On the Physical Necessity of Admissible Temporal Evolution in Rupture–Containment Cosmology (RCC)

This paper examines the physical status of admissible temporal evolution within Rupture–Containment Cosmology (RCC). In RCC, time is treated as a physical field whose evolution must remain finite, bounded, and operationally meaningful over all finite intervals. Cosmological singularities are excluded not through dynamical regularization or speculative ultraviolet physics, but by restricting the class of admissible temporal histories from the outset. The central aim of this work is to clarify whether the admissibility conditions imposed on temporal evolution—most notably boundedness of the tempo field and its logarithmic rate—are merely epistemic consistency requirements or reflect deeper physical necessity. The analysis shows that admissibility is not an arbitrary postulate, but is repeatedly enforced across multiple domains: variational stability of the tempo Lagrangian, coherence of phase evolution, operational requirements of clock synchronization, and the empirical consistency of timing- and propagation-based observations. The paper establishes that unbounded or runaway temporal evolution generically leads to breakdown of physical coherence, loss of operational meaning, or violation of known experimental constraints. Admissible temporal evolution is therefore shown to be a necessary condition for physically meaningful histories, rather than a model-dependent assumption. This work complements and underpins a Friedmann-class cosmological formulation of RCC by identifying admissibility as a structural prerequisite rather than a phenomenological choice. While no specific cosmological model is fixed, the results demonstrate that singularity-free cosmological classes arise naturally once temporal evolution itself is treated as a constrained physical quantity. The paper is intentionally structural in scope. It does not attempt to provide a complete phenomenological cosmology, nor does it derive admissibility from a single microscopic principle. Instead, it demonstrates convergence of necessity across independent physical considerations, thereby motivating further synthesis and model development within the RCC framework.