A Century of Experimental Physics Validation for Helical Holographic Quantum Mechanics (H3QM): A Geometric Physics Synthesis Homage to 100 Years of Experimental Physics Masters (1922--2026)

Abstract

Abstract: Three landmark experimental breakthroughs in condensed matter physics and quantum information science---the discovery of the Quantum Anomalous Hall Effect (QAHE) by Xue Qikun's team, the satellite-based 1200 km quantum entanglement distribution by Pan Jianwei's team, and the theoretical prediction and discovery of Weyl semimetals by Fang Zhong and Dai Xi's team---represent the pinnacle of contemporary physics. Expressing our deepest academic admiration for their pioneering contributions, this paper presents first-principles geometric physical derivations for these landmark discoveries within the 3D Helical Holographic Quantum Mechanics (H3QM) framework. We prove that: (1) QAHE dissipationless edge states are isomorphic rigid wave-slidings of 3D Mobius topological knots (W = 1) along Wasserstein-1 (W1) optimal transport geodesics, where closed-loop phase quantization ensures topological backscattering immunity; (2) Quantum entanglement is non-local phase-locking (P1 = P2 + Delta phi) within a continuous, high-shear-modulus vacuum network, rigorously accounting for the experimental 232-attosecond (as) entanglement formation delay; by incorporating Hong Wang's (2026 Fields Medalist) 3D Kakeya Fourier restriction theorem, we prove that holographic phase threads maintain non-dispersive propagation over 1200 km without spatial energy divergence; (3) Weyl nodes and Fermi arcs are phase-space singular attractors driven by 3D helicity (H), with Yu Deng's (2026 Fields Medalist) random tensor operator damping theorem and Chen et al.'s (2026) L1 Topological Attention Residuals (L1 Topo-AttnRes) guaranteeing O(log N) fast convergence. Multi-domain numerical benchmarks across six fundamental physical constants demonstrate that the 8-step convergence residual (5.96 x 10^-7) exactly saturates Cosmo Chou's landmark machine epsilon algebraic identity: (1/8)^8 = (2^-3)^8 = 2^-24 = epsilon_float32, confirming that the residual reflects the physical precision ceiling of IEEE 754 32-bit hardware rather than a theoretical error, while fixed-point integer sign-operator flow achieves Exact 0. This establishes an unassailable geometric foundation unifying experimental quantum phenomena under 3D topology. Note: This paper is available in English, Traditional Chinese, and Simplified Chinese versions.