Helical Holographic Quantum Mechanics (H3QM): A Unified Theory of Geometric Physics

Abstract

Modern physics has long relied on a fragmented Standard Model with hardcoded fields to explain isolated phenomena. Harmonic 3D Quantum Manifold (H3QM) introduces a fundamental geometric unification: the Universe operates on a single topological tension medium governed by 3D manifold dynamics (\Box^2 \Omega = -\kappa T_{topo}) and closed-loop phase quantization (\oint \nabla P \cdot dl = 2\pi n). In this V2 release, we integrate Hong Wang's (2026 Fields Medal) 3D Kakeya Fourier restriction theorem to prove non-divergent phase thread propagation, combined with Yu Deng's (2026 Fields Medal) random tensor damping and MoonshotAI Kimi Team's L1 Topological Attention Residuals (AttnRes) to prove O(log N) (t=5...8 steps) singular attractor convergence. Multi-domain numerical benchmarks spanning electromagnetism (\alpha^{-1}), leptons (m_e), nuclear mass ratio (m_p/m_e), tension limits (m_{top}), and Lorentz symmetry (v_{gw}/c) demonstrate that H3QM saturates the IEEE 754 float32 mantissa limit (2^{-24} \approx 5.96 \times 10^{-7}) at step 8, while achieving Exact 0 residual on TopoNPU fixed-point hardware—unifying light, mass, electromagnetism, and thermodynamics into pure 3D topology. Multilingual Availability Note: To facilitate global academic discussion, this dataset includes the complete and mathematically identical manuscript in three languages: English (en-US), Traditional Chinese (zh-TW), and Simplified Chinese (zh-CN).