Not evaluated
Bogomolov–Pop and Milnor K-theoretic reconstruction (family 009)
The gist
On October 6, 2026, OpenAI announced three manuscripts, from an unreleased internal model, on reconstruction from Milnor K-theory and the Bogomolov-Pop reconstruction theorem.
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-009-bogomolovpop-milnor-k-theoretic-r1
@misc{discoveria-oai-fam-009-bogomolovpop-milnor-k-theoretic-r1,
author = {{DiscoverIA}},
title = {Bogomolov–Pop and Milnor K-theoretic reconstruction (family 009)},
howpublished = {DiscoverIA registry, entry oai-fam-009-bogomolovpop-milnor-k-theoretic},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-009-bogomolovpop-milnor-k-theoretic#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 manuscripts were correct, the first would show that a function field (the rational functions of an algebraic variety) can be reconstructed from its Milnor K-theory modulo ℓ, an algebraic invariant. The second would deal with Milnor K-theory modulo the characteristic and the third with the Bogomolov-Pop theorem, going by their titles.
What remains unclear
No check of the Lean supplied by OpenAI (a language in which a computer checks every step of a proof) by a third party, nor any other independent assessment, is recorded. The sources read do not give the precise statement claimed by the manuscripts, nor how much of it the Lean covers.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 009.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 · Reconstruction-of…link only, reading not recorded
- Repositorygithub.com · Reconstruction-from…link only, reading not recorded
- Repositorygithub.com · The-Bogomolov-Pop…link only, reading not recorded
- Lean proofgithub.com · 009.mdpage read word for word
- Lean proofgithub.com · BogomolovPopInjectivity.le…link only, reading not recorded
Method
The three manuscripts in the openai/math repository are “Reconstruction of Function Fields from Mod-ℓ Milnor K-Theory” and “Reconstruction from Milnor K-theory modulo the characteristic” (October 5, 2026), then “The Bogomolov-Pop reconstruction theorem” (September 23, 2026). OpenAI supplies lean/docs/009.md and one Lean file, lean/ComparatorChallenges/BogomolovPopInjectivity.lean (one Comparator statement); formalization.yaml carries “review: status: unchecked” but does not list the family in its sources. history.md reports no revision of these manuscripts. 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 (Number theory)
- In openai/math
- family 009, section “Number theory”, 3 manuscripts dated Sep 23, 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
- 6 : 1 read word for word, 5 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 9 of 372, by family number
- 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)
- Not evaluated : Fontaine–Mazur modularity at the prime 2 and 2-adic pro-modularity (family 010)
- Not evaluated : The Ford–Konyagin–Luca conjecture on prime predecessors (family 011)
- Not evaluated : Independent largest prime factors of consecutive integers (family 012)
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