Not evaluated
Lipschitz equivalence without linear isomorphism (family 324)
The gist
On October 6, 2026, OpenAI announced a manuscript dated September 24, 2026 claiming that separable Banach spaces that are Lipschitz equivalent need not be linearly isomorphic.
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-324-lipschitz-equivalence-without-linear-r1
@misc{discoveria-oai-fam-324-lipschitz-equivalence-without-linear-r1,
author = {{DiscoverIA}},
title = {Lipschitz equivalence without linear isomorphism (family 324)},
howpublished = {DiscoverIA registry, entry oai-fam-324-lipschitz-equivalence-without-linear},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-324-lipschitz-equivalence-without-linear#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
If this manuscript held, two separable Banach spaces could be alike in the Lipschitz sense without being linked by a continuous linear bijection with continuous inverse. A separable Banach space is a complete normed vector space with a countable dense subset. A second manuscript concerns “Bi-Lipschitz Absorption of c0 Without a Linear Copy of c0”, a separate statement.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) is supplied by OpenAI itself, with the wording “review: status: unchecked”. No third-party verification is read.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 324.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 · Lipschitz-Equivalent…link only, reading not recorded
- Repositorygithub.com · Bi-Lipschitz-Absorption…link only, reading not recorded
- Lean proofgithub.com · 324.mdpage read word for word
- Lean proofgithub.com · C0Absorption.leanlink only, reading not recorded
- Lean proofgithub.com · LipschitzEquivalence.leanlink only, reading not recorded
Method
Manuscript of September 24, 2026: “Lipschitz Equivalent Separable Banach Spaces Need Not Be Linearly Isomorphic”. Manuscript of September 26, 2026: “Bi-Lipschitz Absorption of c0 Without a Linear Copy of c0”. The claimant supplies lean/docs/324.md and 2 Comparator files: lean/ComparatorChallenges/C0Absorption.lean and lean/ComparatorChallenges/LipschitzEquivalence.lean. Section “Functional analysis”; family present in the sources of formalization.yaml; history.md records 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 (Functional analysis)
- In openai/math
- family 324, section “Functional analysis”, 2 manuscripts 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
- 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 318 of 372, by family number
- 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)
- Not evaluated : Markov type characterizes superreflexivity (family 327)
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