Not evaluated
Termination of fourfold minimal model programs (family 056)
The gist
In the openai/math repository released on October 6, 2026, family 056 groups 5 manuscripts on the termination of minimal model programmes in dimension four, from an unreleased internal model.
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-056-termination-fourfold-minimal-model-programs-r1
@misc{discoveria-oai-fam-056-termination-fourfold-minimal-model-programs-r1,
author = {{DiscoverIA}},
title = {Termination of fourfold minimal model programs (family 056)},
howpublished = {DiscoverIA registry, entry oai-fam-056-termination-fourfold-minimal-model-programs},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-056-termination-fourfold-minimal-model-programs#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
A minimal model programme is a procedure that transforms a geometric space through successive steps. If the manuscripts were correct, it would stop after a finite number of steps for the four-dimensional spaces they treat (compact Kähler manifolds or projective log canonical varieties with rational boundary, according to their titles).
What remains unclear
No Lean (a language in which a computer checks every step of a proof) 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 · …log-canonical-flips-on…link only, reading not recorded
- Repositorygithub.com · …canonical-flips-on…link only, reading not recorded
- Repositorygithub.com · Termination-for…link only, reading not recorded
- Repositorygithub.com · …October-6-2026link only, reading not recorded
- Repositorygithub.com · …September-24-2026link only, reading not recorded
Method
The manuscripts are dated from September 24 to October 7, 2026, including “Termination of generalized log canonical flips on compact Kähler fourfolds” (October 7) and “Termination of generalized-canonical flips on compact Kähler fourfolds” (October 6). Two of them share the title “Finite ordinary minimal model programs on compact Kähler fourfolds” (September 24 and October 6). history.md reports, on October 7, 2026, revisions of three manuscripts, which clarify the outside results their proofs rely on (negativity, codimension-two smoothness, cycle comparison, the relative minimal model programme). 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 056, section “Algebraic and complex geometry”, 5 manuscripts dated Sep 24, 2026
- Lean proof
- none supplied
- Checked by
- no verifier identified
- Sources
- 6 : 6 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 55 of 372, by family number
- Not evaluated : A counterexample to Pixton's original completeness conjecture (family 053)
- Not evaluated : Counterexamples to Kuznetsov's rationality conjecture (family 054)
- Not evaluated : Toda's Gepner conjecture and large-volume stability (family 055)
- Not evaluated : Termination of fourfold minimal model programs (family 056)
- Not evaluated : Campana's abelianity conjecture and special varieties (family 057)
- Not evaluated : The Kollár–Pardon universal-cover conjecture (family 058)
- Not evaluated : Counterexamples to Zariski's multiplicity conjecture (family 059)
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