Not evaluated
The spin-one Haldane gap (family 268)
The gist
On October 6, 2026, OpenAI announced 2 manuscripts on the Haldane gap of spin-one chains: one for the periodic chain, the other with a boundary field.
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-268-spin-one-haldane-gap-r1
@misc{discoveria-oai-fam-268-spin-one-haldane-gap-r1,
author = {{DiscoverIA}},
title = {The spin-one Haldane gap (family 268)},
howpublished = {DiscoverIA registry, entry oai-fam-268-spin-one-haldane-gap},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-268-spin-one-haldane-gap#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
A Heisenberg chain is a row of spins (small magnets) that interact with their neighbours. If the manuscripts held, they would concern the energy gap of the spin-one chain, the interval between the lowest state and the excited states. The question aimed at would be whether the gap would remain bounded below by a positive constant as the chain gets longer.
What remains unclear
No Lean (a language in which a computer checks every step of a proof) is supplied, and no third-party evaluation is read in the sources. They do not say what each of the 2 manuscripts claims to prove.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · README.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-periodic-spin-one…link only, reading not recorded
- Repositorygithub.com · A-boundary-field-gap-for…link only, reading not recorded
Method
2 manuscripts dated September 24, 2026: “The periodic spin-one Haldane gap” and “A boundary-field gap for the spin-one Heisenberg chain”. The family is filed under the section “Mathematical physics” (overview.tex), with no lean/docs/268.md. 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: “Not all have accompanying Lean formalizations.”).
Limits
DiscoverIA has not checked this result itself.
Key facts
- Claimed by
- OpenAI (unreleased internal model)
announced on Oct 6, 2026 - Nature
- new result
- Field
- Mathematics (Mathematical physics)
- In openai/math
- family 268, section “Mathematical physics”, 2 manuscripts dated Sep 24, 2026
- Lean proof
- none supplied
- Revisions
- none reported by the claimant
- Checked by
- no verifier identified
- Sources
- 3 : 3 links only
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
Family with no Lean proof supplied. No third-party evaluation read.
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 262 of 372, by family number
- 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)
- Not evaluated : Bloch's law and spontaneous ferromagnetic order (family 271)
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