What was already known
Elkies and Klagsbrun’s 2024 construction had rank at least 29, improving the rank-at-least-28 record from 2006. The 2026 constructions raise this explicit lower-bound record to at least 31.
What changed and why it matters
Advances a concrete longstanding construction record in arithmetic geometry, with human expertise and AI-assisted search retained in the attribution.
The AI contribution
Levent Alpöge and Ava Howell, both experienced in elliptic-curve research, used an internal variant of Claude according to the news account and the original curve-302 commentary. The specialist record credits the human researchers; this entry retains both forms of attribution.
Limitations
Rank at least 31 is a lower bound, not an unconditional determination of exact rank 31; the original record conditions its exact-rank certification on BSD and GRH. It does not settle whether rational elliptic-curve ranks are bounded. Dujella’s table supports record context but is not a AIProofWatch rerun of point-independence checks; the exact prompting and search process is not fully documented.
Verification evidence
Evidence labels show what supports the claim. Importance rates its impact if correct.
Author claim
The cited source reports the scoped contribution. Statement and significance review does not establish a complete proof audit.
Accessible artifact / proof
The supporting manuscript, formal development or construction data is accessible; AIProofWatch has not independently reproduced its checks.
Correction and publication history
News-led review of the precise source statement, baseline, AI attribution and importance. Historical inclusion without subscriber alerts; no AIProofWatch full proof audit.
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