [ 6, 65, 117, 144 ], "Z": [ 34, 74, 115, 143 ] }, { "X": [ 7, 66, 118, 145 ], "Z": [ 33, 73, 114, 142 ] }, { "X": [ 8, 67, 119, 146 ], "Z": [ 32, 72, 113, 141 ] }, { "X": [ 9, 68, 120, 147 ], "Z": [ 31, 71, 112, 187 ] } ] }, "distance": { "d": 3, "P": { "value": 3, "confidence": "upper_bound", "witness": { "X": [ 106, 153 ], "Z": [ 43, 153 ] } } }, "provenance": { "construction": "Symplectic-halved CPM pair-partition code: Prop. 4 of arXiv:2609.30069. (J,L,P)=(2,8,47); 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 = [[13, 37, 21, 18, 21, 43, 1, 20], [37, 25, 20, 23, 17, 40, 30, 45]] 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 = 95 against the parent's 190. 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" }