Applied ITT - Yang-Mills Mass Gap and Color Confinement via ITT Persistence and Topological Closure

We present an ITT-based approach to the Yang-Mills mass gap and color confinement using the Persistence Criterion, Stratification Theorem, and Sub-Key Recursion Theorem of Pre-Veil Mechanics Volume I (Knight 2026). The mass gap Delta > 0 emerges from the binary S1b/S2 persistence threshold: excitations exist in the physical spectrum if and only if they satisfy the triple closure condition (vanishing phase residue, positive Bloom Quotient, Sₛel >= 1). Because the Allen-Cahn lower bound epsilon > 0 is a strict floor, no zero-energy excitation can satisfy the persistence gate — the mass gap is structural, not tuned. Color confinement follows from the topological closure requirement of the kcurl sub-key: a free quark carries an open phase loop (H¹ (W) != 0), permanently blocking S2 crossing. Confinement is cohomological, not energetic — the missing complementary color sub-sub-keys create a topological defect that cannot be removed by any continuous field deformation. String breaking arises naturally when extending the open loop costs more energy than creating a new quark-antiquark pair from S1a. A complete numerical simulator implementing the Allen-Cahn CTS on 2D and 3D lattices is provided, demonstrating: (1) glueball mass gap — Sₛel reaches stable S2 for pure gauge excitations; (2) color confinement — single quark decays (S1b) while triple-phase baryon is stable (S2) ; (3) quark-gluon plasma deconfinement transition — critical temperature where global Sₛel drops below 1. Results are consistent with lattice QCD benchmarks. Full working Python code included.