Not evaluated
Fujita's freeness conjecture (family 038)
The gist
On October 6, 2026, OpenAI published a manuscript devoted to Fujita's freeness conjecture.
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-038-fujitas-freeness-conjecture-r1
@misc{discoveria-oai-fam-038-fujitas-freeness-conjecture-r1,
author = {{DiscoverIA}},
title = {Fujita's freeness conjecture (family 038)},
howpublished = {DiscoverIA registry, entry oai-fam-038-fujitas-freeness-conjecture},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-038-fujitas-freeness-conjecture#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
If the manuscript held, it would add a new result on this conjecture, which concerns the conditions guaranteeing that a family of functions attached to a geometric object has no point where all of them vanish together. The field is algebraic and complex geometry, the study of shapes defined by equations.
What remains unclear
No independent assessment is recorded, and OpenAI provides no Lean proof (a language in which a computer checks every step of a proof) for this family. The sources read do not say which precise statement the manuscript establishes, nor whether it covers the whole conjecture.
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 · Fujitas-freeness…link only, reading not recorded
Method
OpenAI publishes in its openai/math repository the manuscript “Fujita's freeness conjecture”, dated September 23, 2026, the only manuscript of family 038, filed under the section “Algebraic and complex geometry” of overview.tex. The file history.md reports no revision for this manuscript. The internal model that produced it has not been released. 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 (Algebraic and complex geometry)
- In openai/math
- family 038, section “Algebraic and complex geometry”, 1 manuscript dated Sep 23, 2026
- Lean proof
- none supplied
- Revisions
- none reported by the claimant
- Checked by
- no verifier identified
- Sources
- 2 : 2 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 38 of 372, by family number
- Not evaluated : Threefold log abundance in numerical dimension one in characteristic p>3 (family 035)
- Not evaluated : Numerical semiampleness and generalized minimal models (family 036)
- Not evaluated : The sharp ordinary-double-point volume gap (family 037)
- Not evaluated : Fujita's freeness conjecture (family 038)
- Not evaluated : Nagata's conjecture and maximal Seshadri constants (family 039)
- Not evaluated : Bloch's conjecture for complex surfaces (family 040)
- Not evaluated : Hyperkähler SYZ and projective-space bases (family 041)
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