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。