Ren Matsuoka

Existence-Determining Configuration Theory

Description This paper introduces Existence-Determining Configuration Theory, a framework for representing and manipulating lattice configurations through sequences of directional arrow operations. Rather than relying on matrices or coordinate transformations to describe a config...

Geometric Vorticity Control ver.5 with Supplementary Material ver.3

This repository presents a constructive geometric framework for the three-dimensional incompressible Navier–Stokes equations based on Spherical Coherence Tube Density (CTD), together with its extension to moist atmospheric flows. The core method organises the velocity field into...

Geometric Vorticity Control ver.3 with Supplementary Material ver.2

This paper presents a constructive geometric framework for generating classical solutions to the three-dimensional incompressible Navier–Stokes equations. The proposed method extends the Coherence Tube Density (CTD) framework to a spherical formulation by introducing a three-dime...

Geometric Vorticity Control ver.2 with Supplementary Material

This paper presents a constructive geometric framework for generating classical solutions to the three-dimensional incompressible Navier–Stokes equations. The proposed method extends the Coherence Tube Density (CTD) framework to a spherical formulation by introducing a three-dime...

Geometric Vorticity Control ver.2 with Supplementary Material ver.2

This paper presents a constructive geometric framework for generating classical solutions to the three-dimensional incompressible Navier–Stokes equations. The proposed method extends the Coherence Tube Density (CTD) framework to a spherical formulation by introducing a three-dime...

Inversion Number

The Inversion Number framework presents a novel mathematical structure that distinguishes between numerical magnitude and spatial allocation. Unlike conventional reciprocal operations, inversion is formalized as a conditional transfer of quantity between two distinct spaces A and...

Exclusion Interaction

This work presents a novel theoretical framework treating Pauli-driven atomic repulsion as an independent fundamental interaction, distinct from electromagnetism. We demonstrate that the Pauli exclusion principle generates a short-range, spin-dependent repulsive force mediated by...

Exclusion Interaction

This work presents a novel theoretical framework treating Pauli-driven atomic repulsion as an independent fundamental interaction, distinct from electromagnetism. We demonstrate that the Pauli exclusion principle generates a short-range, spin-dependent repulsive force mediated by...

RM-ABC Conjecture ver4

Building upon the complementary foundations of Modulus Expansion and Anomalar Elliptic Geometry, this paper introduces and proves the RM-ABC Conjecture, an independent arithmetic formulation distinct from the classical Masser-Oesterle conjecture. By expressing the radical and res...