Not evaluated
Critical logarithmic corrections and BKT scaling for the planar XY model (family 216)
The gist
OpenAI claims, in an announcement of October 6, 2026, results on the critical behaviour of the planar XY model, in six 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-216-critical-logarithmic-corrections-bkt-scaling-r1
@misc{discoveria-oai-fam-216-critical-logarithmic-corrections-bkt-scaling-r1,
author = {{DiscoverIA}},
title = {Critical logarithmic corrections and BKT scaling for the planar XY model (family 216)},
howpublished = {DiscoverIA registry, entry oai-fam-216-critical-logarithmic-corrections-bkt-scaling},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-216-critical-logarithmic-corrections-bkt-scaling#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 manuscripts held, they would describe the planar XY model at its critical point: the critical logarithmic correction, the critical correlation exponent and BKT universality. One of them would concern an essential singularity of the correlation length, the distance over which orientations remain linked.
What remains unclear
No Lean is supplied for this family and no third-party evaluation has been read. The precise statement of each result is not known: only the titles of the six manuscripts are available.
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-critical-logarithmic…link only, reading not recorded
- Repositorygithub.com · Critical-Center…link only, reading not recorded
- Repositorygithub.com · The-Critical-Spin-Field…link only, reading not recorded
- Repositorygithub.com · Essential-Singularity-of…link only, reading not recorded
- Repositorygithub.com · The-critical-correlation…link only, reading not recorded
- Repositorygithub.com · BKT-universality-for…link only, reading not recorded
Method
Two manuscripts are dated September 24, 2026: “The critical correlation exponent of the planar XY model” and “BKT universality for height and planar spin fields”. Two are dated October 5, 2026: “The critical logarithmic correction for the planar XY model” and “Critical Center Magnetization in the Planar XY Model”. Two others are also dated October 5, 2026: “The Critical Spin Field of the Planar XY Model” and “Essential Singularity of the Correlation Length in the Planar XY Model”. 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 (Probability and statistical mechanics)
- In openai/math
- family 216, section “Probability and statistical mechanics”, 6 manuscripts dated Sep 24, 2026
- Lean proof
- none supplied
- Revisions
- none reported by the claimant
- Checked by
- no verifier identified
- Sources
- 7 : 7 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 210 of 372, by family number
- Not evaluated : No infinite critical clusters on quasi-transitive graphs (family 213)
- Not evaluated : The Benjamini–Schramm nonuniqueness conjecture (family 214)
- Not evaluated : Massive continuum limits and exact mass asymptotics for planar O(n) models (family 215)
- Not evaluated : Critical logarithmic corrections and BKT scaling for the planar XY model (family 216)
- Not evaluated : The low-temperature Sherrington–Kirkpatrick fluctuation law (family 217)
- Not evaluated : Conformal universality for weakly interacting and disordered Ising models (family 218)
- Not evaluated : GOE universality for random regular graphs with weak disorder (family 219)
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