TEBAC Yang–Mills Program V: Continuum Limit, Non-Triviality, and Final Clay Assembly

This preprint is the fifth and terminal module of the TEBAC Yang–Mills program. Its purpose is to assemble the downstream continuum and axiomatic components required after the YM-IV uniform reconstructed mass-gap/coercivity module. The manuscript consolidates the YM-V terminal chain: +non-triviality+axioms+regulator independence+gap persistence-compatible assembly. \ The document builds on the preceding TEBAC Yang–Mills modules. YM-I fixes the Clay-compatible target and the modular architecture. YM-II constructs the finite-cutoff gauge-invariant reflection-positive lattice layer. YM-III supplies the OS/GNS reconstruction handoff. YM-IV provides the uniform reconstructed mass-gap/coercivity module in the gauge-invariant observable sector. The YM-V master synthesis organizes the final continuum passage. It includes continuum Schwinger compactness, non-triviality through curvature normalization, stability of Osterwalder–Schrader and Wightman structures in the continuum limit, Euclidean covariance restoration, locality and spacelike commutativity, regulator independence, uniqueness of the continuum Schwinger limit, and persistence of the YM-IV mass gap. The logical route is: -I-II-III-IV-V. \ Scope statement: this manuscript is the final terminal assembly module of the TEBAC Yang–Mills chain. It is written as a Clay-compatible assembly manuscript, but it should be read together with the preceding modules and their non-circularity audits. Public claims should remain module-explicit until the full YM-I--YM-V chain has undergone independent expert verification.