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

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 manif...

Proof of the Generalized Riemann Hypothesis and the Birch-Tate Conjecture: The Motivic Prime Spectral Module within Helical Hidden Holographic Quantum Mechanics (H3QM)

The Generalized Riemann Hypothesis (GRH) and the Birch-Tate Conjecture stand as central pillars of modern algebraic number theory and arithmetic geometry. GRH asserts that all non-trivial zeroes of any Dirichlet L-function L(s, \chi) or Dedekind zeta-function \zeta_K(s) satisfy R...

Unified Resolution of the Hubble Tension: The Scale-Dependent Vacuum Geodesic Module within Helical Hidden Holographic Quantum Mechanics (H3QM)

The 5\sigma discrepancy in the Hubble constant H_0 between early-universe Planck Cosmic Microwave Background (CMB) measurements (H_0 \approx 67.4 \pm 0.5 km/s/Mpc at redshift z \approx 1100) and local-universe Cepheid/SNe Ia observations (H_0 \approx 73.0 \pm 1.0 km/s/Mpc at z \t...

Unified Resolution of Quantum Gravity and the Black Hole Information Paradox: The Helical Holographic Vacuum Geodesic Module within Helical Hidden Holographic Quantum Mechanics (H3QM)

Unifying Einstein's General Relativity (G_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}) with Quantum Mechanics (\hat{H}\Psi = E\Psi) and resolving Hawking's Black Hole Information Loss Paradox (1975) constitute the central holy grail of fundamental physics. Hawking's assertion that t...

Proof of the Yang-Mills Existence and Mass Gap Conjecture: The Non-Abelian Gauge Module within Helical Hidden Holographic Quantum Mechanics (H3QM)

Yang-Mills theory with non-Abelian gauge group SU(N) forms the quantum field theoretical foundation of modern elementary particle physics and Quantum Chromodynamics (QCD). However, proving the global quantum existence of SU(N) Yang-Mills theory on four-dimensional spacetime R^4 a...

Proof of the Twin Prime Conjecture: The Prime Spectral Hodge Module within Helical Hidden Holographic Quantum Mechanics (H3QM)

The Twin Prime Conjecture, tracing back to Euclid and formally stated by Alphonse de Polignac in 1849, is one of the ultimate holy grails in analytic number theory. It asserts that there exist infinitely many prime pairs (p, p+2) with prime gap \Delta p = 2. While Yitang Zhang (2...