Yoshiki Ueoka

Domain Number Mathematics V : Two-Endpoint Bessel Decoupling and Representation-Dependent Certification for Jacobi Systems

Domain number mathematics treats the requested resolution, representation class, and certification language as part of the mathematical problem data. Previous papers developed this viewpoint for finite relation networks, finite differential and integral relations, canonical-chart...

Domain Number Mathematics V : Two-Endpoint Bessel Decoupling and Representation-Dependent Certification for Jacobi Systems

Domain number mathematics treats the requested resolution, representation class, and certification language as part of the mathematical problem data. Previous papers developed this viewpoint for finite relation networks, finite differential and integral relations, canonical-chart...

Critical Partition Function Theory IX: From Algebraic Critical Endpoints to Lambert-W Zero Ladders

We connect an algebraic endpoint of a positive critical measure to the complex zeros generated by finite atomicization. The starting point is the Wright interior of Critical Partition Function Theory (CPFT) III, where the inverse mean map develops a finite backward endpoint $a_{\...

Domain Number Mathematics IV: Finite-Resolution Integral Charts, Positive-Density Geometry, and Unit-Circle Weight Certification

Domain number mathematics treats requested mathematical resolution as part of the problem data and permits finite relations or regions to be exact target objects. Earlier work developed this viewpoint for dependency-preserving rational relation networks, finite increment calculus...

Finite Gluing of Anderson Green Functions from Clean Crystals to Strong Disorder

We present a finite-gluing framework for Anderson Green functions that retains the clean-crystal and strong-disorder limits as distinct analytic anchors. The weak anchor is a resolvent expansion about a freely chosen clean reference Hamiltonian. The strong anchor is a random atom...

Finite Gluing of Anderson Green Functions from Clean Crystals to Strong Disorder

We present a finite-gluing framework for Anderson Green functions that retains the clean-crystal and strong-disorder limits as distinct analytic anchors. The weak anchor is a resolvent expansion about a freely chosen clean reference Hamiltonian. The strong anchor is a random atom...

Domain Number Mathematics IV: Finite-Resolution Integral Charts, Positive-Density Geometry, and Unit-Circle Weight Certification

Domain number mathematics treats requested mathematical resolution as part of the problem data and permits finite relations or regions to be exact target objects. Earlier work developed this viewpoint for dependency-preserving rational relation networks, finite increment calculus...

Domain Number Mathematics I : Resolution as Problem Data, Dependency-Preserving Finite Relations, and FRN-2

Many mathematical problems are posed at a level of resolution stronger than what is required by a given task. This paper develops a framework in which requested mathematical resolution is treated as explicit problem data rather than only as a numerical-accuracy parameter. The con...

Critical Partition Function Theory

We formulate a critical-partition-function theory in which a generalized partition function and the differential geometry of its logarithm are primary, while spatial dimension, symmetry, and interaction structure are treated, when identifiable, as quantities to be reconstructed f...

Dual-Anchor Finite Gluing of Anderson Green Functions on General Finite Graphs

We formulate and numerically test a dual-anchor finite-gluing construction for disorder-dependent Anderson Green functions on general finite graphs. For a common realization-dependent Hamiltonian $H_\omega(W)=H_{\rm crys}+WU_\omega,$ the weak-disorder anchor is the ordinary resol...

Domain Number Mathematics III: Finite-Resolution Canonical-Chart Coverage for Second-Order Differential Equations

Domain number mathematics treats requested mathematical resolution as part of the problem data and permits relation-valued or region-valued targets to be exact objects. This paper develops a concrete differential-equation application of that viewpoint. The underlying transformati...

Dual-Anchor Finite Gluing of Anderson Green Functions on General Finite Graphs

We formulate and numerically test a dual-anchor finite-gluing construction for disorder-dependent Anderson Green functions on general finite graphs. For a common realization-dependent Hamiltonian $H_\omega(W)=H_{\rm crys}+WU_\omega,$ the weak-disorder anchor is the ordinary resol...

Domain Number Mathematics I : Resolution as Problem Data, Dependency-Preserving Finite Relations, and FRN-2

Many mathematical problems are posed at a level of resolution stronger than what is required by a given task. This paper develops a framework in which requested mathematical resolution is treated as explicit problem data rather than only as a numerical-accuracy parameter. The con...

Domain Number Mathematics II : Finite Increment Calculus, Differential and Summation Domains, and Resolution-Preserving Gluing

Domain number mathematics treats requested mathematical resolution as part of the problem data and permits relation-valued or region-valued targets to serve as exact mathematical objects. The first paper developed this viewpoint for arithmetic, algebraic relations, dependency-pre...

Domain Number Mathematics III: Finite-Resolution Canonical-Chart Coverage for Second-Order Differential Equations

Domain number mathematics treats requested mathematical resolution as part of the problem data and permits relation-valued or region-valued targets to be exact objects. This paper develops a concrete differential-equation application of that viewpoint. The underlying transformati...

All-degree polynomial first-integral rigidity on a Darboux locus of a Chazy-type family

We study polynomial first integrals of the two-parameter third-order family $p'''+p p''+(b+1)(p')^2+(q p^2+e)p'=0,\qquad e\in\C^\times.$ After the polynomial change of variables \(y=p'\), \(w=p''+p p'\), the associated three-dimensional vector field contains a distinguished Darbo...

All-degree polynomial first-integral rigidity on a Darboux locus of a Chazy-type family

We study polynomial first integrals of the two-parameter third-order family $p'''+p p''+(b+1)(p')^2+(q p^2+e)p'=0,\qquad e\in\C^\times.$ After the polynomial change of variables \(y=p'\), \(w=p''+p p'\), the associated three-dimensional vector field contains a distinguished Darbo...

All-Order Polynomial First-Integral Rigidity on the Toda-Compatible Slice of a Chazy-Type Family

We classify, without an a priori degree bound, the polynomial first integrals of the autonomous third-order family $p'''+p p''+k(p')^2+\left(\frac{p^2}{4}-\sigma\right)p'=0, (k,\sigma)\in\C^2.$ This is the constant-shift slice characterized by $2K'(p)=p$ in the more general equat...

All-Order Polynomial First-Integral Rigidity on the Toda-Compatible Slice of a Chazy-Type Family

We classify, without an a priori degree bound, the polynomial first integrals of the autonomous third-order family $p'''+p p''+k(p')^2+\left(\frac{p^2}{4}-\sigma\right)p'=0, (k,\sigma)\in\C^2.$ This is the constant-shift slice characterized by $2K'(p)=p$ in the more general equat...

Critical Partition Function Theory VI

We study the rank-one scaling equation that arises in the two-variable sector of Critical Partition Function Theory (CPFT), $a\Phi\Phi''+bu\Phi'\Phi''-c(\Phi')^2=0,$ with normalized local data $\Phi(0)=\Phi'(0)=1$. The individual ingredients used below---nonlocal linearization of...