Not evaluated
The Grothendieck homotopy hypothesis (family 312)
The gist
In its release of October 6, 2026, OpenAI presents a manuscript, from an unreleased internal model, on the Grothendieck homotopy hypothesis, in topology.
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-312-grothendieck-homotopy-hypothesis-r1
@misc{discoveria-oai-fam-312-grothendieck-homotopy-hypothesis-r1,
author = {{DiscoverIA}},
title = {The Grothendieck homotopy hypothesis (family 312)},
howpublished = {DiscoverIA registry, entry oai-fam-312-grothendieck-homotopy-hypothesis},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-312-grothendieck-homotopy-hypothesis#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
The sources read give the manuscript's subject and its method, the “elementary expansions”, but not its precise statement. If the manuscript held, it would bring a result on this hypothesis, whose scope is not specified.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) was supplied by OpenAI itself, and its tracking file marks it “unchecked”. No third-party verification is recorded. The sources read do not say whether the Lean statement matches the manuscript's statement.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 312.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 · The-Grothendieck-homotopy…link only, reading not recorded
- Lean proofgithub.com · 312.mdpage read word for word
- Lean proofgithub.com · GrothendieckElementaryExpa…link only, reading not recorded
Method
The openai/math repository holds the manuscript “The Grothendieck homotopy hypothesis via elementary expansions”, dated September 24, 2026. The file lean/docs/312.md describes the scope of the Lean formalisation, with one Comparator statement: lean/ComparatorChallenges/GrothendieckElementaryExpansion.lean. In formalization.yaml the family is among the listed sources; history.md reports no revision of this manuscript. 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 (Topology)
- In openai/math
- family 312, section “Topology”, 1 manuscript dated Sep 24, 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
- 4 : 1 read word for word, 3 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 306 of 372, by family number
- Not evaluated : The Kervaire invariant problem at the prime three (family 309)
- Not evaluated : Quillen's conjecture in rational homology (family 310)
- Not evaluated : Chai's invariant-ideal conjecture (family 311)
- Not evaluated : The Grothendieck homotopy hypothesis (family 312)
- Not evaluated : Finite generation for the K(n)-local sphere (family 313)
- Not evaluated : The chromatic Smith fixed-point problem for finite p-groups (family 314)
- Not evaluated : The four-dimensional Singer conjecture (family 315)
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