Verification Bandwidth Under Correlated Evaluators: What an Effective-Sample-Size Statistic Measures in an Acceptance Cascade

Abstract

Organizational verification is representable as an orthogonal projection whose rank bounds what an organization detects about itself, but that formalization assumes one evaluator per acceptance test and supplies no procedure for estimating the projection. This paper establishes what a panel buys. Every aggregation rule that neither flags what no member flagged nor clears what every member flagged has a detection probability lying between the unanimous and the disjunctive rule, and the width of that bracket is the probability the panel disagrees, which vanishes as evaluator errors become correlated. Above a correlation level, therefore, no aggregation rule recovers detection the evaluator set does not collectively possess, however well designed. For evaluators whose inspection directions carry a geometric correlation, a closed-form folded dichotomization maps that geometry to the correlation of their errors and lies strictly below the identity, so the effective-sample-size statistic already used to audit evaluator panels is an upper bound on the rank of the acceptance projection. The statistic is borrowed and cited; what is new is that it measures a rank. Two consequences follow: randomly constituted panels saturate near the square root of the state-space dimension, and the independently verifiable share of a transferred specification is capped accordingly. Includes zharnikov-2026bn-verification-bandwidth.yaml (Paper Spec v0.1.0) — a machine-readable specification of the paper’s claims, assumptions, and dependencies. The paper’s full machine-first bundle (the SPINE claim/dependency graph and the ONTOLOGY term module) lives in the public repository; see https://github.com/spectralbranding/paper-spec for the standard. This PDF is generated programmatically from that machine-first source under a research-as-repository model.