Not evaluated
Positive-temperature Bose–Einstein condensation and quantum depletion (family 267)
The gist
OpenAI claims, in an announcement of October 6, 2026, results on Bose-Einstein condensation and quantum depletion in dilute gases, in five manuscripts.
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-267-positive-temperature-boseeinstein-r1
@misc{discoveria-oai-fam-267-positive-temperature-boseeinstein-r1,
author = {{DiscoverIA}},
title = {Positive-temperature Bose–Einstein condensation and quantum depletion (family 267)},
howpublished = {DiscoverIA registry, entry oai-fam-267-positive-temperature-boseeinstein},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-267-positive-temperature-boseeinstein#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 held, they would treat Bose-Einstein condensation at positive temperature in a dilute gas of hard spheres; the ground state belongs to another manuscript. Quantum depletion (the share of particles outside the condensate) would be studied for this gas and for fixed bounded repulsive potentials. A condensate bound, uniform in density, would concern dilute Bose gases.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) is supplied by the claimant and marked “review: status: unchecked” in formalization.yaml. No third-party check has been read. It is not known which of the five manuscripts the Lean covers.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 267.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 · Bose-Einstein…link only, reading not recorded
- Repositorygithub.com · Quantum-Depletion-and…link only, reading not recorded
- Repositorygithub.com · Quantum-Depletion-for…link only, reading not recorded
- Repositorygithub.com · A-density-uniform…link only, reading not recorded
- Repositorygithub.com · Ground-state-condensation…link only, reading not recorded
- Lean proofgithub.com · 267.mdpage read word for word
- Lean proofgithub.com · HardSphere.leanlink only, reading not recorded
Method
Five manuscripts, dated September 24, September 27 and October 5, 2026, including “Bose-Einstein condensation at positive temperature in the dilute hard-sphere gas”. A Comparator statement is described in lean/docs/267.md, with the file lean/ComparatorChallenges/HardSphere.lean. The family is absent from the `sources` of formalization.yaml; history.md reports 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 (Mathematical physics)
- In openai/math
- family 267, section “Mathematical physics”, 5 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
- 8 : 1 read word for word, 7 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 261 of 372, by family number
- Not evaluated : Strong cosmic censorship near two-ended Kerr data (family 264)
- Not evaluated : The two-dimensional gapped area law (family 265)
- Not evaluated : Exactly three mutually unbiased bases in dimension six (family 266)
- Not evaluated : Positive-temperature Bose–Einstein condensation and quantum depletion (family 267)
- Not evaluated : The spin-one Haldane gap (family 268)
- Not evaluated : The Laughlin gap and stability under scalar disorder (family 269)
- Not evaluated : Threshold and positive-energy bound states of the BFSS model (family 270)
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