Experimental Physical Validation of Helical Holographic Quantum Mechanics (H3QM): Geometric Physics Derivations of Topological Insulators, Quantum Entanglement, and Weyl Semimetals — A Tribute to Breakthroughs by Xue, Pan, Fang, and Dai

Three landmark breakthroughs in modern condensed matter physics and quantum information science — the experimental discovery of the Quantum Anomalous Hall Effect (QAHE) by Xue Qikun's team, the satellite-based long-distance quantum entanglement and teleportation by Pan Jianwei's team, and the theoretical prediction and discovery of topological electronic materials and Weyl semimetals by Fang Zhong and Dai Xi's team — represent the highest achievements of contemporary experimental and materials physics. Expressing our deepest academic admiration for their pioneering contributions, this paper presents a complete geometric physical derivation of these three landmark experimental discoveries within the framework of 3D Helical Holographic Quantum Mechanics (H3QM). We prove that: (1) QAHE dissipationless edge states are isomorphic rigid wave-slidings of 3D Möbius topological knots (𝒲=1) along stress-minimum geodesic paths (W₁ optimal transport); (2) Quantum entanglement is the global phase-locking (P₁ = P₂ + Δφ) of connected topological phase threads inside a rigid vacuum gear network; (3) Weyl fermions and Fermi arcs in Weyl semimetals are phase-space singular attractors driven by 3D helicity (ℋ) and their holographic boundary cuts. We express profound recognition for their experimental data, demonstrating that their discoveries serve as the direct physical proofs of H3QM geometric physics. Note: This paper is available in English, Traditional Chinese, and Simplified Chinese versions.