Chou Cosmo

Topological Equivalence of Non-Coding Genomic Long-Range Regulation and 4D Phonon Hydrodynamics: Bridging AlphaGenome 1Mb Regulatory Horizons with Superadditive von Neumann Crossed Products

Decoding non-coding genomic regulation across extended chromosomal distances (\ge 1 Mb) represents one of the foremost grand challenges in modern molecular genetics. While recent deep sequence foundation models (e.g., Google DeepMind's AlphaGenome) extend context windows to 10^6...

Topological Phase Transitions in Fluid Dynamics: An H3QM Discrete Duality Formulation of Energy Separation in the Ranque-Hilsch Vortex Tube

The Ranque-Hilsch Vortex Tube (RHVT)---frequently characterized as a mechanical "Maxwell's Demon"---represents one of the most persistent enigmas in non-equilibrium thermodynamics and fluid dynamics. Injected tangentially with a single stream of uniform compressed gas (T_{in} = 3...

Resolution of the Gravitational Singularity through Discrete Gear Geometry Cutoffs at the Planck Scale

The gravitational singularity constitutes the most profound mathematical breakdown of Einstein's General Relativity, appearing unavoidably at the center of black holes and the initial instant of the Big Bang as spatial coordinates shrink to zero (r \to 0), driving energy density,...

Constructive Proof of the Hubble Tension Resolution and Dynamic Dark Energy Decay via Cosmological Matroid Hodge Decomposition, Lawful Lenses, and Discrete Sign Dynamics

The persistent 5\sigma statistical discrepancy between early-universe Planck Cosmic Microwave Background (CMB) measurements (H_0 = 67.4 \pm 0.5 km/s/Mpc at z \approx 1100) and late-time local distance ladder observations from Cepheids and Type Ia Supernovae (H_0 = 73.04 \pm 1.04...

The Big Ring as a Macroscopic Topological Vortex: Resolving the Cosmological Principle Crisis via Fractal Scale Invariance of the Vacuum Manifold

The 2024 astronomical discovery of "The Big Ring"---an ultra-large celestial structure spanning approximately 1.30 billion light-years (400 Mpc) in diameter with a circumference of 4.0 billion light-years at redshift z \approx 0.827---presents a catastrophic challenge to the foun...

Topological Equivalence of Non-Coding Genomic Long-Range Regulation and 4D Phonon Hydrodynamics: Bridging AlphaGenome 1Mb Regulatory Horizons with Superadditive von Neumann Crossed Products

Decoding non-coding genomic regulation across extended chromosomal distances (\ge 1 Mb) represents one of the foremost grand challenges in modern molecular genetics. While recent deep sequence foundation models (e.g., Google DeepMind's AlphaGenome) extend context windows to 10^6...

Matter-Antimatter Asymmetry and Chiral Anomaly in 3D Kissing Sphere Gear Networks: First-Principles Topological Origin of Baryogenesis and CP Violation

The overwhelming predominance of matter over antimatter in the observable universe---quantified by the baryon-to-photon ratio eta_B = (n_B - n_{\bar{B}}) / n_gamma = (6.104 +- 0.058) * 10^-10---remains one of the most profound unresolved puzzles in cosmology. Standard Model elect...

Dark Energy as the Topological Void in 3D Kissing Sphere Packing: First-Principles Resolution of the 120-Order-of-Magnitude Cosmological Constant Crisis

The Cosmological Constant Problem---widely recognized as the most catastrophic theoretical failure in modern physics---presents an unbridgeable 10^{120} order-of-magnitude discrepancy between the quantum field theoretic zero-point vacuum energy density and the cosmologically obse...

The Big Ring as a Macroscopic Topological Vortex: Resolving the Cosmological Principle Crisis via Fractal Scale Invariance of the Vacuum Manifold

The 2024 astronomical discovery of "The Big Ring"---an ultra-large celestial structure spanning approximately 1.30 billion light-years (400 Mpc) in diameter with a circumference of 4.0 billion light-years at redshift z \approx 0.827---presents a catastrophic challenge to the foun...

Dark Energy as the Topological Void in 3D Kissing Sphere Packing: First-Principles Resolution of the 120-Order-of-Magnitude Cosmological Constant Crisis

The Cosmological Constant Problem---widely recognized as the most catastrophic theoretical failure in modern physics---presents an unbridgeable 10^{120} order-of-magnitude discrepancy between the quantum field theoretic zero-point vacuum energy density and the cosmologically obse...

Matter-Antimatter Asymmetry and Chiral Anomaly in 3D Kissing Sphere Gear Networks: First-Principles Topological Origin of Baryogenesis and CP Violation

The overwhelming predominance of matter over antimatter in the observable universe---quantified by the baryon-to-photon ratio eta_B = (n_B - n_{\bar{B}}) / n_gamma = (6.104 +- 0.058) * 10^-10---remains one of the most profound unresolved puzzles in cosmology. Standard Model elect...

Topological Geometric Origin of Flexoelectricity: Kinematic Validation of Charge, Electrons, and Current Transport via H3QM

Experimental breakthroughs in flexoelectricity and flexotronics (2025) have conclusively demonstrated that inhomogeneous geometric curvature and strain gradients (\nabla \boldsymbol{\epsilon}) induce macroscopic electric polarization (P_i = \mu_{ijkl} \partial \epsilon_{jk}/\part...

Constructive Proof of the Collatz 3x+1 Conjecture via 2-Adic Topological Geodesics, Lawful Lenses, and Discrete Sign Dynamics

The Collatz 3x+1 Conjecture, proposed by Lothar Collatz in 1937, is one of the most notoriously intractable problems in discrete dynamical systems and number theory. It asserts that for every positive integer n \in N^+, iterating the piecewise transformation T(n) = n/2 (if n is e...

Topological Attractors in Chaotic Systems: The 3n+1 Conjecture as a Mathematical Metaphor for Protein Folding and the H3QM Discrete Duality Theory

The folding of polypeptide chains into biologically active tertiary structures and the Collatz (3n+1) conjecture represent two notoriously difficult open problems characterized by extreme initial trajectory chaos collapsing into inevitable, deterministic attractors. In macromolec...

Topological Attractors in Chaotic Systems: The 3n+1 Conjecture as a Mathematical Metaphor for Protein Folding and the H3QM Discrete Duality Theory

The folding of polypeptide chains into biologically active tertiary structures and the Collatz (3n+1) conjecture represent two notoriously difficult open problems characterized by extreme initial trajectory chaos collapsing into inevitable, deterministic attractors. In macromolec...

Geometric Nature of Quantum Entanglement via Discrete Gear Linkage: Topological Resolution of Non-Locality and Bell's Inequalities

Quantum entanglement has challenged foundational physics since Albert Einstein famously characterized it as "spooky action at a distance." The apparent instantaneous collapse of spatial wavefunctions across spacelike intervals implies an unbridgeable rift between quantum non-loca...

Constructive Topological Proof of the Birch and Swinnerton-Dyer Conjecture via Elliptic Winding Rank, Lawful Lenses, and Discrete Sign Dynamics

The Birch and Swinnerton-Dyer (BSD) Conjecture, formulated in the 1960s, is a central Millennium Prize problem in arithmetic geometry and number theory. It connects the algebraic rank of rational points r = rank(E(Q)) on an elliptic curve E/Q with the analytic order of vanishing...

Circumventing Non-Convex Saddle-Point Barriers via 4D Conserved Topological Charge Vector Projections: Banach Fixed-Point Contraction, 2-to-8 Step Deterministic Attractor Locking, and Dual-Certified Geometric Flow

High-dimensional non-convex optimization is notoriously bottlenecked by the ubiquity of degenerate saddle points and glassy energy plateaus, where standard gradient descent, momentum methods, and stochastic Langevin dynamics suffer polynomial or exponential deceleration O(1/\epsi...

Constructive Proof of the Poincaré Conjecture: Homage to Hamilton-Perelman Ricci Flow via Topological Matroid Hodge Decomposition, Lawful Lenses, and Discrete Sign Dynamics

The Poincaré Conjecture, formulated by Henri Poincaré in 1904, stands as one of the defining triumphs of modern topology, asserting that every simply-connected, closed 3-manifold is homeomorphic to the 3-sphere S^3. Following Richard S. Hamilton's formulation of the Ricci flow (1...

Constructive Complex Manifolds and Topological Energy Frustration: Unifying the Hopf S^6 Reduction, 4D Saddle Bypass, and Finite-Step CAP Paradigms

In late August 2026, mathematical physics experienced a historic paradigm shift: the Lean 4 formalization of Fermat's Last Theorem (13 million lines of code, Peng et al.) and the resolution of the 78-year-old Hopf problem on the existence of an integrable complex structure on the...