Not evaluated
Directional zero–one laws and ballisticity in random environments (family 220)
The gist
On October 6, 2026, OpenAI announced three manuscripts on random environments: two directional zero–one laws and one result linking directional transience and ballisticity.
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-220-directional-zeroone-laws-ballisticity-random-r1
@misc{discoveria-oai-fam-220-directional-zeroone-laws-ballisticity-random-r1,
author = {{DiscoverIA}},
title = {Directional zero–one laws and ballisticity in random environments (family 220)},
howpublished = {DiscoverIA registry, entry oai-fam-220-directional-zeroone-laws-ballisticity-random},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-220-directional-zeroone-laws-ballisticity-random#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
A zero–one law states that an event has probability either zero or one, never an intermediate value. If these manuscripts held up, such laws would exist for certain random environments, and directional transience would imply ballisticity (a non-zero speed in the long run in that direction). The titles do not state the assumptions of that last result.
What remains unclear
OpenAI itself supplies the Lean (a language in which a computer checks every step of a proof), and its review is marked “unchecked”. No third-party check or evaluation has been read.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 220.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 · …for-finite-range…link only, reading not recorded
- Repositorygithub.com · …under-strict-ellipticity…link only, reading not recorded
- Repositorygithub.com · Directional-transience…link only, reading not recorded
- Lean proofgithub.com · 220.mdpage read word for word
- Lean proofgithub.com · DirectionalBallisticity.le…link only, reading not recorded
- Lean proofgithub.com · DirectionalWalk.leanlink only, reading not recorded
- Lean proofgithub.com · VelocityHemisphere.leanlink only, reading not recorded
Method
Three manuscripts are published: “A directional zero–one law for finite-range-dependent random environments” (October 5, 2026), “A directional zero–one law under strict ellipticity” (September 23, 2026) and “Directional transience implies ballisticity” (September 23, 2026). OpenAI supplies lean/docs/220.md and 3 Comparator statements: lean/ComparatorChallenges/DirectionalBallisticity.lean, lean/ComparatorChallenges/DirectionalWalk.lean and lean/ComparatorChallenges/VelocityHemisphere.lean. 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: “describes the scope of the Lean formalization”).
Limits
No named third party: the recorded checks come from the claimant or from a platform tool. The claimant supplies a Lean proof; as of this date, DiscoverIA has found no independent verification of this proof or of the result.
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 220, section “Probability and statistical mechanics”, 3 manuscripts dated Sep 23, 2026
- Lean proof
- supplied by the claimant, marked “unchecked” (not reviewed) in its repository
- Revisions
- none reported by the claimant
- Checked by
- claimant (Lean supplied, not checked by a third party)
- Sources
- 8 : 1 read word for word, 7 links only
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
Family with a Lean proof supplied by the claimant. No third-party check read; the source marks this proof as not reviewed (“unchecked”).
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 214 of 372, by family number
- 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)
- Not evaluated : Directional zero–one laws and ballisticity in random environments (family 220)
- Not evaluated : The Mézard–Parisi formula for diluted spin glasses (family 221)
- Not evaluated : Perceptron free energies and microscopic jamming (family 222)
- Not evaluated : Conformal limits of square-lattice random-cluster interfaces (family 223)
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