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
- Jeremy Carroll
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