Not evaluated
The Phillips–Toms formula for minimal integer actions (family 302)
The gist
In its release of October 6, 2026, OpenAI presents two manuscripts, one on the equality of the radius of comparison and half the mean dimension.
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-302-phillipstoms-formula-minimal-integer-actions-r1
@misc{discoveria-oai-fam-302-phillipstoms-formula-minimal-integer-actions-r1,
author = {{DiscoverIA}},
title = {The Phillips–Toms formula for minimal integer actions (family 302)},
howpublished = {DiscoverIA registry, entry oai-fam-302-phillipstoms-formula-minimal-integer-actions},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-302-phillipstoms-formula-minimal-integer-actions#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 this manuscript held, one of the two quantities could be deduced from the other, in the field of operator algebras. The setting appears only in the family title, “The Phillips–Toms formula for minimal integer actions”, and not in the manuscript titles; the sources read do not detail it.
What remains unclear
The sources read do not explain how the manuscript whose title concerns complex cobordism relates to this family. No Lean formalisation (a language in which a computer checks every step of a proof) is supplied, and no third-party assessment has been read.
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 · Filtered-products-and…link only, reading not recorded
- Repositorygithub.com · Radius-of-comparison…link only, reading not recorded
Method
The openai/math repository holds two manuscripts, dated September 25, 2026. They are titled “Radius of comparison equals half the mean dimension” and “Filtered products and boundary-preserving compression in complex cobordism”. The family sits in the “Operator algebras” section of overview.tex; history.md reports no revision of these manuscripts. 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 (Operator algebras)
- In openai/math
- family 302, section “Operator algebras”, 2 manuscripts dated Sep 25, 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 296 of 372, by family number
- Not evaluated : The Kirchberg–Rørdam character criterion (family 299)
- Not evaluated : The Popa–Vaes quadratic strong-operator paving conjecture (family 300)
- Not evaluated : Classification by trace cones after Razak–Jacelon stabilization (family 301)
- Not evaluated : The Phillips–Toms formula for minimal integer actions (family 302)
- Not evaluated : From ordinary to strong pure infiniteness (family 303)
- Not evaluated : The Hilbert–Smith conjecture in every dimension (family 304)
- Not evaluated : Counterexamples to disk embedding and Wall's manifold conjecture (family 305)
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