Not evaluated
Campana's orbifold Iitaka conjecture and logarithmic subadditivity (family 033)
The gist
In its release of October 6, 2026, OpenAI presents five manuscripts on Campana's orbifold Iitaka conjecture and logarithmic subadditivity.
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-033-campanas-orbifold-iitaka-conjecture-r1
@misc{discoveria-oai-fam-033-campanas-orbifold-iitaka-conjecture-r1,
author = {{DiscoverIA}},
title = {Campana's orbifold Iitaka conjecture and logarithmic subadditivity (family 033)},
howpublished = {DiscoverIA registry, entry oai-fam-033-campanas-orbifold-iitaka-conjecture},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-033-campanas-orbifold-iitaka-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
According to their titles, the manuscripts concern orbifold and logarithmic Iitaka subadditivity, in algebraic and complex geometry. The logarithmic Kodaira dimension of a space comes into play. If they were correct, they would bring results on this subject, but the sources read do not specify their exact scope.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) is supplied by OpenAI itself: its review field reads “unchecked”, and no third-party verification is recorded. It contains only one Comparator statement for five manuscripts.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 033.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 · Orbifold-and-logarithmic…link only, reading not recorded
- Repositorygithub.com · Logarithmic-Kodaira…link only, reading not recorded
- Repositorygithub.com · The-reverse-logarithmic…link only, reading not recorded
- Repositorygithub.com · Projective-Hodge-lines…link only, reading not recorded
- Repositorygithub.com · B-semiampleness-for…link only, reading not recorded
- Lean proofgithub.com · 033.mdpage read word for word
- Lean proofgithub.com · LogKodairaFiberNegative.le…link only, reading not recorded
Method
The five manuscripts are dated September 10, 26 and 27, 2026: “Orbifold and logarithmic Iitaka subadditivity”, “Logarithmic Kodaira dimension and whole-fiber variation”, “The reverse logarithmic Kodaira inequality and additivity”, “Projective Hodge lines and ordinary Iitaka subadditivity” and “B-semiampleness for compact log-smooth Kähler fibrations”. The formalisation is in lean/docs/033.md and lean/ComparatorChallenges/LogKodairaFiberNegative.lean; the family is absent from the sources of formalization.yaml, and history.md reports no revision. 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: “describes the scope of the Lean formalization”).
Limits
No named third party: the recorded checks come from the claimant or from a platform tool. The claimant supplies a Lean proof; as of this date, DiscoverIA has found no independent verification of this proof or of the result.
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 033, section “Algebraic and complex geometry”, 5 manuscripts dated Sep 10, 2026
- Lean proof
- supplied by the claimant, marked “unchecked” (not reviewed) in its repository
- Revisions
- none reported by the claimant
- Checked by
- claimant (Lean supplied, not checked by a third party)
- Sources
- 8 : 1 read word for word, 7 links only
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
Family with a Lean proof supplied by the claimant. No third-party check read; the source marks this proof as not reviewed (“unchecked”).
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 33 of 372, by family number
- Not evaluated : Modularity over imaginary quadratic fields (family 030)
- Not evaluated : Uchida's conjecture for open Galois homomorphisms (family 031)
- Not evaluated : Rational Hodge conjecture for CM abelian varieties (family 032)
- Not evaluated : Campana's orbifold Iitaka conjecture and logarithmic subadditivity (family 033)
- Not evaluated : Log abundance and effective Iitaka fibrations (family 034)
- 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)
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