OpenAI · proposed Goldfeld analytic densities and 2-converse
Provider preprint in the October 2026 public collection. The selected manuscript is a proposal here; a release announcement is not independent expert acceptance.
1 cited passage ↓1 problem ↓Record fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb ↓
The exact passages cited in OpenMath. Each passage identifies how its wording was recorded.
The provider claims analytic ranks 0 and 1 each have density 1/2 among signed squarefree quadratic twists of every E/Q ordered by absolute parameter.
Passage ID: birch-and-swinnerton-dyer-conjecture:bsd-openai-goldfeld:v1
Source item: Theorems 1.1–1.2, PDF page 2; separation of mean-rank assertion, page 3
Source record: openai-goldfeld@git-fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb
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Problem publication v17
Source assessment
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
Research activity
Company AI proposals: Selmer converses, leading terms and twist densities
The October provider release proposes low-corank converses and exact leading terms, alongside a distinct analytic twist-density theorem. The pinned manuscripts state companion dependencies.
These source-reported proposals are not established progress here. No corresponding external formal-code execution or proof-dependency audit is asserted; asymptotic twist densities do not resolve every curve.
History
Proposed half-densities for analytic ranks in twist families
Question
Birch and Swinnerton-Dyer conjecture
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No OpenMath execution recorded
External manuscript. No OpenMath proof execution, formalization or independent mathematical acceptance is inferred.
Resource revision: fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb
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c417858c9fe566daacb7738741dc66e211eea148b3da587eb5ee68eaad208d64Recorded authorship
OpenAI
The provider attributes this manuscript to its internal AI model. Mathematical acceptance, paper-to-formal correspondence and independent reproduction are not established by OpenMath.
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OpenAI · proposed Goldfeld analytic densities and 2-converse
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