Sui

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...

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...

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 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...