Proposed
Proposed source assertion awaiting assessment ↗
Only the cited assertion with its exact assumptions. This report does not resolve the canonical Problem or establish independent OpenMath mathematical review.
Observed Oct 10, 2026
Theorem · version 1
Proposed full BSD at Selmer corank zero or one
Earlier version 1. View current version 2 →
Statement
For E/Q and some prime q, if s_q(E) = corank_{Z_q} Sel_{q∞}(E/Q) belongs to {0,1}, then rank E(Q) = ord_{s=1}L(E,s) = s_q(E), Sha(E/Q) is finite, and the full normalized BSD leading-term formula holds.
Assumptions
- Full q-power Selmer group with local Kummer conditions at every place, not only the finite q-Selmer group.
- Some prime q; no extra reduction, CM, rational torsion, isogeny or residual-representation restriction is claimed.
- Full L-function, total Néron real period and full point-lattice regulator of Theorem 1.1.
Scope
A provider proposal depending on companion low-corank converse and two-primary inputs. Algebraic rank ≤1 alone does not establish this Selmer-corank hypothesis.
This source presents a theorem with a proposed proof. Its wording does not establish acceptance or independent mathematical review.
Evidence
Source reports
Connections
In this problem · publication v10 · Selected context
Birch and Swinnerton-Dyer conjecture →
Special case · Proposed
Relationship not independently reviewed. This concerns its use in this problem.
Sources
OpenAI · proposed full BSD from low Selmer corank →
- Theorem 1.1 and normalization, PDF page 3; companion dependencies §2 → · Original passage ↗
Recorded wording
The provider claims full BSD for E/Q whose full q-power Selmer group has corank 0 or 1 for some prime q, without additional reduction or residual hypotheses.
paraphrase · Only metadata and original OpenMath paraphrases are published; full text stays upstream.
OpenAI · Preprint · Publication date Oct 7, 2026
Provider preprint in the October 2026 public collection. The selected manuscript is a proposal here; a release announcement is not independent expert acceptance.
OpenAI · proposed full BSD from low Selmer corank — manuscript ↗No OpenMath execution recorded
Revision & attribution
Source revision: fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. Observed Oct 10, 2026.
The provider attributes this manuscript to its internal AI model. Mathematical acceptance, paper-to-formal correspondence and independent reproduction are not established by OpenMath.
OpenAI · proposed full BSD from low Selmer corank — manuscript: fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. External manuscript. No OpenMath proof execution, formalization or independent mathematical acceptance is inferred.
History
Statement versions
Statement versions and problem publication versions are separate. A new publication can update context or sources while retaining the same statement.
Assessment history · 1
Assessments retained in these publication records. Earlier statement versions retain their own source histories.
Proposed
Proposed source assertion awaiting assessment ↗
Only the cited assertion with its exact assumptions. This report does not resolve the canonical Problem or establish independent OpenMath mathematical review.
Observed Oct 10, 2026 · Source passage →
Record details
- Claim ID
- claim-bsd-openai-low-selmer-proposal
- Statement version
- 1
- SHA-256
- 5ee54912209aff7e74fdc17b7aa1466b410ed9ff0d579234fd31f2fa5c48ac9a