We develop a conservative Θ–closure framework in Modal Triplet Theory (MTT) that relates Standard Model gauge couplings to internal geometric overlap integrals. Starting from experimentally measured couplings at the electroweak scale, we evolve them via one–loop renormalization group equations to a common matching scale µΘ = 5 TeV and extract explicit numerical targets for the nonabelian overlap ratios I₂/I₁ and I₃/I₁. We formulate precise admissibility conditions on the internal geometry, including bounded projection and uniform spectral gap requirements, and prove the existence of a nonempty Θ–region consistent with these constraints. To address the normalization of nonabelian harmonic representatives, we introduce a high–coherence (twistor) corner that provides canonical massless gauge modes with controlled corrections suppressed by the inverse gap. The paper establishes the quantitative targets, normalization framework, and falsifiability criteria of Θ–closure without assuming unification or a specific ultraviolet completion. Explicit geometric realization and independent cross-checks are deferred to companion papers, completing the conservative closure of the gauge sector at leading order.
Peter Nero (Thu,) studied this question.