Local Green, Global Red VI - Blind Spots Under Nonlinear Aggregation and Adjoint Probing

Title. Local Green, Global Red VI - Blind Spots Under Nonlinear Aggregation and Adjoint Probing Abstract. A finite evaluator is represented by a real observation matrix Q. If two states produce the same observation, every deterministic rule that sees only that observation gives them the same verdict. Thresholds, voting, ranking, and other nonlinear post-processing therefore preserve every direction in ker Q. The Gram response QᵀQx vanishes exactly on ker Q and lies in its orthogonal complement. Results. The paper proves observation-only post-processing invariance, a singular-value bound on distance to the observation kernel, the Gram-kernel identity, a centered two-query directional identity, and exact recovery of the Gram response by averaging over the full finite sign cube. Artifacts. The deposit contains a self-contained Python implementation with branch-aware tests and a break-detect-restore mutation, four Lean theorems with an axiom report, two executable teaching notebooks, and generated figures. Earlier live-model and distributed or topological prototypes are retained as research history but excluded from the evidentiary surface. Reproduction. uv run --isolated --frozen --extra dev python verify_deposit.py --lean Scope. The work proves finite real-matrix statements and reports deterministic fixtures. It does not evaluate a language model, certify an operational system, establish stochastic-optimization convergence, or prove the deferred distributed and geometric extensions.