On 25 March 2026 I started a dedicated long-form research project on the Beal Conjecture. The success condition is intentionally strict: a complete general proof, or an explicit primitive counterexample.

Label every claim

I use explicit states: KNOWN, DERIVED, CANDIDATE, and REFUTED. The labels prevent an attractive intermediate observation from slowly turning into “basically proved.”

Primary sources over memory

The research has moved through exponent and valuation reductions, Frey-curve and modular approaches, multi-Frey literature, effective finiteness, S-unit and height bounds, primitive-divisor mechanisms, and repeated checks for exceptional primes and circular reasoning.

I have not solved the Beal Conjecture. Failed routes stay in the record so the project becomes more accurate instead of merely looking more successful.

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I started this project on 2 February 2026. The Vesuvius Challenge looks from a distance like an ink-detection problem. The closer I looked, the more it became a full systems problem.

The pipeline is the result

Reading a scroll that cannot be physically opened requires volumetric data, geometric reconstruction, surface extraction, flattening or unwrapping, ink prediction, and human-verifiable output.

A strong model is not enough if the surface geometry is wrong. A clean rendering is not enough if the mapping cannot be reproduced and audited.

Interfaces matter in research

Comparing 3D surfaces, extracted patches, flattened coordinates, and ink predictions makes visualization and metadata part of the scientific method rather than secondary engineering.

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