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Conjecture Hunters
Mathematics has thousands of open conjectures — rules experts believe but nobody has proven. Some are actually false; you only need a single counterexample to settle them. Finding that needle in a combinatorial haystack, with a cheap way to verify, is exactly what massive parallel compute does better than a human. The AI proposes, exact arithmetic decides. Gemma looks at a graph and proposes a small change (add or remove an edge). An exact evaluator, written in Rust for ~31x the speed of Python, computes the conjecture's gap. If the gap crosses zero, that's a counterexample. Because the verdict is exact integer arithmetic — no floating point, no approximation — the AI cannot hallucinate or cheat a false positive. Every hit is written to a crash-proof ledger the instant it's found. It works. The system refuted the Jia-Song conjecture (2018), still listed as open in a 2024 survey. The smallest counterexample is the friendship graph: the quantity the conjecture claimed never drops below 0.80051 is 0.79844 there. We proved it with an integer certificate (59^2 = 3481 > 3456) — zero floating point — and confirmed it with a second, independent method. We even found a transcription error in the original paper and proposed the corrected bound. Scale on AMD: a swarm attacks 20 conjectures at once, saturating every core (20-lane QC green; 115,000+ exact evaluations in ~20s; durable ledger active). Gemma is served on the MI300X via vLLM on the full ROCm + PyTorch stack, and a LoRA loop fine-tunes Gemma on AMD hardware so it proposes better over time. On the MI300X this scales toward millions of evaluations per second. Reproducible: one docker run executes the refutation, the 20-lane QC, and the swarm. The repo is public with full commit history and regenerates the certificate — you verify it yourself in seconds. The search finds it; exact arithmetic proves it.
13 Jul 2026
