Module independence 

Measured validator dependence (PSP-9 system 8, Paper III Lemma 5.1 and Corollary 5.2).

“Correlation among redundant validators is measured, never assumed away.” This module computes, from matched labeled verdicts, each validator’s miss rate q_i, the pairwise miss correlation κ_ij, the empirical pairwise joint miss, and the conservative conjunctive-ensemble bound ρ_eff = min_{i<j} u_ij over pairwise joint-miss upper confidence bounds.

Statistics discipline (Gates R and T):

• Matched strata. q_i, q_j, κ_ij, and the joint miss for a pair are all computed over the same jointly evaluated candidate set.
• Degenerate marginals (q ∈ {0, 1}) use the empirical joint miss directly, as Lemma 5.1 requires; they are never assigned κ = 0.
• Exact only at n = 2. For n > 2 validators the bound is deliberately conservative; it is never tightened by inferring higher-order joints from pairwise correlations, and n is reported beside it. A three-validator bound tighter than its best pair would be a defect, not a better certificate.
• Point estimates are diagnostics. A certified ρ_eff uses upper confidence bounds and a minimum matched sample count; below it the status is insufficient evidence, not a number.
• No energy attenuation. Correlation controls the reported risk bound; it never rewrites the fixed quadratic energy weights. The former attenuate_weight helper is removed for that reason.

Structs

IndependenceStats

Independence statistics computed from the verdict ledger.

PairStats

Matched-stratum statistics for one validator pair.

VerdictRecord

One validator’s verdict on one candidate: did it miss an unsafe state?

Enums

EnsembleCertification

Certification status of the ensemble bound.

Constants

DEFAULT_MIN_PAIR_SAMPLES

Minimum matched samples per pair before a certificate may be issued.

Functions

compute

Compute independence statistics from a verdict ledger.

compute_with_floor

Compute with an explicit matched-sample floor for certification.

miss_std

Standard deviation of a Bernoulli miss indicator: σ = sqrt(q(1-q)).

pairwise_joint_miss

Lemma 5.1’s exact pairwise joint miss: q_i q_j + κ σ_i σ_j.