This manuscript presents a constructive Euclidean framework for SU(N) gauge theory in which a spectral mass gap arises through twist-compression dynamics. The formulation is gauge-invariant, analytically and numerically verified, and satisfies the core constructive QFT criteria. Revision Summary (October 2025)This version incorporates all peer-review and editorial feedback received since the initial publication. Revisions include:• Clarified Gupta–Bleuler constructive equivalence (§ 4.2).• Added explicit labeling of the energy-scaling analysis and separation of parameters λ and ρ (§ 3.4).• Expanded ultraviolet and asymptotic-freedom discussion, citing Glimm–Jaffe and constructive measure results (§ 9, § 14, App. C.5).• Added evidence that the nonlinear term arises dynamically, referencing the QFT Confinement Series reproducibility archive (§ 2.1, App. E).• Introduced gauge-invariant diagnostic analysis (§ A.9).• Edited language throughout for clarity, consistency, and modest tone. The original v1.0 record remains available under the same concept DOI for historical reference.All revisions are presented in good faith to strengthen rigor, transparency, and reproducibility.