- The AI system Theo-Conjecture solved a 35-year-old math conjecture about the residue of a prime graph, originally posed by the Graffiti program and studied by Paul Erdős and William Staton.
- The proof confirmed Staton's prediction and discovered an unexpected second-order term in the asymptotic expansion, refining the relationship between residue and prime count.
- The residue, a fast graph invariant based on vertex degrees, provides a lower bound for the size of the largest independent set, which in this case relates to the prime-counting function.
- The asymptotic result shows residue equals (ζ(2)-1) n/log n, with the zeta function appearing naturally from multiplicative structure.
- The collaboration between human mathematician Randy Davila and the AI system highlights an iterative loop of proposing, testing, and revising conjectures.