The Shared Circle in Modal Triplet Theory: Exact Phase Transport, Interpretive Roles, and Physical Boundaries

Modal Triplet Theory repeatedly uses a common circle in its bundle, proto-spinor, finite-operator, and compactification descriptions. This paper states what that circle currently means and what it does not yet explain. Its rigorous role is common phase and holonomy data carried by a Hermitian line bundle with connection. On the selected q79 finite symbol, one universal flat line pulls back to the determinant-sign sector, tensors the three trace lanes, and commutes with the finite projectors, complex quarter-turn, and Reynolds-Hessian operator. This is an exact same-source phase-transport result. It neither adds a seventh compact coordinate nor identifies compact phase with Lorentzian time. A physical mass claim still requires a selected Dirac or two-point operator and a dispersion or pole theorem; inertia requires an effective response or worldline coefficient; gravity requires the four-dimensional action and universal stress response; and time requires a Lorentzian evolution and an explicit clock or ordering map. The proposed unification of mass, inertia, gravity, and time is therefore retained as a research program organized by one shared differential line, not as a current derivation of those observables.