Intrinsic-Flatness Admissibility: A Deterministic Collapse Framework for Vertex-Minimal Polyhedral Tori

Description (Abstract) This document establishes a deterministic admissibility framework for the construction and classification of intrinsically flat polyhedral tori embedded in three-dimensional Euclidean space. Rather than treating the problem as a search or optimization task over continuous parameters, the framework formalizes intrinsic flatness as a binary admissibility condition governed by constraint-induced collapse. The approach emphasizes the elimination of impossible construction routes prior to execution and supports certification of infeasibility and minimality through replayable collapse witnesses. The analysis is non-constructive and intentionally non-enabling: it specifies admissibility conditions and collapse criteria without disclosing ordering rules, propagation mechanics, or realization procedures.