Theory of Impossibility: Core, Representations, Dynamics, and Admissible Physical Structure

This paper develops a formal theory from a single ontological prohibition: effective collapse of distinction is impossible. The theory is organized into levels. The core level fixes observational distinction, observational equivalence, and admissible transformation. The representation level introduces scalar cost, obstruction to gluing, directed cost geometry, entropy as multiplicity, and sector decomposition. The bridge level constructs a continuum model in which obstruction emerges as gluing failure, sigma acts as a compensator, and effective couplings acquire scale dependence through composition covariance. From the Central Law of irreducible residue follow no-go results for free erasure, free reduction, and uncoupled nontrivial sectors. The theory also yields structural consequences concerning dimensionality, signature, observer status, canonical constants of admissibility, and experimentally accessible residuals. The theory is falsifiable: any realized instance of effective collapse without residue and without cost would refute it.