Yoshiki Ueoka

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...

Spectral Endomorphism Factorization and Exceptional Degree-Two Root Correspondences in Codimension-Three Lefschetz Failure

Let $X$ be a smooth rational surface obtained by resolving the generically reduced quadratic-root correspondence attached to a controlled codimension-three weak Lefschetz failure. The preceding Pfaffian analysis produces a pulled-back rank-two quotient bundle $Q$, a nowhere-zero...

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...

Product-Core Stratification of Large Effective Multiplier Rank in Symmetric Frobenius Algebras

Let $A$ be a $2n$-dimensional commutative symmetric Frobenius algebra over a field $k$, let $U=V^\perp$ with $\dim U=\dim V=n$, let $L\subset A$ contain the unit, and consider the Frobenius trilinear form induced by multiplication on $(L/k1)\times U\times V$. Write $(c,a,b)$ for...

Canonical Chain–Node Encoding and Finite-Width Return Renormalization for the Accelerated Collatz Map

We select a canonical orientation of an alternating signed-binary representation of positive odd integers and refine it into a chain--node encoding, called the canonical CPE. The signed representation itself is classical in spirit and closely matches the alternating binary system...

Resonant Gap Certificates and Rooted Dyadic Ancestry in Finite Collatz Record Ladders

We study first passages between consecutive dyadic record thresholds for the shortcut Collatz map, using shifted coordinates in which the two branches are \(\A(x)=3x/2\) on even states and \(\B(x)=(x+1)/2\) on odd states. A record endpoint carries a terminal layer of suffixes who...

An Oscillatory Christoffel--Darboux Transfer from Finite-Height RH Verification to Local Toeplitz--Hankel Positivity

Let $\xi(s)=\frac12s(s-1)\pi^{-s/2}\Gamma(s/2)\zeta(s),\qquad$ $F(x)=\frac{\xi'}{\xi}\!\left(\frac1{1-x}\right)=\sum_{m\ge0}f_mx^m,$ and define the symmetric Toeplitz--Hankel coefficients $g_{ij}=f_{|i-j|}-f_{i+j+1}+\delta_{ij}f_0.$ The adjacent matrices $M_n=\begin{pmatrix}g_{nn...

Spectral Endomorphism Factorization and Exceptional Degree-Two Root Correspondences in Codimension-Three Lefschetz Failure

Let $X$ be a smooth rational surface obtained by resolving the generically reduced quadratic-root correspondence attached to a controlled codimension-three weak Lefschetz failure. The preceding Pfaffian analysis produces a pulled-back rank-two quotient bundle $Q$, a nowhere-zero...

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...

Quadratic Apolar Residues and Pfaffian Root Correspondences in Codimension-Three Lefschetz Failure

Let $\kk$ be an algebraically closed field of characteristic zero, let $S=\Sym(V)$ with $\dim V=3$, and let $A=S/\Ann(F)$ be a compressed standard-graded Artinian Gorenstein algebra of socle degree $2m+1$, where $m\ge2$. We study a corank-one failure of multiplication by a genera...

Discernibility Profiles and Mechanism Repertoires of Legal Reply Systems in Shogi

For a fixed legal shogi position and a legal candidate move, consider the complete finite set of legal replies. We observe each reply through three shogi-specific components: actor action edges lost after the reply ($\Lost$), actor action edges newly gained ($\Gain$), and the com...

Product-Core Stratification of Large Effective Multiplier Rank in Symmetric Frobenius Algebras

Let $A$ be a $2n$-dimensional commutative symmetric Frobenius algebra over a field $k$, let $U=V^\perp$ with $\dim U=\dim V=n$, let $L\subset A$ contain the unit, and consider the Frobenius trilinear form induced by multiplication on $(L/k1)\times U\times V$. Write $(c,a,b)$ for...

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...

Directional Jet Packets, Euclidean Resolution Forests, and Sharp Low-Cost Root Returns for Primitive Binary Quadratic Germs

Let $R=\kk[[x,y]]$ over an algebraically closed field of characteristic zero, and let $q=a u^2+2buv+c v^2\in R\otimes_\kk\Sym^2(V^*)$ be a primitive binary quadratic germ with nonzero discriminant $\Delta(q)=b^2-ac$. Iterated point blowups of the coefficient ideal $(a,b,c)$ produ...

Discernibility Profiles and Mechanism Repertoires of Legal Reply Systems in Shogi

For a fixed legal shogi position and a legal candidate move, consider the complete finite set of legal replies. We observe each reply through three shogi-specific components: actor action edges lost after the reply ($\Lost$), actor action edges newly gained ($\Gain$), and the com...

Canonical Chain–Node Encoding and Finite-Width Return Renormalization for the Accelerated Collatz Map

We select a canonical orientation of an alternating signed-binary representation of positive odd integers and refine it into a chain--node encoding, called the canonical CPE. The signed representation itself is classical in spirit and closely matches the alternating binary system...

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...

Quadratic Apolar Residues and Pfaffian Root Correspondences in Codimension-Three Lefschetz Failure

Let $\kk$ be an algebraically closed field of characteristic zero, let $S=\Sym(V)$ with $\dim V=3$, and let $A=S/\Ann(F)$ be a compressed standard-graded Artinian Gorenstein algebra of socle degree $2m+1$, where $m\ge2$. We study a corank-one failure of multiplication by a genera...

Resonant Gap Certificates and Rooted Dyadic Ancestry in Finite Collatz Record Ladders

We study first passages between consecutive dyadic record thresholds for the shortcut Collatz map, using shifted coordinates in which the two branches are \(\A(x)=3x/2\) on even states and \(\B(x)=(x+1)/2\) on odd states. A record endpoint carries a terminal layer of suffixes who...

Sharp Defect Envelopes for Orthogonal-Dual Product Spaces

Let $A$ be a finite-dimensional commutative symmetric Frobenius algebra over a field $k$, with $\dim_k A=2n$. Let $U\subset A$ have dimension $n$, put $V=U^\perp$, and let $L\subset A$ contain $1$ with $\dim_k L=m+1$. Classical linear additive combinatorics minimizes a single pro...