From Chaos to Life in Medium-Free Topological Dynamics: Complete Numerical Verification of the Trinity Graph Process (Phases 0–6: Topology → Chaos → Matter → Chemistry → Selection)

Title From Chaos to Life in Medium-Free Topological Dynamics: Complete Numerical Verification of the Trinity Graph Process (Phases 0–6: Topology → Chaos → Matter → Chemistry → Selection) Authors Jia, Baolong (贾宝龙) Description Can a minimal graph-dynamical system spontaneously generate the complete hierarchy from chaos through matter, chemistry, and replication to Darwinian selection — without any externally imposed spatial structure or biological rules? This paper presents a comprehensive numerical verification of the Trinity Graph Process (TGP) — a medium-free dynamical system on directed graphs governed by four bounded-rate parameters (v₁, v₂, v₃, v₄) and three interacting mechanisms: Paradox-Referential selection (PR), Entity-Relation substrate (ER), and Lazy Evaluation conflict resolution (LE). Through 500+ simulations across system sizes N = 50 to N = 80,000, eight parallel-universe ensembles, and up to 1.5 × 10⁶ ticks, we establish a complete evolutionary hierarchy spanning seven phases: Phase 0–2 (Topology → Chaos → Fractals): Deterministic Chaos (VERY HIGH confidence): Universal positive Lyapunov exponents λ > 0 in 78/78 configurations. Scaling law λ ≈ 1.04·N^(−0.60) (R² = 0.975). Chaos originates from the self-referential topological feedback loop. Strange Attractor: Fractal correlation dimension D₂ = 1.85 ± 0.05; graph fractal dimension d_B = 2.57 ± 0.28. Topological Gliders: Persistent triangles survive chaos with 95–99% tick-to-tick persistence. Phase 3–4 (Matter → Interactions): Emergent Matter: Directed triangles form elementary particles with a Boltzmann mass spectrum: E(w) = 0.55w + 0.43w² (R² > 0.999999). Universal weight ratio R = w₀/w₁ = 3.1226 ± 0.0048. Particle Physics: Five distinct collision outcomes (scatter, bind, fuse, annihilate, asymmetric destruction) satisfying detailed balance. Phase 4.5–5 (Chemistry → Replication): Emergent Chemistry: Edge-sharing dimers with linear binding energy t₁/₂ = 4.65 + 1.24w. Mutual bonds 1.28× stronger than one-way bonds (graph-theoretic covalent vs. ionic). Template-Directed Inheritance: Parent-child weight correlation r = 0.295 ± 0.005, temperature-independent across a 40× range. Phase 6 (Darwinian Selection): At low decoherence (dec ≤ 10), natural selection emerges spontaneously: heavy particles (w=3) achieve 75× higher fitness than light particles (w=0). Confirmed at N = 80,000 with 1.5M ticks. Universal Constants (8-universe verification): R = 3.1226 ± 0.0048 (0.15% precision) α_SOC = 1.4700 ± 0.0001 (invariant to 4th decimal across 8 universes) D₂ = 1.624 ± 0.008 Lyapunov λ = +0.2774 ± 0.0107 (8/8 universes chaotic) The complete evolutionary chain VOID → TOPOLOGY → CHAOS → MATTER → CHEMISTRY → REPLICATION → SELECTION is now computationally verified, each phase emerging spontaneously from the PR⇔ER⇔LE dynamics without external coding. The Phase 5→6 transition confirms the JiaBaolong Axiom's prediction that life requires PR dominance over LE — the axiom-level explanation for why life requires non-equilibrium conditions. This is the third paper in a series formalizing the JiaBaolong Axiom System's Trinity Universe Theory, following the foundational axiom paper (Zenodo 19440952) and the cosmology formalization paper (Zenodo 19469833). Two Rust simulators and Python analysis scripts are included. Results are fully reproducible. Version History v1 (April 2026): Initial release — Phase 0–2 (chaos, fractals, gliders), 400+ simulations, N