The Central Circle: Inertia, Mass, Gravity, and Time as Shared Coherence Bookkeeping in Modal Triplet Theory

Modal Triplet Theory (MTT) treats physical description as conditional: observables, effective dynamics, and probabilities exist only within admissible regimes where projection from a higher-dimensional modal structure remains stable. Within this framework, many quantities that are traditionally treated as independent—mass, inertia, gravity, and time—arise from shared structural constraints rather than from distinct dynamical mechanisms. This paper identifies and analyzes a single internal structure reused across all coherent sectors of MTT: a central circle Scen1S^1_{\mathrm{cen}}Scen1. We show that the universality and spectral rigidity of this circle force it to act as a global coherence bookkeeping channel. Inertia appears as the cost of rethreading coherence when localized histories are accelerated; gravity appears as the spatial redistribution of coherence capacity required to maintain admissibility; time ordering arises from the noninvertibility of projection along this shared channel; and fermion family structure emerges from discrete holonomy sectors of the same circle. The paper is synthetic rather than derivational. Familiar results—including Newtonian inertia, the equality of inertial and gravitational mass, null propagation of photons, and the Einstein field equations—are shown to arise as constraint-preserving encodings within admissible regimes, without introducing new dynamics. Detailed derivations and consistency checks are provided in appendices. By isolating the role of the central circle, this work clarifies why mass, gravity, and time exhibit universality, why gravitational energy lacks a local density, and why effective descriptions terminate sharply at horizons and selection fronts. The analysis unifies several previously separate results within the MTT corpus and provides a structural lens for understanding the emergence and limits of physical description.