Admissible Response Geometry and the Structure of Meaning in High-Dimensional Language Models

This paper develops a response-geometric account of meaning in high-dimensional language models. It does not identify meaning with tokens, coordinates, neurons, attention heads, sparse features, or raw hidden-state directions. Instead, meaning is defined as a structural status acquired by hidden-state variations through a hierarchy of admissible response conditions. For each admissible downstream readout, an ordered second-order response form is decomposed into a symmetric readable sector and an antisymmetric response sector. The symmetric sector defines a readable quotient; the antisymmetric sector defines a response operator on that quotient. A variation is meaningful in the stronger sense only when it is readable, response-generating, stable across an admissible readout family, and compatible with the simultaneous admissibility constraints that define the admissible meaning core. The framework separates raw representation, decodability, response generation, readout-family stability, and admissible core membership. It explains why probe success is not full semantic involvement, why output change is not by itself admissible meaning, and why superposition and polysemanticity arise naturally in high-dimensional models. The final thesis is that meaning in a high-dimensional language model is stable admissible response, not raw representation.