Modal Triplet Theory: Foundation

Modal Triplet Theory (MTT) is a mathematically rigorous fixed-point framework in which observable 3+1-dimensional physics emerges as the coherent sector of a dissipative flow on a higher-dimensional space. Three commuting filter bundles define a joint harmonic projector, selecting a coherent sector whose dynamics satisfy a Fundamental Contractivity Condition (FCC). Under explicit standing assumptions—bounded geometry, uniform spectral gaps, projector regularity, and coherent-sector dissipation—we prove existence and uniqueness of a stable coherent fixed point. Stability under disturbances is quantified using Ornstein–Uhlenbeck analysis with a correct bundlewise summability criterion, and curvature–gap couplings are derived using representation-correct Bochner–Weitzenböck identities. Selection is formulated through admissibility barriers and an optimal admissible projection, enforcing exact conservation laws without introducing stochastic collapse or additional dynamics. Within the coherent sector, the framework recovers a Lorentzian 1+3 spacetime, causal and unitary effective dynamics, and controlled reductions to quantum mechanics, quantum field theory on curved spacetime, general relativity, and the Standard Model. The theory yields explicit quantitative predictions while remaining compatible with current experimental constraints.