Local Green, Global Red

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.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-11
DOI
https://doi.org/10.5281/zenodo.22699198
Primary Topic
Ethics and Social Impacts of AI
Type
preprint
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preprint

Local Green, Global Red

Jeremy Carroll
Zenodo (CERN European Organization for Nuclear Research)
Ethics and Social Impacts of AI
preprint

Local Green, Global Red

Jeremy Carroll
preprint en

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.

Zenodo (CERN European Organization for Nuclear Research)
Ethics and Social Impacts of AI
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