Time as a Conditionally Admissible Order Parameter: Regime Transitions, Coherence Thresholds, and Topological Cosmogenesis

This note proposes a regime-based reading of the claim that “time is not fundamental.” Time is treated not as a universal primitive but as a conditionally admissible order parameter that becomes usable only when an availability structure supports coherence. We formalize an availability-first vocabulary in which an operational cost functional governs which transitions are feasible, how they compose, and when stable global ordering can be extracted. In coherent regimes, costs induce an effective trajectory geometry and permit a time-like ordering via systematic asymmetries of reconstruction cost. At coherence thresholds, an update operator δ* reorganizes admissibility and fractures the dominant basin into multiple components. In collapsed regimes, topology dominates: component counts and component-size distributions carry the primary signatures. On this basis, cosmogenesis is reinterpreted as the establishment of coherence (and thus the admissibility of time), replacing a privileged “beginning in time” with a threshold of admissibility. Keywords time; cosmology; quantum gravity; problem of time; emergent spacetime; admissibility; coherence; regime transitions; topology; scale-free fragmentation; reconstruction cost; δ*