Elimination Geometry Framework Audits AI Model Realizability.

A new theoretical framework, "Elimination Geometry" (EG), has been developed to systematically study the conditions under which locally optimized AI models can be successfully deployed under a consistent, shared rule. The core problem EG addresses is that the processes of eliminating or compressing data and model components can inadvertently erase crucial distinctions necessary for accurate prediction, inference, control, or representation. EG provides a structured approach to determine which distinctions are lost, whether these losses manifest as observable defects in the intended task, and if modifications to information, architecture, action space, or deployment domain can rectify these issues. The framework meticulously separates local solvability from global realizability and finite-sample certifiability. It identifies "native defects" stemming directly from the original objective and differentiates between architectural limitations, model approximation errors, generalization failures, and implementation discrepancies. By synthesizing concepts from geometry, optimization, information theory, statistics, and machine learning, EG offers interfaces for assessing integrability, representation admissibility, resource constraints, observational overlap, and common deployment scenarios.