Canonical Tightening Uniqueness: Standalone Theorem Note

We establish a uniqueness principle for tightening operators acting on filtered structures modulo negligible perturbations. Given a tightening operator T defined on a family F with negligible ideal N, we prove that every F ∈ F admits a unique canonical core obtained as the limit of iterative tightening, independent of representatives modulo negligible deviations. The theorem formalizes the collapse of small perturbations and identifies a unique metastable fixed point governed solely by essential structure. This note records the canonical tightening uniqueness result for reference and citation, serving as a standalone foundation for subsequent stability and rigidity developments. This standalone theorem note documents the canonical tightening uniqueness result used implicitly in earlier barrier-equivalence work and explicitly in forthcoming stability–rigidity arguments. It provides a foundational hinge for the Version 6.3 tightening architecture, recording uniqueness at the core level independent of negligible structure.