Coherent-Sector Universality and Controlled Truncation in Modal Triplet Theory

We develop a general framework for coherent-sector reduction in Modal Triplet Theory (MTT), establishing precise conditions under which effective truncations of internal modular dynamics are mathematically controlled and physically robust. Assuming bounded internal geometry, a uniform spectral gap, and regularity of the coherent projector, we prove that the dynamics admits a controlled reduction to a coherent sector with explicit operator-norm error bounds. Such reductions define a universality class stable under small perturbations of the microscopic structure, ensuring that effective temporal dynamics depend only weakly on internal details. The analysis is model-independent and relies on standard operator perturbation theory rather than on specific geometric constructions. A comparative appendix situates these results alongside other controlled reduction frameworks in high-energy theory, emphasizing structural parallels without asserting formal equivalence. This work provides a methods-level foundation for the universal and robust use of coherent-sector truncations across the Modal Triplet Theory corpus.