Coherence-Driven Collapse as the Origin of Time, Mass, and Geometry

This preprint introduces a deterministic collapse-based framework in which time, mass, and spacetime geometry emerge from the statistics of modal-collapse events. The key dynamical quantity is the coherence factor Ξ, defined by the average inter-collapse interval. Ξ governs the conversion between coordinate and physical time (dτ = Ξ dt), determines inertial mass (m = E/Ξ²), and generates the effective metric (g_tt = –Ξ⁻², g_rr ∝ Ξ^p with p ≈ 1.9). Smooth Schrödinger evolution and general relativistic geometry are recovered as limiting cases of the same dynamical system: rare collapse cycles produce classical behaviour, fluctuating collapse produces quantum behaviour, and runaway collapse (Ξ → 0) gives rise to gravitational collapse and the breakdown of smooth geometry. The runaway regime mathematically enforces a lowest-frequency electromagnetic emission channel, predicting that radiation in collapse-driven transients must begin in the radio band and only later extend to higher frequencies. The accompanying supplementary TXT document provides the complete proof set of all five falsifiable predictions, with no tunable parameters: (1) universal radio-first ordering of electromagnetic discharge in runaway events, (2) universal curvature exponent p ≈ 1.9, (3) classical stability when ⟨ΔN_eff⟩ < 0, (4) time dilation fully determined from collapse-interval statistics, and (5) radio-only discharge at the onset of runaway collapse. This work proposes that collapse dynamics — rather than measurement or spacetime postulates — constitute the fundamental mechanism from which quantum behaviour, classical stability, and gravitational collapse all emerge.