AIProofWatch
← Archive

OpenAI reports: Modularity over imaginary quadratic fields

OpenAI reports modularity of every elliptic curve over every imaginary quadratic number field, with an automorphic representation matching the local parameters at all places.

Sources for this record

What was already known

Modularity over the rationals and known special classes over other fields do not supply the unrestricted imaginary-quadratic result. Matching good-prime point counts alone is also a narrower assertion.

What changed and why it matters

Establishes the unrestricted imaginary-quadratic elliptic-curve modularity target with full local compatibility.

The AI contribution

OpenAI attributes these manuscripts to its internal model. The entry does not infer individual human contributions beyond that publisher attribution.

Limitations

The base fields are imaginary quadratic. The statement does not claim modularity for elliptic curves over all number fields or all higher-dimensional abelian varieties. Preprint. This is a source-statement and significance assessment, not a proof audit. No independent checking or successful formal compilation is asserted by this entry.

Verification evidence

Evidence labels show what supports the claim. Importance rates its impact if correct.

Author claim

The publisher reports the scoped result. AIProofWatch has not independently validated its correctness.

Accessible artifact / proof

The original written argument is accessible. Availability does not establish a successful proof check or Lean verification.

Correction and publication history

2026-10-11 · publication

Historical report added after statement, scope, and importance review. No proof audit or formal checking asserted; subscriber alerts disabled.

Read this published revision