The Phase Transition from Nothing to Something: From Primordial Soup to Particle Zoo in Four Parameters

Title The Phase Transition from Nothing to Something: From Primordial Soup to Particle Zoo in Four Parameters Authors Jia, Baolong (贾宝龙) Description Can matter emerge from pure relational dynamics with no predefined geometry, no predefined particles, and no material substrate? This paper investigates the spontaneous emergence of particle-like structures in a bounded-rate graph process (BRGP) — a stochastic dynamical system on finite directed graphs where nodes and edges evolve under local rules subject to four integer rate constraints (v₁, v₂, v₃, v₄). We provide the first rigorous operational definitions of what constitutes a "particle" in a dynamic graph: a subgraph that is simultaneously persistent (exponentially long-lived), localized (bounded diameter), propagating (moves across the graph at bounded velocity), and interaction-capable (non-trivial collision outcomes). Key results: Cycle Persistence Theorem: Directed n-cycles satisfy all four particle criteria under the condition v₃ > v₄ (edge creation exceeds deletion), with persistence growing exponentially as (v₃/v₄)ⁿ. Self-Repair Theorem: Certain subgraph motifs encode their own reconstruction rules in their topology — the graph-theoretic realization of the principle "structure = information = program." Persistence Phase Transition: At the critical ratio v₃/v₄ = 1, a sharp phase transition occurs: below it, no persistent structures survive (primordial soup); above it, particle-like structures proliferate (emergent matter). Collision Algebra: Five interaction outcomes are classified — elastic scattering, merging (fusion), annihilation, fission, and catalysis — with an approximate conservation law for total "cycle mass" analogous to baryon number conservation. Particle Taxonomy: Simple cycles correspond to fermions, traveling edge-waves to bosons, hub-spoke structures to massive particles at rest, and orientation-reversed cycles to antiparticles. Three Falsifiable Predictions: Concrete numerical predictions for (a) the sharpness of the persistence phase transition, (b) a discrete velocity spectrum for propagating structures, and (c) the dominance of merging vs. scattering as a function of v₃/v₄. This paper is the second in a series formalizing the JiaBaolong Axiom System's Trinity Universe Theory. It addresses the "Phase 0 → Phase 1" transition (from primordial soup to stable motifs) in the emergent evolution hierarchy established in the companion paper on Mediumless Topological Cosmology. Keywords particle emergence, bounded-rate graph dynamics, directed cycles, self-repair, persistence phase transition, topological matter, pre-geometric physics, collision algebra, topological fermions, emergent conservation laws, JiaBaolong Axiom, Trinity Graph Process 中文关键词 粒子涌现、有界速率图动力学、有向环、自修复、持久性相变、拓扑物质、前几何物理、碰撞代数、拓扑费米子、涌现守恒律、贾宝龙公理、三元图过程