Physical Universality vs Cultural Contingency: Why Geometric Semantic Architectures Work for Physical Dimensions and Fail for Human Conceptual Categories

Abstract

This paper documents and explains a precise ceiling in geometric AI architectures: physically grounded semantic dimensions encode cleanly across all corpora and languages because physical reality forces the same distributional patterns universally, while culturally contingent dimensions reflect local conceptual frameworks that vary across linguistic communities. Temperature, speed, and luminosity opposition achieve reliable geometric structure in any corpus. Moral, epistemic, and social opposition do not. The paper characterises this ceiling as a property of the domain rather than a limitation of the architecture, distinguishes between the two using experimental evidence across multiple corpus sources, and identifies the mathematical track as the calibration reference for diagnosing and resolving the limitation. Candidate interventions including multi-corpus grounding and compositional decomposition of abstract concepts into physically grounded primitives are proposed. The ceiling has direct implications for AI safety research: bias that is geometric is bias that can be measured, and bias that can be measured can in principle be corrected.