An AI‑assisted prover called VGPT‑RSI has produced formally verified certificates for two statements that sit alongside the Riemann Hypothesis.
The system built a finite boundary certificate for an inequality on a safe lower curve, converting a numerical boundary into a formally audited lower bound using interval arithmetic and Arb/FLINT ball arithmetic, then checked it in Coq. It also created a finite Lagarias‑route certificate, formalising a piece of the Lagarias criterion that equivalently restates RH, and verified that piece in Coq as well. The output isolates the exact open problems: a full formalisation of Lagarias’ equivalence, a global tail theorem beyond any finite bound, and a reduction of potential counter‑examples to a narrow class of extremal integers.
This matters because it shows an AI can organise complex proof dependencies, generate machine‑checkable artifacts, and transparently flag what it cannot yet resolve. It moves the conversation from speculative AI “proofs” to reproducible, peer‑reviewable progress on a famously intractable problem.
The work is a reminder that even sophisticated AI remains a tool, not a replacement for deep mathematical insight, and that formal verification still hinges on human‑driven theory building.