CosmicThinker25/Phase-tunneling-genesis: Phase-Tunneling Cosmogenesis: Structural Origin of a Critical Phase Mass in a Finite-Window Regime

Title: Phase-Tunneling Cosmogenesis: Structural Origin of a Critical Phase Mass in a Finite-Window Regime Abstract & Repository Description: This repository contains the full reproduction package (manuscript, Python source code, and generated datasets) for the study of Phase-Tunneling Cosmogenesis. This work investigates the emergence of non-trivial dynamical histories from a pre-dynamical regime within the framework of CPT-symmetric ("Twin") cosmology. Key Scientific Contributions: The central finding of this work is the identification of a robust critical phase mass, mϕ,crit≃1.965, which marks a sharp structural bifurcation in the phase configuration space. By analyzing the competition between a periodic effective potential, Hubble friction, and a decaying rotational source term, we demonstrate that: Finite-Window Criticality: The "escape sector" (Sector C)—characterized by trajectories that avoid immediate relaxation—is intrinsically a finite-window phenomenon (occurring within ΔN≃9.2 e-folds). It is defined by transient non-relaxation rather than asymptotic divergence. Asymptotic Null Result: Extending the integration to arbitrarily late times (N→∞) yields a universal synchronization (Δϕ→0). This null result confirms that the critical threshold is not an eternal attractor but a geometric feature governing the emergence of transient complexity (interpreted as Barbour-style "Time Capsules"). Quantum Tunneling Prior: We introduce a semiclassical WKB tunneling mechanism as a prior for initial conditions. The analysis reveals that the classical threshold (mϕ,crit) is structurally robust and insensitive to the specific choice of the quantum prior (WKB vs. Uniform), as demonstrated by differential survival maps included in the analysis. A primordial rotational coupling is shown to act as a catalyst by reducing the Euclidean action via a Stark-like effect. Contents of this Repository: Manuscript: The full PDF of the paper (vFinal). Source Code (src/): Python scripts for phase dynamics integration, sector classification, and WKB tunneling probability computation. Figures (figs/): High-resolution plots, including the "Money Plot" demonstrating the robustness of the critical threshold against initial condition priors. Plain English Summary: How Time Escapes the Trap How does a universe "start" if there is no time before it? This project explores a model of Cosmogenesis (the origin of the cosmos) where time is not a background stage, but a temporary "escape" from a static state. In this model, the universe—and its "twin" partner—start locked in synchronization. To create a history, they must break apart. We found a specific "magic number" or critical mass (1.965) that determines whether a universe can break free and develop a history or if it immediately collapses back into silence. Three Big Ideas in this Work: The Window of Opportunity: We show that "time" as we know it is a temporary bubble. If you run the clock forever, everything eventually syncs back up. Real physical history happens only in a brief, finite window of expansion. The Critical Threshold: Just like a rocket needs escape velocity to leave Earth, the phase of the universe needs a specific mass to escape immediate collapse. We calculated this value precisely at 1.965. The Quantum Kick: Before the clock starts, quantum mechanics rolls the dice. We modeled how the universe "tunnels" through a barrier to get started. Crucially, we found that the rules of the game (the 1.965 threshold) don't change regardless of how the dice are rolled—the structure of the universe is robust. This repository provides the code and data used to discover these numbers, allowing anyone to replicate the simulations of these "Time Capsules" and see the boundary between a universe that happens and one that never was.