Brief

A new research paper introduces VGPT-RSI, a verifiable AI-assisted reasoning system designed to make formal progress on complex mathematical problems like the Riemann Hypothesis. The system successfully constructed and verified a finite boundary certificate for an RH-adjacent inequality and initiated a formal certificate for the Lagarias criterion. VGPT-RSI also explicitly identified the remaining mathematical obstructions, demonstrating its capability to produce certified progress while acknowledging genuine mathematical challenges. AI

Researchers have introduced ZX-Calculus, an extension of Martin-Lof Dependent Type Theory, that integrates trace-indexed types, presheaf semantics, and belief revision. The calculus includes formal proofs for trace types, sheaf semantics, and AGM belief revision postulates, with a significant portion verified in Coq. A key finding is the failure of B^AGM to satisfy the sheaf composition law for sequential revision, highlighting a previously unrecognized tension between path-dependent belief revision and functor consistency. AI

Researchers have developed a new AI method called Inductive Deductive Synthesis that uses a proof checker within its implementation loop. This approach, which is analogous to chain-of-thought but with formally verified intermediate states, allows AI to generate formally verified systems. The system takes specifications as input and produces verified implementation prototypes, with plans to integrate with other proof assistants like Verus for Rust output. AI