Not evaluated
Pointwise multiple ergodic averages for mixing transformations (family 154)
The gist
On October 6, 2026, OpenAI announced, from an unreleased internal model, four manuscripts on multiple ergodic averages for mixing transformations.
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-154-pointwise-multiple-ergodic-averages-mixing-r1
@misc{discoveria-oai-fam-154-pointwise-multiple-ergodic-averages-mixing-r1,
author = {{DiscoverIA}},
title = {Pointwise multiple ergodic averages for mixing transformations (family 154)},
howpublished = {DiscoverIA registry, entry oai-fam-154-pointwise-multiple-ergodic-averages-mixing},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-154-pointwise-multiple-ergodic-averages-mixing#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 were correct, they would bring results on the pointwise convergence of triple and fourfold ergodic averages for mixing transformations, according to their titles. A multiple ergodic average is an average of products of values taken at linked times. One manuscript treats triple averages with distinct integer slopes.
What remains unclear
No Lean file (Lean is a language in which a computer checks every step of a proof) is supplied, and no third-party evaluation is recorded. It is not known whether specialists have reviewed the 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 · Pointwise-Multiple…link only, reading not recorded
- Repositorygithub.com · …fourfold-ergodic-averages…link only, reading not recorded
- Repositorygithub.com · Triple-ergodic-averages…link only, reading not recorded
- Repositorygithub.com · …triple-ergodic-averages…link only, reading not recorded
Method
The four manuscripts of family 154 are dated October 4, 2026. One is titled “Pointwise Multiple Ergodic Averages for Mixing Transformations”. A second is titled “Pointwise convergence of fourfold ergodic averages for mixing transformations”. A third is titled “Triple ergodic averages with distinct integer slopes”. The fourth is titled “Pointwise convergence of triple ergodic averages for mixing transformations”. They are filed under the section “Dynamical systems and ergodic theory” of overview.tex; 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 (Dynamical systems and ergodic theory)
- In openai/math
- family 154, section “Dynamical systems and ergodic theory”, 4 manuscripts dated Oct 4, 2026
- Lean proof
- none supplied
- Revisions
- none reported by the claimant
- Checked by
- no verifier identified
- Sources
- 5 : 5 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 150 of 372, by family number
- Not evaluated : A C¹ counterexample to Shub’s entropy conjecture (family 151)
- Not evaluated : Zero entropy does not guarantee a smooth positive-volume model (family 152)
- Not evaluated : Arithmetic classification of Bernoulli convolutions (family 153)
- Not evaluated : Pointwise multiple ergodic averages for mixing transformations (family 154)
- Not evaluated : A counterexample to periodic tiling in dimension three (family 155)
- Not evaluated : Borsuk's conjecture fails in dimension nine (family 156)
- Not evaluated : The Euclidean plane cannot be colored with five colors (family 158)
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