Moving-Reference Arrows of Time Without the Past Hypothesis: Unified Dynamical Theorems, Classification and Uniqueness, Topology-Controlled Mixing, and Cosmological Realizations with Visual Diagnostics

This work provides a testable framework linking entropy production, topology, and cosmological evolution without invoking special initial conditions. We present a unified theorem-level framework for the arrow of time without the Past Hypothesis (PH), combining: (i) dynamical theorems showing generic creation of an entropy gap when the accessible entropy ceiling moves while relaxation proceeds at finite rate; (ii) a classification and uniqueness theorem showing that, under time-symmetric microscopic laws and typical initial conditions, any persistent macroscopic arrow must be of moving-reference (MR) type; and (iii) cosmological realizations specifying ceiling forcing eta (t) and topology-controlled mixing lambdaₑff (t) = lambda (t) * mu2 (t). We restore detailed appendices (resolution cutoffs ℓcut, closed/special-function solutions, and S2 derivations), add a gravitational-capacity worked example, and provide a submission-ready numerical validation protocol. Two executable visuals are included: an epoch-wise curve for x (t) = Δ/ (kB M) and a direct comparison of Smax (t) and S (t) to display Δ (t).