docs/HISTORICAL_EXACT_FOM11.md

Historical exact-distance reference with FOM 100/9

This configuration publishes one canonical-deduplicated CSS-BB code:

• parameters: [[288,50,8]];
• exact FOM in the legacy result: 50*8^2/288 = 100/9 ~= 11.11111111;
• source stage: campaign4_milp_exact;
• source status: both sectors reported distance 8, with all 100 logical MILPs optimal;
• target status: exact non-winner (100/9 < 12).

Two stored polynomial orientations reduce to the same canonical CSS code. The release therefore contains one row, with provenance for both source rows. The supplied H_X and H_Z matrices were reconstructed again from the canonical polynomial representation; their ranks, CSS commutation, and canonical registry identity were replayed successfully.

Evidence boundary

This is a historical Campaign 4 legacy MILP-exact result, not a current Stage 2 certificate. The legacy JSONL preserves the solver summary (d_x=d_z=8, 100/100 logical problems optimal), but it does not preserve a portable proof/witness artifact bound under the current hardened certificate schema. Consequently:

• exact_distance=8 reports the historical all-optimal MILP result;
• modern_replayable_distance_certificate=false;
• publication_certificate=false and pipeline_promotion=false;
• the row must not be presented as a new Stage 2 strict win.

Run python -B scripts/verify_historical_exact_fom11.py . to verify file hashes, reconstruct the matrices, check GF(2) ranks and CSS commutation, and recompute the rational FOM. That verifier checks the published identity and summary bindings; it does not recreate the omitted legacy MILP proof search.

中文说明

该配置发布一个规范去重后的 [[288,50,8]] CSS-BB 码，历史 MILP 结果中 精确 FOM 为 100/9 ~= 11.1111，因此它是 exact non-winner。两个 X/Z 方向共 100 个逻辑问题均记录为 optimal。矩阵、秩、对易关系和 registry 身份已经重新回放核验。

但这条记录来自历史 Campaign 4，并非当前 Stage 2 的现代证书；旧结果未 保存符合当前 hardened schema 的可移植 proof artifact。因此数据中明确 保留 modern_replayable_distance_certificate=false，不能把它描述成新的 Stage 2 认证胜者。