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 "provenance": {
  "authors": [
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  "construction": "Open-boundary planar bivariate-bicycle code with f = 1 + y + x^2 (support {(0,0),(0,1),(2,0)}) and g = y + x + x^2 y (support {(0,1),(1,0),(2,1)}), built on an 8x12 rectangular lattice via research/local2d/boundary_engine.py::build_planar followed by reduce_weights (0 qubits removed; max row weight 6 after reduction). k = 12 is stable across lattice sizes (8x6 and 10x10 both give k = 12) and equals the mixed volume of the support pair. Layout: the standard stacked bilayer grid, layers = 2.",
  "origin": "submission",
  "date": "2026-07-25",
  "model": "Claude Opus 5",
  "notes": "Found by an automated search that optimized the LATTICE ASPECT RATIO rather than the polynomial supports: for this family the merit is k*s0*s1/2, the geometric mean of the per-axis transfer-graph distance slopes, so a balanced rectangle beats a square. The same (f,g) on a 12x12 square lattice gives [[288,12,8]] at kd^2/n = 2.67; on 8x12 it gives this code at kd^2/n = 4.00 - identical distance on two-thirds of the qubits. Strictly dominates the board's [[198,12,7]] (lower n, equal k, higher d, equal w). DISTANCE: d = 8 held flat across 20k, 100k, 250k and 1M trials/side, plus an independent 1M-trial re-refutation on two fresh seeds (verdict corroborated on both), with dX = dZ = 8 witnessed. NOVELTY: a literature check read the LaTeX sources of arXiv:2504.08887, 2504.09171, 2606.19482 and 2607.05897 and found no match and no dominator. arXiv:2504.08887 has an exhaustive table over its Eq. (9) families giving minimal n = 264 for (k=12, d=8), but this (f,g) is provably NOT of Eq. (9) form: that form needs a single M in GL(2,Z) sending an f-difference to (1,0) and a g-difference to (0,1), and across all 3x3 difference pairs the determinants are 2,3,5 / 3,4,7 / 5,7,12, never 1. It is also not a two-block group-algebra code - a 2BGA at n=192 would have exactly 96 X- and 96 Z-checks of uniform weight, whereas this has 90 and 90 with weights {2:18, 4:18, 6:54} - so Lin-Pryadko's exhaustive n<=200 2BGA enumeration cannot contain it either. novelty is therefore recorded as new_parameters, which the schema notes is a submitter claim rather than a verifier-proved fact. LAYOUT HEADROOM: the radius here (3.6056) has not been optimized; the board's geometric efficiency g scales as r^-4, so this entry is likely improvable by relayout alone.",
  "novelty": "new_parameters",
  "references": [
   "arXiv:2504.08887 (Liang, Eberhardt, Chen -- planar bivariate-bicycle codes; this code is provably NOT of their Eq. (9) form)",
   "arXiv:2410.11942 (Liang, Yang, Iosue, Chen -- open-boundary theory)"
  ]
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