Not evaluated
A counterexample to Pietsch's metric-entropy duality conjecture (family 329)
The gist
On October 6, 2026, OpenAI announced counterexamples to Pietsch's duality conjecture for metric entropy, 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-329-counterexample-pietschs-metric-entropy-r1
@misc{discoveria-oai-fam-329-counterexample-pietschs-metric-entropy-r1,
author = {{DiscoverIA}},
title = {A counterexample to Pietsch's metric-entropy duality conjecture (family 329)},
howpublished = {DiscoverIA registry, entry oai-fam-329-counterexample-pietschs-metric-entropy},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-329-counterexample-pietschs-metric-entropy#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 the manuscript were correct, Pietsch's duality conjecture would be false. The repository files this work under the section “Functional analysis”.
What remains unclear
The Lean code (Lean is a language in which a computer checks every step of a proof) was supplied by OpenAI itself, and no third-party verification is recorded; formalization.yaml carries the entry “review: status: unchecked”. The sources read do not give the exact setting of the conjecture or the statement of the counterexamples.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 329.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 · Counterexamples-to-the…link only, reading not recorded
- Lean proofgithub.com · 329.mdpage read word for word
- Lean proofgithub.com · MetricEntropyDuality.leanlink only, reading not recorded
Method
The openai/math repository contains one manuscript, “Counterexamples to the duality conjecture for metric entropy”, dated September 24, 2026 (family 329, section “Functional analysis” of overview.tex). The file lean/docs/329.md, which “describes the scope of the Lean formalization”, comes with 1 Comparator statement, lean/ComparatorChallenges/MetricEntropyDuality.lean; note recorded: family present in the `sources` of formalization.yaml. According to history.md, no revision is reported for the manuscripts of this family; commit fd4aeeb of October 7, 2026. 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).
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 329, section “Functional analysis”, 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 323 of 372, by family number
- Not evaluated : The cotype–cotype conjecture under the approximation property (family 326)
- Not evaluated : Markov type characterizes superreflexivity (family 327)
- Not evaluated : Fixed points of nonexpansive maps in reflexive Banach spaces (family 328)
- Not evaluated : A counterexample to Pietsch's metric-entropy duality conjecture (family 329)
- Not evaluated : A negative answer to Kalton's Lipschitz-free approximation question (family 330)
- Not evaluated : Asymptotic midpoint uniform convexity without asymptotically uniformly convex renorming (family 331)
- Not evaluated : Metric Markov cotype two for ℓ_1 (family 332)
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