VGPT-RSI for RH-Adjacent Formal Progress: Boundary Certificates, Verified Finite Lagarias Inequalities, and Explicit Failure Localization
arXiv:2606.15096v1 Announce Type: new Abstract: The Riemann Hypothesis remains one of the central unsolved problems in mathematics. Rather than claiming proof, we investigate whether a verifiable AI-assisted reasoning system can produce reliable, formally checked partial progress while explicitly identifying the remaining mathematical obstructions. We apply the Verifiable Growing Physical Transformer with Recursive Self-Improvement (VGPT-RSI) to two RH-adjacent certification tasks. First, we construct and verify a finite RH-boundary certificate for inequality on a parameterized safe lower curv
The development showcases a practical application of advanced AI in formal mathematics, coinciding with increasing AI capabilities in complex problem-solving.
This demonstrates AI's potential to contribute provable, verifiable progress on foundational mathematical problems, reducing human error and accelerating research.
The ability of AI to generate and verify 'boundary certificates' and 'finite Lagarias inequalities' suggests a new paradigm for mathematical discovery and verification, moving beyond mere conjecture.
- · AI research labs
- · Mathematics community
- · Formal verification platforms
- · Traditional manual proof methods
AI becomes a more trusted partner in high-stakes intellectual domains like mathematics.
Accelerated progress in other hard sciences through AI-assisted formal verification and hypothesis generation.
Potential for AI to independently identify and resolve fundamental scientific problems previously inaccessible to human-only methods.
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Read at arXiv cs.AI