Not evaluated
Goldfeld's conjecture (family 006)
The gist
On October 6, 2026, OpenAI released two manuscripts from an unreleased internal model on Goldfeld's conjecture, which concerns the rank of elliptic curves.
DiscoverIA status on October 12, 2026: not evaluated, meaning no third-party evaluation found.
AI draft, not reviewedWhat has not been reviewed?
Text written by an AI (DiscoverIA pipeline), on . The status and its sources come from the registry; only the explanatory text has not been reviewed. A reported error is corrected, then the text is reviewed.
Cite this entry
A single status snapshot since Oct 12, 2026: a citation always points to a dated snapshot.
Cite snapshot 1, Oct 12, 2026
APA citation with the dated link
BibTeX @misc, key discoveria-oai-fam-006-goldfelds-conjecture-r1
@misc{discoveria-oai-fam-006-goldfelds-conjecture-r1,
author = {{DiscoverIA}},
title = {Goldfeld's conjecture (family 006)},
howpublished = {DiscoverIA registry, entry oai-fam-006-goldfelds-conjecture},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-006-goldfelds-conjecture#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
Goldfeld's conjecture concerns the mean analytic rank (a quantity defined from a function attached to the curve) of a family of elliptic curves obtained by “quadratic twisting”. If the manuscripts held, they would bring results on this subject; the sources read do not give their precise statement.
What remains unclear
No Lean proof (checkable by computer) is supplied for this family, and no third-party assessment is recorded. The sources read do not say where the question stood before the announcement.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · README.md
Step 1 of 4 on the scale: not evaluated. Next step: under review.
- Announced
- Recordednot evaluated
- nextTo follow
What this status means
Source reading : Source read word for word (level 3 of 3)
The result is declared neither right nor wrong.
To move to “Under review”: a public review under way. To “Peer reviewed”: a journal publication or a review by named experts.
Sources
- Main sourcegithub.com · CONTENTS.mdlink only, reading not recorded
- Repositorygithub.com · Goldfelds-analytic…link only, reading not recorded
- Repositorygithub.com · The-mean-analytic-rank-of…link only, reading not recorded
Method
In the openai/math repository, family 006 comprises two manuscripts: "Goldfeld's analytic density conjecture and the 2-converse for elliptic curves" (dated October 7, 2026) and "The mean analytic rank of quadratic twists of elliptic curves" (dated October 6, 2026). For each, history.md records, on October 7, 2026, a version that updates citations to revised manuscripts in the collection. The absence of Lean is inferred from the absence of the file lean/docs/006.md; OpenAI's README states that not all manuscripts have a Lean formalisation. DiscoverIA status: not evaluated, meaning that no third-party evaluation has been found in the sources read. Set on October 12, 2026 from github.com (page read, quotation checked word for word: “Not all have accompanying Lean formalizations.”).
Limits
DiscoverIA has not checked this result itself.
Key facts
- Claimed by
- OpenAI (unreleased internal model)
announced on Oct 6, 2026 - Nature
- new result
- Field
- Mathematics (Number theory)
- In openai/math
- family 006, section “Number theory”, 2 manuscripts dated Oct 6, 2026
- Lean proof
- none supplied
- Checked by
- no verifier identified
- Sources
- 3 : 3 links only
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
Family with no Lean proof supplied. No third-party evaluation read.
Source: github.comread word for word
An observation is added; none is ever erased.
In the same set
openai/math: 719 manuscripts in 372 families from an unreleased internal model · entry 6 of 372, by family number
- Not evaluated : Quasi-Riemann hypothesis: zero-free half-plane Re(s) > 7/8 (family 003)
- Not evaluated : Hilbert's tenth problem over Q (family 004)
- Not evaluated : Irrationality of Catalan's constant (family 005)
- Not evaluated : Goldfeld's conjecture (family 006)
- Not evaluated : Two-point Chowla and the corrected binary Elliott conjecture (family 007)
- Not evaluated : The Deligne–Drinfeld conjecture (family 008)
- Not evaluated : Bogomolov–Pop and Milnor K-theoretic reconstruction (family 009)
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