Not evaluated
The two-dimensional gapped area law (family 265)
The gist
On October 6, 2026, OpenAI announced two manuscripts, one on a two-dimensional area law, the other on approximating ground states on a square grid.
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-265-two-dimensional-gapped-area-law-r1
@misc{discoveria-oai-fam-265-two-dimensional-gapped-area-law-r1,
author = {{DiscoverIA}},
title = {The two-dimensional gapped area law (family 265)},
howpublished = {DiscoverIA registry, entry oai-fam-265-two-dimensional-gapped-area-law},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-265-two-dimensional-gapped-area-law#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 system is said to have a spectral gap when the gap between its ground state (the lowest energy) and the next levels does not close as the system grows. An area law ties the entanglement (quantum correlation) of a region with the rest to the size of its boundary rather than to its volume. PEPS are states described by a tensor network. If the manuscripts were correct, they would link this gap to a limit on entanglement and to an approximation of these states by PEPS.
What remains unclear
No third-party assessment has been found, and no Lean (a language in which a computer checks every step of a proof) is supplied. The sources read do not give the precise statements of the two manuscripts.
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 · A-two-dimensional-area…link only, reading not recorded
- Repositorygithub.com · Polynomial-PEPS…link only, reading not recorded
Method
Two manuscripts, both dated September 24, 2026. The first is titled “A two-dimensional area law from a global spectral gap”. The second is titled “Polynomial PEPS approximation of gapped square-grid ground states”. The section of overview.tex for family 265 is “Mathematical physics”, and 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: “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 265, 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 259 of 372, by family number
- Not evaluated : Sharp one-dimensional Lieb–Thirring inequalities (family 262)
- Not evaluated : The ionization and generalized ionization conjectures (family 263)
- 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)
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