Not evaluated
Log abundance and effective Iitaka fibrations (family 034)
The gist
In the openai/math repository released on October 6, 2026, family 034 groups 14 manuscripts on log abundance and effective Iitaka fibrations, 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-034-log-abundance-effective-iitaka-fibrations-r1
@misc{discoveria-oai-fam-034-log-abundance-effective-iitaka-fibrations-r1,
author = {{DiscoverIA}},
title = {Log abundance and effective Iitaka fibrations (family 034)},
howpublished = {DiscoverIA registry, entry oai-fam-034-log-abundance-effective-iitaka-fibrations},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-034-log-abundance-effective-iitaka-fibrations#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
Abundance and Iitaka fibrations belong to algebraic and complex geometry, which studies shapes defined by equations; the word “effective” refers to statements whose bounds are explicit. If these manuscripts were correct, they would provide results of this kind, notably for compact Kähler fourfolds, according to their titles.
What remains unclear
At least one manuscript, “Conditional good minimal models for compact Kähler fourfolds”, is presented as conditional: its revision states the remaining hypotheses explicitly (Iitaka subadditivity, effective abundance). 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.
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-abundance-for-compact…link only, reading not recorded
- Repositorygithub.com · Uniform-indices-for-semi…link only, reading not recorded
- Repositorygithub.com · Conditional-good-minimal…link only, reading not recorded
- Repositorygithub.com · Log-abundance-in…link only, reading not recorded
- Repositorygithub.com · Minimal-metrics-and…link only, reading not recorded
- Repositorygithub.com · Fourfold-nonvanishing-by…link only, reading not recorded
- Repositorygithub.com · Lifting-sections-from-the…link only, reading not recorded
- Repositorygithub.com · Schnell-fiber-spaces-and…link only, reading not recorded
- Repositorygithub.com · Uniform-log-Iitaka…link only, reading not recorded
- Repositorygithub.com · Uniform-Pluricanonical…link only, reading not recorded
- Repositorygithub.com · Relative-denominators-and…link only, reading not recorded
- Repositorygithub.com · Arithmetic-Stein-degree…link only, reading not recorded
- Repositorygithub.com · Uniform-effective-log…link only, reading not recorded
- Repositorygithub.com · Abundance-after…link only, reading not recorded
Method
The manuscripts are dated from September 24 to October 6, 2026; they include “Log abundance for compact Kähler spaces under logarithmic Iitaka subadditivity” (October 6) and “Log abundance in characteristic zero” (September 24). history.md reports, on October 7, 2026, a revision of the first, which supplies multiplier-ideal arguments for the induction. 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 034, section “Algebraic and complex geometry”, 14 manuscripts dated Sep 24, 2026
- Lean proof
- none supplied
- Checked by
- no verifier identified
- Sources
- 15 : 15 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 34 of 372, by family number
- 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)
- Not evaluated : The sharp ordinary-double-point volume gap (family 037)
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