Equivalence Structures in Mathematical Models of Consciousness: A Preliminary Algebraic and Geometric Investigation

This exploratory paper proposes a mathematical programme for studying equivalence structures in models relevant to consciousness. It inherits four provisional explanatory orientations, Variation, Trajectory, Generativity, and Repertoire, and considers their cross-classification with ontological, relational, and manifestational registers. Equivalence is treated as relative to a specified domain, invariant, representational map, and modeling or experimental context. The intended investigation compares transformation-action equivalence, orbit and homotopy relations, equivalences of changing relational structures, and equivalences of admissible path families. It addresses preservation and information loss across algebraic, geometric, topological, categorical, and observational translations, emphasizing that identical manifestations may conceal relational differences and that mathematical correspondence does not independently establish phenomenal identity. The current draft develops foundational criteria, the four orientation-specific equivalences, cross-orientation and cross-register comparisons, algebraic and geometric preservation conditions, protocol-indexed empirical discrimination, the limits of phenomenal inference, and a comparative synthesis of research priorities. The sixteen-section main text and Appendices A–F are drafted; independent specialist review remains planned. No empirical evidence concerning consciousness is claimed.