Changmin Wei

A Variational Functional Equivalent Framework for the Riemann Hypothesis: Hilbert Kernel Spectral Measure Model (Chinese‑English Dual‑Document)

This paper constructs a quadratic energy functional defined on the space of signed Borel measures. Using a Hilbert integral kernel, the Riemann Hypothesis is equivalently trans formed into a non-negativity condition of the steady-state measure of gradient flow. The full framework...

A Framework of Computational Entropy and Border

This article work develops a coupled framework of computational entropy and the border‑rank theory within Geometric Complexity Theory (GCT). This article carefully distinguish statistical complexity of typical instances from worst‑case circuit complexity, and construct three self...

A Framework of Computational Entropy and Border

This article work develops a coupled framework of computational entropy and the border‑rank theory within Geometric Complexity Theory (GCT). This article carefully distinguish statistical complexity of typical instances from worst‑case circuit complexity, and construct three self...

Weighted Stratified Sieve and Lattice Matrix Noise Constraints: Formal Verification of the Twin Prime Conjecture(with Lean 4 Formalization)

This paper establishes a stratified weighted sieve framework based on lattice matrix noise identification, studying the asymptotic behavior of the twin prime counting function π2(X). By controlling the sieve remainder, an asymptotic main term estimate for the counting function is...

Limit Cycles as Topological Charges: A Lie Algebroid Cohomology Approach to Hilbert's 16th Problem

This paper presents a framework that reformulates the counting problem of isolated compact closed leaves (limit cycles) in polynomial foliations as a topological charge pairing problem on a singular adapted Lie algebroid, providing an explicit upper bound for the finiteness of li...

Proof of the High-Dimensional Kakeya Maximal Conjecture (n ≥ 4) Based on the UTE General Transport Equation Framework

The high-dimensional Kakeya maximal conjecture is a central open problem in harmonic analysis and geometric measure theory, systematically formulated by Fefferman in 1971. The two-dimensional case was proven by Davies in 1971; the three-dimensional case was completed by Wang and...

Limit Cycles as Topological Charges: A Lie Algebroid Cohomology Approach to Hilbert's 16th Problem

This paper presents a framework that reformulates the counting problem of isolated compact closed leaves (limit cycles) in polynomial foliations as a topological charge pairing problem on a singular adapted Lie algebroid, providing an explicit upper bound for the finiteness of li...

Global Regularity of the Three-Dimensional Navier–Stokes Equations via Geometric Regularization of the Universal Transport Equation

This paper addresses the existence and uniqueness of global smooth solutions to the three-dimensional incompressible Navier–Stokes equations. By constructing the Universal Transport Equation (UTE), the original system is lifted to a complete Riemannian manifold of uniformly negat...

Global Regularity of the Three-Dimensional Navier–Stokes Equations via Geometric Regularization of the Universal Transport Equation

This paper addresses the existence and uniqueness of global smooth solutions to the three-dimensional incompressible Navier–Stokes equations. By constructing the Universal Transport Equation (UTE), the original system is lifted to a complete Riemannian manifold of uniformly negat...

Universal Transport Equation and the Master Spectral Program: A Unifying Framework for the Millennium Problems

This paper proposes the Universal Transport Equation (UTE) and the Master Spectral Pro gram (MSP), extending Grothendieck’s theory of motives into the realm of noncommutative geometry and computational complexity, with the aim of providing a unified mathematical foundation for th...

A Complete and Rigorous Proof of the Jacobian Conjecture with Lean4 Formal Verification

This paper presents a rigorous mathematical proof of the complex-field Jacobianconjecture. The conjecture states that if �:ℂ� → ℂ� is a polynomial mapping whoseJacobian determinant is a non-zero constant over the entire domain, then � must bea polynomial automorphism of ℂ�. The p...

A Complete and Rigorous Proof of the Collatz Conjecture with Lean4 Formal Verification

This paper presents a complete, verifiable, and rigorous pure mathematical proof ofthe Collatz conjecture (the 3x+1 problem), based on asymptotic analysis of discreteiterative dynamical systems, the boundedness axiom of infinite orbits, and a strictcontradiction method. The stand...

A Complete and Rigorous Proof of the Jacobian Conjecture with Lean4 Formal Verification

This paper presents a rigorous mathematical proof of the complex-field Jacobianconjecture. The conjecture states that if �:ℂ� → ℂ� is a polynomial mapping whoseJacobian determinant is a non-zero constant over the entire domain, then � must bea polynomial automorphism of ℂ�. The p...

A Complete Proof That No Odd Perfect Numbers Exist, Version v2.0 (Chinese‑English Dual‑Document)

This archive contains two separate PDF manuscripts (Chinese and English versions v2.0). This paper presents a complete argument that no odd perfect numbers exist. Based on Euler’s classical structural characterization for odd perfect numbers, we combine multiplicative properties...

Spectral Geometric Prism Model: A Unified Field Framework via Finite-Action Constraints

We propose the Spectral Geometric Prism Model (SGPM), a unified field framework built upon finite-action topological constraints to resolve infrared divergences arising from noncompact physical spacetime. Single compactification via finite Yang–Mills action yields a topological h...

A Spectral-Geometric Proof of the Goldbach Conjecture

This paper presents a proof of the Goldbach Conjecture: every even integer2N ≥4 can be expressed as the sum of two prime numbers. The argument is builtwithin spectral geometry. We embed the prime-pair decomposition condition intothe zero locus of a singular spectral potential def...

A Spectral-Geometric Proof of the Goldbach Conjecture

This paper presents a proof of the Goldbach Conjecture: every even integer2N ≥4 can be expressed as the sum of two prime numbers. The argument is builtwithin spectral geometry. We embed the prime-pair decomposition condition intothe zero locus of a singular spectral potential def...

Global Regularity via Spherical Compactification for the 3D Navier–Stokes System

The global regularity problem of the three-dimensional incompressibleNavier–Stokes equations is one of the most famous unsolved mathematicalproblems listed on the Clay Mathematics Institute Millennium Prize list.Over the past decades, a large number of scholars have carried out e...

The Birch–Swinnerton-Dyer Conjecture via the Θ-Isomorphism and Arithmetic–Analytic Volume Correspondence

Version 2 (August 5, 2026): This paper presents a full unconditional global proof of the Birch–Swinnerton-Dyer conjecture for all rational elliptic curves, superseding Version 1. The proof establishes two core results: (1) the equality between algebraic rank and analytic rank; (2...