Uniqueness
View article: Supplementary Material – Short Communication for the Convexity–Coercivity Criterion
Supplementary Material – Short Communication for the Convexity–Coercivity Criterion Open
We present a concise mathematical framework guaranteeing existence, uniqueness, and stability of minimizers for variational functionals of the form E[u] = ∫_Ω ( W(∇u(x)) + V(u(x)) ) dx, under explicit convexity and growth conditions (C1)–(…
View article: Інтегро-диференціальні системи стохастичних параболічних рівнянь зі змінними показниками нелінійності
Інтегро-диференціальні системи стохастичних параболічних рівнянь зі змінними показниками нелінійності Open
Some nonlinear second order parabolic system with the variable exponents of nonlinearity, integral term, and the white noise is considered. The existance and uniqueness of the weak solution for the corresponding initial-boundary value prob…
View article: HTTM: Head-wise Temporal Token Merging for Faster VGGT
HTTM: Head-wise Temporal Token Merging for Faster VGGT Open
The Visual Geometry Grounded Transformer (VGGT) marks a significant leap forward in 3D scene reconstruction, as it is the first model that directly infers all key 3D attributes (camera poses, depths, and dense geometry) jointly in one pass…
View article: Model of Three Species Commensalism-Amensalism Symbiosis with Beddington-DeAngelis Functional Responses
Model of Three Species Commensalism-Amensalism Symbiosis with Beddington-DeAngelis Functional Responses Open
This study investigates the dynamical behavior of a three species ecological system involving unilateral interactions of commensalism and amensalism with Beddington–DeAngelis functional responses. The positivity, boundedness, existence, an…
View article: Multivalued backward stochastic differential equations with jumps and moving boundary
Multivalued backward stochastic differential equations with jumps and moving boundary Open
We prove existence and uniqueness for a one-dimensional multivalued backward stochastic differential equation with jumps. The equation involves a time-indexed family of maximal monotone operators $k_t(\cdot)$ associated with increasing fun…
View article: GaoZheng G-Framework and GaoZheng G-Algebra: Applied Mathematics Volume II – LBOPB, Life-Science Monoids, and Generative Precision Medicine
GaoZheng G-Framework and GaoZheng G-Algebra: Applied Mathematics Volume II – LBOPB, Life-Science Monoids, and Generative Precision Medicine Open
This second applied-mathematics volume (Applied Mathematics Volume II) extends the GaoZheng G-Framework and GaoZheng G-Algebra from law-space field theories, GRL, and quantum computing (developed in the first applications volume) to life s…
View article: Towards Computational UIP in Cubical Agda
Towards Computational UIP in Cubical Agda Open
Some advantages of Cubical Type Theory, as implemented by Cubical Agda, over intensional Martin-Löf Type Theory include Quotient Inductive Types (QITs), which exist as instances of Higher Inductive Types, and functional extensionality, whi…
View article: Density of rainbow triangles and properly colored $K_4$'s
Density of rainbow triangles and properly colored $K_4$'s Open
T.-W. Chao and H.-H. H. Yu showed in 2023 that a graph with $R$ red, $G$ green, and $B$ blue edges has at most $\sqrt{2 RGB}$ rainbow triangles. They proved this bound using the entropy method. We give a computer-free flag-algebra proof of…
View article: Source Code and Data Model Suite for The Primordial Ignition Hypothesis (PIH): Coupled Kinetic Advantage Simulator (CKAS) and Foundational HISS Models
Source Code and Data Model Suite for The Primordial Ignition Hypothesis (PIH): Coupled Kinetic Advantage Simulator (CKAS) and Foundational HISS Models Open
This archive contains the complete source code and data models used to generate the quantitative proofs presented in the manuscript, "The Primordial Ignition Hypothesis (PIH)." The framework verifies that life's emergence is governed by an…
View article: HTTM: Head-wise Temporal Token Merging for Faster VGGT
HTTM: Head-wise Temporal Token Merging for Faster VGGT Open
The Visual Geometry Grounded Transformer (VGGT) marks a significant leap forward in 3D scene reconstruction, as it is the first model that directly infers all key 3D attributes (camera poses, depths, and dense geometry) jointly in one pass…
View article: Simultaneously recover two constant coefficients and a polygon with a single pair of Cauchy data for the Helmholtz equation
Simultaneously recover two constant coefficients and a polygon with a single pair of Cauchy data for the Helmholtz equation Open
This paper is concerned with an inverse boundary value problem for the Helmholtz equation over a bounded domain. The aim is to reconstruct two constant coefficients together with the location and shape of a Dirichlet polygonal obstacle fro…
View article: Fractional-Order Modeling and Stability Analysis of HIV Infection with and Without Antiretroviral Therapy Treatment
Fractional-Order Modeling and Stability Analysis of HIV Infection with and Without Antiretroviral Therapy Treatment Open
This article formulates and examines a fractional-order model for Human Immunodeficiency Virus (HIV) infection using Caputo’s derivative in order to model memory-reliant dynamics. The model describes interactions among uninfected, infected…
View article: Consistency–Defect Gradient Flows and No–Meta Self–Purification in Value–Anchored Multi–Agent Systems
Consistency–Defect Gradient Flows and No–Meta Self–Purification in Value–Anchored Multi–Agent Systems Open
This paper develops a structural “blueprint” for no-meta self-purification in value-anchored multi-agent systems built on entropy–transport (ET) gradient flows. The starting point is an analytic background where macroscopic dynamics of law…
View article: Curvature-driven pattern formation in biomembranes: A gradient flow approach
Curvature-driven pattern formation in biomembranes: A gradient flow approach Open
In this work, we study a phase-field model for curvature-driven pattern formation in biomembranes. The model is derived as a gradient flow of an energy functional that approximates the two-phase Canham--Helfrich energy. This leads to a Cah…
View article: Radon-Transform-Based Similarity Measures for Non-Affine Deformable Image Registration
Radon-Transform-Based Similarity Measures for Non-Affine Deformable Image Registration Open
Deformable Image Registration (DIR) is a fundamental problem in biomedical imaging that analyzes organ displacements and deformations by comparing images from different states. DIR becomes particularly challenging when analyzing images tha…
View article: PSAN Tri-Fork: Momentum-Gated Kuramoto Control for Human-AI Cognitive Synchronization
PSAN Tri-Fork: Momentum-Gated Kuramoto Control for Human-AI Cognitive Synchronization Open
We present the Phase-Synchronized Attention Network (PSAN) Tri-Fork architecture—the first closed-loop cognitive control system that achieves predictive human-AI phase-locking via momentum-gated Kuramoto coherence classification (τ_R(t) = …
View article: Generalized Sobolev Embeddings on $L^p$ Spaces with Respect to Anisotropic Radon Measures
Generalized Sobolev Embeddings on $L^p$ Spaces with Respect to Anisotropic Radon Measures Open
This paper investigates generalized Sobolev embedding theorems in the context of $L^p$ spaces defined with respect to anisotropic Radon measures. Classical Sobolev embeddings are fundamental in analysis, linking different function spaces a…
View article: The Landscape of Tensor Rank: Algorithmic Complexity and Geometric Constraints
The Landscape of Tensor Rank: Algorithmic Complexity and Geometric Constraints Open
Tensor decomposition, and specifically the determination of tensor rank, presents a fundamental challenge in diverse scientific and engineering disciplines, from signal processing and data analysis to quantum computing and algebraic comple…
View article: Tracial States and Rigidity for Simple C*-Algebras
Tracial States and Rigidity for Simple C*-Algebras Open
This paper explores the intricate relationship between tracial states and various notions of rigidity for simple C*-algebras. Tracial states, as positive, normalized, and trace-preserving linear functionals, provide a crucial link between …
View article: Ergodic Theory for Fractional SDE with Singular Coefficients
Ergodic Theory for Fractional SDE with Singular Coefficients Open
We show existence and uniqueness of invariant measures for SDE of the form \[ dX_t = g(X_t)dt + u(X_t)dt + dW^H_t \] where $W^H$ is a fractional Brownian motion (fBm) with Hurst parameter $H\in (0,\frac{1}{2})$, $u$ is a linearly dispersiv…
View article: Cauchy problem for a Schrödinger-type equation related to the Riemann zeta function
Cauchy problem for a Schrödinger-type equation related to the Riemann zeta function Open
We study the Cauchy problem in the space $H^1(Σ)$ for a nonlinear damped Schrödinger equation of the form \[ i u_t + Δu + i λu \, ζ(|u|+1) = 0, \quad u(0,x) = u_0, \] where $ζ$ denotes the Riemann zeta function. This equation involves a da…
View article: Feldtheorie V5: A Fractal Governance System for Structural Isomorphism Research ->The Regime Integration Gradient (v_RIG): A Fundamental Velocity Scale for Consciousness as 2D→3D Information Transfer
Feldtheorie V5: A Fractal Governance System for Structural Isomorphism Research ->The Regime Integration Gradient (v_RIG): A Fundamental Velocity Scale for Consciousness as 2D→3D Information Transfer Open
This short preprint presents a supplementary theoretical exploration accompanying the Feldtheorie V6 publication. It outlines a side‑theory connecting entropy governance duality with discrete spacetime concepts (“Tesseract‑Zeitscheiben‑Phy…
View article: A Python Engine and Exact Lattice Construction for Rotational Tessellations from the Heronian 13–14–15 Triangle
A Python Engine and Exact Lattice Construction for Rotational Tessellations from the Heronian 13–14–15 Triangle Open
We study the classical Heronian triangle with side lengths 13–14–15 and its role as a building block for exact planar tessellations with 12-fold rotational symmetry. Starting from explicit Cartesian coordinates, we construct a fundamental …
View article: Non-perturbative Yang-Mills Mass Gap, Yang–Mills–Black-Hole Equivalence Black-Hole Paradox Resolution Gravity Emergence and "Gravity Death" at the Reversible Limit UNDER THE VOID BOUNDARY CONDITION
Non-perturbative Yang-Mills Mass Gap, Yang–Mills–Black-Hole Equivalence Black-Hole Paradox Resolution Gravity Emergence and "Gravity Death" at the Reversible Limit UNDER THE VOID BOUNDARY CONDITION Open
View article: Cauchy problem for a Schrödinger-type equation related to the Riemann zeta function
Cauchy problem for a Schrödinger-type equation related to the Riemann zeta function Open
We study the Cauchy problem in the space $H^1(Σ)$ for a nonlinear damped Schrödinger equation of the form \[ i u_t + Δu + i λu \, ζ(|u|+1) = 0, \quad u(0,x) = u_0, \] where $ζ$ denotes the Riemann zeta function. This equation involves a da…
View article: Error Controllability Under Finite-Order Discipline: PSWF/DPSS Extremal Windows Uniqueness, Integer Leading Terms (Spectral Flow/Index of Projection Pairs), and $10^{-3
Error Controllability Under Finite-Order Discipline: PSWF/DPSS Extremal Windows Uniqueness, Integer Leading Terms (Spectral Flow/Index of Projection Pairs), and $10^{-3 Open
Under unified Fourier normalization \widehat f(\xi)=\int_{\mathbb R}f(t)e^{-2\pi i t\xi}\,dt (frequency in cycles), we construct error discipline around time-limiting--band-limiting concatenated operators: windowing main leakage, multiplic…
View article: Maximal Solutions and Stochastic Free Boundary Formulations for Stochastic Willmore and Surface Diffusion Flows on $\R^2$
Maximal Solutions and Stochastic Free Boundary Formulations for Stochastic Willmore and Surface Diffusion Flows on $\R^2$ Open
We study the stochastic Willmore flow and the stochastic surface diffusion flow for closed or non-closed curves on $\mathbb{R}^2$ in this paper. We equivalently formulate them as a stochastic one-phase Stefan problem (or a stochastic free …
View article: TDRTC DYNAMICAL SPECTRAL CASCADES AND THE UNIQUENESS OF THE −5/3 SPECTRAL EXPONENT
TDRTC DYNAMICAL SPECTRAL CASCADES AND THE UNIQUENESS OF THE −5/3 SPECTRAL EXPONENT Open
Description This record contains the preprint: “TDRTC dynamical spectral cascades and the uniqueness of the -5/3 spectral exponent” Author: Ning Zhang (Independent Researcher, Hong Kong SAR, P.R. China) Contact: [email protected] Th…
View article: Geomagnetic Perturbations as Empirical Proxies for Non-Local Information Transfer: A Fully Satellite-Validatable Metric within the Swygert Theory of Everything AO (TSTOEAO)
Geomagnetic Perturbations as Empirical Proxies for Non-Local Information Transfer: A Fully Satellite-Validatable Metric within the Swygert Theory of Everything AO (TSTOEAO) Open
This paper introduces the first satellite-validatable metric for detecting non-local information transfer through geomagnetic fluctuations within the Swygert Theory of Everything AO (TSTOEAO). Using GOES-16/17, Swarm A/B/C, and INTERMAGNET…
View article: Generalized Sobolev Embeddings on $L^p$ Spaces with Respect to Anisotropic Radon Measures
Generalized Sobolev Embeddings on $L^p$ Spaces with Respect to Anisotropic Radon Measures Open
This paper investigates generalized Sobolev embedding theorems in the context of $L^p$ spaces defined with respect to anisotropic Radon measures. Classical Sobolev embeddings are fundamental in analysis, linking different function spaces a…