Local Green, Global Red V: A Finite No-Recovery Theorem for Composed Evaluation, with Lean 4 Proofs
Year: 2026
Type: preprint
Abstract: This v0.1 preprint studies a finite linear model of composed evaluation. A system has sites, directed interfaces, contractive translations, and evaluators that observe selected interface defects through non-expansive linear measurements. The paper proves that evaluator scores are always bounded above by true defect mass, but that the converse can fail sharply: even with complete interface coverage, all evaluators can report zero while global inconsistency is arbitrarily large. The main witness is an explicit six-site construction with three component sites, three overlap sites, six watched interfaces, and three evaluators. It gives exact All-Green score vectors with prescribed positive defect mass, showing that no finite-valued recovery function of the evaluator scores can uniformly bound the true inconsistency. The paper also states the exact soundness criterion, explains why trivial per-interface blind spots are sufficient but not necessary, and separates raw false green from quotient/non-exact defect. The release includes claim-ledger accounting, exact-arithmetic Python replays, computational tests, notebooks, and Lean 4 declarations for the abstract observer statements and explicit defect calculations. The results apply only to concrete evaluation systems that instantiate the stated finite linear model; no claim is made about any particular AI system, evaluation suite, or organization.
Author: Carroll, Jeremy
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212261808
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