Author

William J. Wesley

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Preprint Sep 2026

An elementary proof of the 2-regularity of Pythagorean triples

We give a new proof of the fact that every 2-coloring of the positive integers contains a monochromatic Pythagorean triple. This result was originally proven by Heule, Kullmann, and Marek with SAT solvers in 2016, answering a decades-old question of Graham. This proof uses elementary techniques and requires neither len...

William J. Wesley · 0 citations

Preprint Sep 2026

The Fibonacci numbers are not 3-accessible

A $D$-diffsequence is a sequence of integers $x_1<\dots<x_k$ such that $x_{i+1} -x_i \in D$ for $1 \le i \le k-1$. The set $D$ is called $r$-accessible if every $r$-coloring of the positive integers contains arbitrarily long monochromatic $D$-diffsequences. This note proves that the set of Fibonacci numbers is not 3-ac...

William J. Wesley · 0 citations

Preprint Aug 2026

Autonomous Mathematical Discovery in an Open-World Multi-Agent Environment

The Station is evaluated, an open-world multi-agent environment in which AI agents from different model families pursue a shared research goal without a central coordinator or scripted pipeline, providing a transparent record of how discoveries emerged.

Stephen Chung, Wenyu Du, William J. Wesley · 2 citations