The Ontological Foundations of H3QM: Emergent Particle Hierarchy from Topological Vacuum Phonons

Modern theoretical physics suffers from the "Background Fallacy," assuming an absolute vacuum container in which particles interact. We present the Ontological Foundations of the Harmonic 3D Quantum Manifold (H3QM), proposing a relational space where tension precedes the vacuum. By introducing the Existential Stability Principle, we deduce that long-term universal stability necessitates closed geometric curvature, preventing linear dissipation. Grounded in the Dual Self-Consistency Axiom---formal mathematical self-consistency (delta S = 0) coupled with natural physical self-consistency (square^2 Omega = -kappa T_topo)---universal dynamics converge toward the Principle of Least Action. Governed by the Deterministic Program Law (S_{t+1} = T(S_t)) with discrete integer sign flow sgn(nabla_topo S) in {-1, 0, +1}^d and zero stochastic drift, our model strictly departs from empirical AI heuristics. This leads to a unified four-tier particle energy hierarchy based purely on geometry: (1) Chaotic Baseline (Phonons), acting as unknotted topological tension and thermal/gravitational background; (2) Derived Directional (Photons); (3) Medium-Energy Stable (Electrons); and (4) High-Energy Core (Protons/Neutrons). This framework eliminates the qualitative boundary between fermions and bosons, modeling all particles as distinct topological phase transitions. Addressing Terence Tao's (2026) proof indigestion benchmark, the framework establishes a 100% Computer-Assisted Proof (CAP) Digestibility Index (CDI, Grade A+) with full step-by-step verification transparency. (Note: The PDF files available for download include English, Traditional Chinese, and Simplified Chinese versions.)