Admissibility, Proto Time, and the Empirical Structure of Ordered Continuation

This work makes explicit a structural layer that is already implicit across established physics: that ordered existence arises from admissible continuation under constraint, rather than from clocks, observers, probabilities, or new physical laws. By reorganizing standard formalisms in electromagnetism, general relativity, plasma physics, and orbital mechanics, we define proto time as the orderability of survivable transitions. We show that collapse corresponds to exhaustion of admissible continuation, and that metric time emerges only in regimes where ordering is thick, regular, and recurrent. No existing physical equations are modified, and no new dynamics, constants, or forces are introduced. The framework is formulated using admissibility graphs, null congruences, Raychaudhuri focusing, dispersive cutoffs, and boundary conditions. It yields a dimensionless diagnostic language for persistence, ordering integrity, and closure versus leakage, and it identifies a domain-independent topology of continuation represented by directed acyclic graphs. Empirical validation protocols are provided across multiple regimes, including electromagnetic propagation in plasmas, near-horizon behavior in curved spacetime, and planetary day and night cycles. Planetary rotation and orbital dynamics serve as a natural large-scale testbed demonstrating that ordering exists universally, while clock regularity varies due to rotation rate, axial tilt, orbital resonance, and relativistic effects. The contribution is explanatory and diagnostic rather than ontological. It clarifies why physical propagation, time ordering, and stability are selective rather than generic outcomes of equations, and it provides falsification criteria based on structural impossibility rather than statistical correlation. Applications include wave propagation engineering, sensing and navigation, strong-field inference, and admissibility-first computation. Keywords (by domain) Foundations of Physics admissibility proto time ordered continuation collapse as exhaustion structural selection partial order directed acyclic graphs persistence under constraint Relativity and Gravitation general relativity null congruences Raychaudhuri equation caustic formation horizons spacetime structure affine parameter ordering Electromagnetism and Plasma Physics electromagnetic propagation geometric optics plasma dispersion waveguiding cutoffs and resonances MMS spacecraft data corridor confinement Time and Dynamics time ordering metric time emergence clocks and recurrence ordering versus duration relativistic time dilation failure of clocks near boundaries Planetary Science and Orbital Mechanics planetary rotation day night cycles solar day versus sidereal day spin orbit resonance axial tilt orbital eccentricity comparative planetology Mathematics and Topology graph theory partial orders recurrence equivalence topological quotients ordering integrity acyclicity Computation and Systems admissibility first computation failure modes bounded continuation structural stability recursion control diagnostic invariants Engineering and Applications wave propagation engineering robust communications sensing and navigation strong field inference stability diagnostics system design under constraint