Not evaluated
Relative independence of the separable quotient problem (family 323)
The gist
In its release of October 6, 2026, OpenAI claims, using an unreleased internal model, the relative independence of the separable quotient problem, the subject of a manuscript.
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-323-relative-independence-separable-quotient-r1
@misc{discoveria-oai-fam-323-relative-independence-separable-quotient-r1,
author = {{DiscoverIA}},
title = {Relative independence of the separable quotient problem (family 323)},
howpublished = {DiscoverIA registry, entry oai-fam-323-relative-independence-separable-quotient},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-323-relative-independence-separable-quotient#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 manuscript belongs to functional analysis. The sources read do not say what “relative” means here, nor which axioms the independence refers to. If it held, an answer to the problem could not be drawn from those axioms alone.
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.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 323.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 · Relative-independence-of…link only, reading not recorded
- Lean proofgithub.com · 323.mdpage read word for word
- Lean proofgithub.com · SeparableQuotientNegative.…link only, reading not recorded
Method
The openai/math repository contains the manuscript “Relative independence of the separable quotient problem”, dated September 23, 2026 and filed under “Functional analysis” in overview.tex. The file lean/docs/323.md describes the Lean formalisation, with one Comparator statement (lean/ComparatorChallenges/SeparableQuotientNegative.lean). The family is absent from the “sources” of formalization.yaml; 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 (Functional analysis)
- In openai/math
- family 323, section “Functional analysis”, 1 manuscript 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
- 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 317 of 372, by family number
- Not evaluated : A four-dimensional counterexample to Borel rigidity (family 320)
- Not evaluated : A counterexample to Wall's finite D(2) conjecture (family 321)
- Not evaluated : Tingley's sphere-isometry problem (family 322)
- Not evaluated : Relative independence of the separable quotient problem (family 323)
- Not evaluated : Lipschitz equivalence without linear isomorphism (family 324)
- Not evaluated : The complete Crouzeix conjecture (family 325)
- Not evaluated : The cotype–cotype conjecture under the approximation property (family 326)
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