Admissibility and Symmetry Loss: A Structural Account of Bidirectional Possibility and Filtered Observation in the Tier 2 → Tier 3 → Tier 4 Transition

This paper examines the structural relationship between possibility, admissibility, and observation within the Paton System. At Tier 2, systems exist as fields of multiple potential configurations, including bidirectional and symmetric structures. At Tier 3, admissibility filtering constrains continuation, allowing only internally consistent trajectories to persist. At Tier 4, observation reflects only directionally stable projections of those admissible structures. The framework demonstrates that symmetry loss is not a fundamental absence of structure, but a consequence of constraint filtering. What appears asymmetric at the observational level is the result of admissibility selection, not the structure of underlying possibility. This work formalises the Tier 2 → Tier 3 → Tier 4 transition as a compression process: Possibility → Constraint Filtering → Observable Projection The paper introduces no new physical laws. It provides a structural interpretation of how observed asymmetry emerges from symmetric possibility through admissibility. Positioned within the Paton System, this work links: Tier 2 (structured possibility) Tier 3 (admissibility filtering) Tier 4 (observational projection) into a unified account of symmetry loss and observable structure.