Source authenticated

A Rank- $31$ Record for an Elliptic Curve over $\mathbb{Q}$

Two tiers, and only the first is the record. Rank $\ge 31$ is unconditional: 31 explicit points, independence asserted via the leaderboard's stated general practice of exact 2-descent (not reproduced here - see the verification note). Rank exactly 31 is conditional on GRH and BSD, per the submitters' commentary, in the same style as the sibling record's Bober-bound argument; no numeric derivation has been published for this curve specifically. The entry is a partial result because the open question - whether ranks are unbounded at all - remains unanswered by any single record.

Exact FrontierDelta

proved→proved

Scope and record

Occurred: Oct 29, 2026

Delta type: REGISTRY REVISION

Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-co-developed. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: A Rank-$31$ Record for an Elliptic Curve over $\mathbb{Q}$ · Elliptic curve rank record (31)

Confidence: Not scored

Registry verification: unreviewed · announcement · partial

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Attribution

VibeMathed
registry · event recorded by

Claude
model · ai model contributor · Anthropic

Levent Alpöge
human · human collaborator

Ava Howell
human · human collaborator

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: A Rank- $31$ Record for an Elliptic Curve over $\mathbb{Q}$

specialist registry · passed

Recomputed by this site on 24 August 2026 from the leaderboard's own JSON, in exact rational arithmetic: all 31 witness points satisfy the curve equation with residual exactly zero (nine carry fractional coordinates, handled exactly rather than as floating point), all 31 are pairwise distinct, and the discriminant recomputed from the a-invariants matches the published value exactly. All 20 listed bad primes divide that discriminant and multiply out to account for the whole of it with nothing left over, and each passed a Miller-Rabin probable-primality check, including the 80-digit one. What was NOT checked, same limitation as the sibling entry: that the 31 points are independent in $E(\mathbb{Q})$ modulo torsion. The leaderboard states its site-wide practice is exact 2-descent with no floating point in the decision; that computation was not reproduced. Also unlike the sibling entry, no announcement article or public numeric derivation of the GRH+BSD argument (a Bober-bound $\Delta$ , a root number) exists for this specific curve at time of writing - the "exactly 31" claim rests on the submitters' commentary alone.