Yoshiki Ueoka

Query-Relative Quotients and Certificate-Carrying Observation Reducts

We present a framework for reducing a finite set of legal moves or legal replies in a fixed shogi position while preserving exactly the distinctions required by declared queries. Our preceding work first formalized complete positions and canonical legal actions as foundational ob...

Value-Space Contractions for Fixed-Diagonal Rank Fibers\\ of Symmetric Matrices in Characteristic Two

Let $K$ be a field of characteristic two and let $k=K^2$ be its subfield of squares. For a prescribed diagonal vector $d=(d_1,\ldots,d_n)\in K^n$, we study the symmetric matrices of diagonal $d$, graded by rank. The associated quasilinear quadratic form $q_d(x)=\sum_{i=1}^n d_i x...

Weak Vishik Equivalence and Linear $2$-Basis Blindness for Totally Singular Quadratic Forms

Let $K$ be a field of characteristic two, put $k=K^2$, and let $U\subset K$ be the value space of an anisotropic totally singular quadratic form. For $a\in K\setminus k$, the anisotropic dimension after the one-step extension $K(\sqrt a)/K$ is $\oneprofile_U(a)=\dim_{k(a)}k(a)U=\...

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...

Query-Relative Quotients and Certificate-Carrying Observation Reducts

We present a framework for reducing a finite set of legal moves or legal replies in a fixed shogi position while preserving exactly the distinctions required by declared queries. Our preceding work first formalized complete positions and canonical legal actions as foundational ob...

Weak Vishik Equivalence and Linear $2$-Basis Blindness for Totally Singular Quadratic Forms

Let $K$ be a field of characteristic two, put $k=K^2$, and let $U\subset K$ be the value space of an anisotropic totally singular quadratic form. For $a\in K\setminus k$, the anisotropic dimension after the one-step extension $K(\sqrt a)/K$ is $\oneprofile_U(a)=\dim_{k(a)}k(a)U=\...

A Local Toeplitz--Hankel Criterion Equivalent to the Riemann Hypothesis

Let $\xi(s)=\frac12 s(s-1)\pi^{-s/2}\Gamma(s/2)\zeta(s)$ be the completed Riemann xi-function, and let $F(x)=\frac{\xi'}{\xi}\!\left(\frac{1}{1-x}\right)=\sum_{n\ge 0} f_nx^n$ initially denote its germ at the origin. We introduce the real symmetric Toeplitz--Hankel matrix $c_{ij}...

Value-Space Contractions for Fixed-Diagonal Rank Fibers\\ of Symmetric Matrices in Characteristic Two

Let $K$ be a field of characteristic two and let $k=K^2$ be its subfield of squares. For a prescribed diagonal vector $d=(d_1,\ldots,d_n)\in K^n$, we study the symmetric matrices of diagonal $d$, graded by rank. The associated quasilinear quadratic form $q_d(x)=\sum_{i=1}^n d_i x...

A Sharp Multiplier-Dimension Threshold for Orthogonal-Dual Product Spaces

Let $A$ be a finite-dimensional commutative symmetric Frobenius algebra over a field $k$, let $\dim_k A=2n$, and let $U\subset A$ be an $n$-dimensional subspace with orthogonal complement $V=U^\perp$. For a multiplier subspace $L\subset A$, write $LU$ for the span of all products...

A Local Toeplitz--Hankel Criterion Equivalent to the Riemann Hypothesis

Let $\xi(s)=\frac12 s(s-1)\pi^{-s/2}\Gamma(s/2)\zeta(s)$ be the completed Riemann xi-function, and let $F(x)=\frac{\xi'}{\xi}\!\left(\frac{1}{1-x}\right)=\sum_{n\ge 0} f_nx^n$ initially denote its germ at the origin. We introduce the real symmetric Toeplitz--Hankel matrix $c_{ij}...

A Sharp Multiplier-Dimension Threshold for Orthogonal-Dual Product Spaces

Let $A$ be a finite-dimensional commutative symmetric Frobenius algebra over a field $k$, let $\dim_k A=2n$, and let $U\subset A$ be an $n$-dimensional subspace with orthogonal complement $V=U^\perp$. For a multiplier subspace $L\subset A$, write $LU$ for the span of all products...

Query-Relative Soundness of Legal-Reply Compression in Shogi : Quotient Criteria, Canonical Repair, and Action-Edge Counterexamples

Compressing a finite set of legal Shogi replies into coarse classes can reduce the amount of downstream checking, but such compression is meaningful only relative to what is being asked about those replies. We formalize this point as a query-relative quotient condition. For a pos...

Query-Relative Soundness of Legal-Reply Compression in Shogi : Quotient Criteria, Canonical Repair, and Action-Edge Counterexamples

Compressing a finite set of legal Shogi replies into coarse classes can reduce the amount of downstream checking, but such compression is meaningful only relative to what is being asked about those replies. We formalize this point as a query-relative quotient condition. For a pos...

Reply-Induced Deletion Geometry in Shogi : Incidence Structures, Fragility Spectra, and Co-Deletion Graphs

We introduce a finite combinatorial structure for measuring how a legal Shogi move's immediate board-influence relation is destroyed by the opponent's legal one-ply replies. For a position $P$ and a legal candidate move $m$, rows index all legal replies and columns index the move...

Reply-Induced Deletion Geometry in Shogi : Incidence Structures, Fragility Spectra, and Co-Deletion Graphs

We introduce a finite combinatorial structure for measuring how a legal Shogi move's immediate board-influence relation is destroyed by the opponent's legal one-ply replies. For a position $P$ and a legal candidate move $m$, rows index all legal replies and columns index the move...