AI agent swarm of 20 Claude models proves first nontrivial lower bounds for Naslund's crossing problem, formalized in Lean
burny_tech · x · 2026-11-16
Researcher Arth Singh released Lean-formalized lower bounds above the trivial n for Naslund's crossing problem: over every field, r+s ≥ 4n/3 (n≥3), ≥ 15n/11 (n≥5), ≥ 67n/49 (n≥7), and ≥ n+3 (n≥4), with P(4)=7 exactly; at n=4 splittings approach 6 in characteristic 0 and all but seven positive characteristics. The 4n/3 proof fits in one page. All theorems and proofs were found by a multi-agent research harness of 20 Claude agents (Opus 5.5 workers, a Fable 5.2 lead) — the author's main goal was improving the swarm harness itself, with mathematics as the byproduct. Paper and repo are public on alphaXiv and GitHub.
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