Papers

Selected Works / Publications

These manuscripts represent JTPMATH's (non-exhaustive) research in analytic number theory, ergodic theory, and high-dimensional probability, introducing new frameworks such as Burns Law, λ-divergence, and oscillatory prime models. The works below are organized by research area.

I. Analytic Number Theory, Prime Structure, and Burns Law

• Prime Gaps, Falconer Distance, and Burns Law: Literature Revisited
  August 2025
• Determinants on Logarithmically-Traceable Invertibles and the Commutator Identity
  September 2025
• A Determinant Functional on Logarithmically Traceable Invertibles
  September 2025
• Incompatibility of Riemann-type Bounds with Collatz Convergence under Burns Law
  October 2025
• Prime Gap Instability and Collapse of the Riemann Hypothesis
  March 2025
• The Prime Factorization Law of Exponentiation: A Proof of Beal’s Theorem
  March 2025

II. Ergodic Theory, Mixing, and Random Dynamics

• k-Fold Mixing from 2-Fold Mixing via Conditional Expectation
  April 2025
• Ergodic Variance Amplification and the Failure of Square-Root Control for Möbius Averages
  September 2025
• AI-Augmented Derivation of the Bellec–Fritz Bound on SP{x,1+x,2+x,3+2x,4}
  November 2025

III. High-Dimensional Probability, Geometry, and Analysis

• From Quadratic Forms to Curvature Flow: A High-Dimensional Probability Route to Geometric Evolution
  November 2025
• From Lenses to Moduli: A New Intuition for Teichmüller Space
  February 2025
• The Mean Value Property for Mean Curvature and Its Laplace-Type Equation
  February 2025
• Exploring I-adic Completion in Numerical and Algebraic Differential Equation Methods
  October 2024

IV. Interdisciplinary Mathematical Physics / Cognitive Systems

• Cognitive Physics: A Framework for Understanding Meaning as a Physical System
  February 2025
• On the Nonexistence of Free Rational Curves in Singular Fano Varieties
  March 2025
• Diffusion Geometry and the Additive Structure of the Primes
  March 2025