Yoshiki Ueoka

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

Resonant Terminal Layers and Critical Interfaces in Finite Collatz Bridges

We study finite orbit segments of the shortcut Collatz map in shifted coordinates. A terminal word is called multiplier-supercritical when its linear multiplier exceeds one. For a bridge ending at height $k$ with overshoot $U$, we prove an exact depth-by-depth criterion for termi...

Observation Transport and Synchronization Contracts in Finite Legal Reply Systems of Shogi

A legal candidate move in shogi induces a finite system of all legal replies. Previous work represented such a system by reply observations, discernibility sets, an inclusion-minimal discernibility skeleton, and a profile symbol. This paper studies what happens when the observati...