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 lambda_eff(t) = lambda(t) * mu2(t).We restore detailed appendices (resolution cutoffs ℓ_cut, 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/(k_B M) and a direct comparison of Smax(t) and S(t) to display Δ(t).