VGPT-RSI for RH-Adjacent Formal Progress: Boundary Certificates, Verified Finite Lagarias Inequalities, and Explicit Failure Localization

The article presents the application of the Verifiable Growing Physical Transformer with Recursive Self-Improvement (VGPT-RSI) to tackle certification tasks related to the Riemann Hypothesis (RH). It details the construction and verification of a finite RH-boundary certificate using advanced arithmetic techniques and formal verification in Coq, alongside the initiation of a formal Lagarias-route certificate. This work is significant as it showcases the capability of VGPT-RSI to produce verifiable mathematical progress while explicitly identifying remaining challenges, which could enhance the reliability of AI-assisted proofs in complex mathematical domains.