# Metrics and evidence semantics

## Code parameters and FOM

- `n`: physical qubits.
- `k`: encoded logical qubits, recomputed as `n-rank(H_X)-rank(H_Z)` over GF(2).
- `d`: minimum weight of a nontrivial logical Pauli operator.
- `FOM = k*d^2/n`: a rate–distance-squared tradeoff. The target is strictly `FOM>12`.

An upper bound on `d` produces an upper bound on FOM; it does not show that the code is good. A lower bound on `d` produces a lower bound on FOM. `fom.exact` is populated only when distance is exact and trusted.

## Evidence classes

- `CERTIFIED_EXACT_WIN`: exact trusted distance, strict target passed, independent release gate complete. Count is zero here.
- `EXACT_NON_WIN`: exact trusted distance, target not passed.
- `REJECTED_WITH_WITNESS`: a replayable logical operator proves `d` below the required threshold.
- `FORMAL_OPEN_LOWER_BOUND`: a rigorous low-weight exclusion exists, but the target distance is not proved and no replayable witness has excluded it.
- `UPPER_BOUND_ONLY`: interesting only by an advisory BP/OSD signal; no positive proof credit.

## Search-only metrics

Stage-1 fitness and `combined_score` guide sampling and diversity. They are not paper claims. The intended proof-safe fitness gives positive distance credit only to formal lower bounds or exact results; BP/OSD scalar upper bounds receive no positive proof credit. A representative policy is:

`fitness = (0.10 + 0.25*min(1,(k/n)/0.25) + 0.45*min(1,FOM_lb/12) + 0.20*min(1,FOM_exact/12)) * (1-negative_penalty)`

`combined_score = min(0.999, 0.8*best_fitness + 0.199*diversity)`

## Important limitations

- The search-oracle UNSAT records are pinned solver/runtime evidence, not portable DRAT/LRAT certificates.
- BP/OSD fields are explicitly suffixed `_advisory` because the scalar output has no included logical-operator bits.
- Novelty means “not matched by the pinned registry replay,” not a proof of absence from all literature.
- The campaign and snapshot are in progress; later sealed rounds can change the ranking.