docs/METRICS.md

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.