Yoshiki Ueoka

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 V

We develop a local physical-size scale-flow theory for critical phenomena within critical partition-function theory (CPFT), without assuming a renormalization-group transformation, a Hamiltonian, disorder, randomness, or a nonlinear sigma model as primitive input. The starting po...

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...

Critical Partition Function Theory II

We formulate a reconstruction theory for universal critical partition-function representatives in the presence of irrelevant corrections. The central object is the leading critical component of the logarithmic partition function, $K_c=\log Z_c$, defined through a weighted scaling...

Critical Partition Function Theory II

We formulate a reconstruction theory for universal critical partition-function representatives in the presence of irrelevant corrections. The central object is the leading critical component of the logarithmic partition function, $K_c=\log Z_c$, defined through a weighted scaling...

Maximal Compound Curvature as a Complete Observable for Finite Partition Functions

Let $Z^g(\beta)=\sum_{j=1}^{m}g_j e^{-\beta e_j},$ $\qquad 0<g_j,\qquad e_1<\cdots<e_m,$ be a primitive finite weighted partition function. Its Hankel compound partition functions are $\tau_r^g(\beta)$ $=\det\!\bigl(M_{a+b}(\beta)\bigr)_{a,b=0}^{r-1},$ $\qquad$ $M_n(\beta)=\sum_j...

Finite Partition-Function Curvatures

Let $Z(\beta)=\sum_{j=1}^{m}g_j e^{-\beta e_j},\qquad$ $0<g_j,\quad e_1<\cdots<e_m,$ be a primitive finite weighted canonical partition function, and let \(K=(\log Z)''\) be its log-partition curvature. Physically, \(K\) is the canonical energy variance and satisfies \(C_V=k_B\be...

Boundary-Generated Overlap Measures under Principal Jacobi Extensions

Let $H_n$ be a finite real symmetric Jacobi matrix, let $H_nu=\lambda u$, and embed $u$ by zeros into a larger principal Jacobi extension $\widehat H$. The squared overlaps of the embedded vector with the eigenvectors of $\widehat H$ define a probability measure $\nu$ on shifted...

Bounded Ownership-Transfer Ranks and Multilayer Strategy Certificates in Finite Shogi Legal-Move Systems

We study a finite-horizon reachability problem in finite state systems generated by the ordinary local movement, promotion, drop, and King-safety rules of shogi. A fixed non-king physical token is labelled by provenance, and the terminal event is its first ownership transfer to t...

Maximal Compound Curvature as a Complete Observable for Finite Partition Functions

Let $Z^g(\beta)=\sum_{j=1}^{m}g_j e^{-\beta e_j},$ $\qquad 0<g_j,\qquad e_1<\cdots<e_m,$ be a primitive finite weighted partition function. Its Hankel compound partition functions are $\tau_r^g(\beta)$ $=\det\!\bigl(M_{a+b}(\beta)\bigr)_{a,b=0}^{r-1},$ $\qquad$ $M_n(\beta)=\sum_j...

Finite Partition-Function Curvatures

Let $Z(\beta)=\sum_{j=1}^{m}g_j e^{-\beta e_j},\qquad$ $0<g_j,\quad e_1<\cdots<e_m,$ be a primitive finite weighted canonical partition function, and let \(K=(\log Z)''\) be its log-partition curvature. Physically, \(K\) is the canonical energy variance and satisfies \(C_V=k_B\be...

Directional Discriminant Packets and Bounded Scalar-Profile Loci for Primitive Binary Quadratic Germs

Let $q=a u^2+2buv+c v^2\in k[[x,y]]\otimes\Sym^2(V^*)$ be a primitive binary quadratic germ over an algebraically closed field of characteristic zero, and let $D=\Disc(q)=b^2-ac$. Along a chosen path of point blowups, the lowest $\Sym^2(V^*)$-valued coefficient packets and the sc...

Perfect-Power Quadratic-Trace Lucas Towers

Let $r,s\in\Z$ be coprime, with $r$ odd and $s\ne0$, and put $z=r+s\sqrt{-2},\qquad D=r^2-2s^2,\qquad Q=r^2+2s^2,$ $B_n=\frac{z^{2n}+\bar z^{2n}}2.$ Assume that, for an odd integer $f\ge3$, one has a perfect-power endpoint $B_f=\sigma A^f$ with $\sigma\in\{\pm1\}$ and $A>0$. For...

Target-Relative Provenance Requests and Versioned Observation Contracts in Finite Legal Reply Systems of Shogi

We study finite observation systems in which a visible value is always recorded, while one provenance coordinate is requested only on selected visible fibers. The omission event is typed as \(\NR\), rather than represented as a missing or null provenance value. For an episode sys...

Same-Label Sibling Staircases for Primitive Binary Quadratic Germs

Let $q=a u^2+2buv+c v^2\in k[[x,y]]\otimes\Sym^2(V^*)$ be a primitive binary quadratic germ over an algebraically closed field of characteristic zero. We study the normalized low-cost same-label fork $B_3\longrightarrow(B_1,B_1),$ where the parent and both branch children have th...

Chronological Residual Quotients and Constant-Coordinate Certificate Kernels in Finite Legal Reply Systems of Shogi

We develop a chronological certificate theory for finite legal-reply systems arising from shogi. At each checkpoint, complete legal replies induce a finite full carrier relation together with mediator-wise projected witness sets. Future checkpoints act by synchronized intersectio...

Exact Root-Label Realization Loci in Low-Cost Proximity-Decorated Binary Quadratic Paths

Let $q\in k[[x,y]]\otimes\Sym^2(V^*)$ be a primitive framed binary quadratic germ over an algebraically closed field of characteristic zero. A maximal primitive blowup path carries multiplicities, free/satellite proximity, and exceptional types $B$, $M$, and $N$, where a constant...

Projective-Class Transport and Exact Low-Cost Realization of Proximity-Decorated Binary Quadratic Paths

Let $q\in k[[x,y]]\otimes\Sym^2(V^*)$ be a primitive framed binary quadratic germ over an algebraically closed field of characteristic zero. A maximal primitive blowup path carries multiplicities, free/satellite proximity, and three exceptional types: constant-root branch $B$, mo...

Target-Relative Provenance Requests and Versioned Observation Contracts in Finite Legal Reply Systems of Shogi

We study finite observation systems in which a visible value is always recorded, while one provenance coordinate is requested only on selected visible fibers. The omission event is typed as \(\NR\), rather than represented as a missing or null provenance value. For an episode sys...