Author

Ji-Zhou Guo

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Preprint Aug 2026

Reinhardt's Maximum-Perimeter Polygon Problem for n=16, 32, and 64

A convex polygon is called small if its diameter is at most one. Reinhardt proved the universal perimeter bound $\operatorname{perim}(P)\le U_n:=2n\sin(\pi/(2n))$, and the bound is attained whenever $n$ has a nontrivial odd divisor. The remaining power-of-two cases have resisted exact solution beyond $n=8$. We give com...

Ji-Zhou Guo, Yitao Luo · 0 citations

Preprint Aug 2026

An $n^2\log\log n$ Lower Bound for Permanent Circuits with Valid Division

We prove an $n^2\log\log n$ lower bound for rational arithmetic circuits computing the permanent over characteristic zero. Additions and scalar operations are free, while every nonscalar multiplication or valid division has unit cost. If $L_{\mathrm{div}}(\mathrm{per}_n)$ denotes the resulting complexity, then $\liminf...

Ji-Zhou Guo · 0 citations

Preprint Aug 2026

Logarithmic Chowla Correlations Across All Shift Scales

Let $\lambda(n)=(-1)^{\Omega(n)}$ be the Liouville function. We prove a fixed power-logarithmic bound for its logarithmically weighted two-point correlations across the full shift range. There is an absolute $c>0$ such that every sufficiently large $x$ admits a single set $\mathcal E_x\subseteq[1,x]$ with $|\mathcal E_...

Ji-Zhou Guo · 1 citation · ⚡1