Not evaluated
Optimal-order randomized k-server on arbitrary metrics (family 110)
The gist
On October 6, 2026, OpenAI announced, with an unreleased internal model, two manuscripts on the randomized k-server problem, with a squared-logarithmic bound.
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-110-optimal-order-randomized-k-server-arbitrary-r1
@misc{discoveria-oai-fam-110-optimal-order-randomized-k-server-arbitrary-r1,
author = {{DiscoverIA}},
title = {Optimal-order randomized k-server on arbitrary metrics (family 110)},
howpublished = {DiscoverIA registry, entry oai-fam-110-optimal-order-randomized-k-server-arbitrary},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-110-optimal-order-randomized-k-server-arbitrary#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
In the k-server problem, servers move over the points of a space with distances to answer requests that arrive one at a time. The manuscripts would claim a squared-logarithmic bound for the randomized k-server problem (where the algorithm makes random choices) on arbitrary metrics.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) is supplied by OpenAI itself, and its tracking file carries the mention “unchecked”. No third-party verification is recorded. It is not known how far the 2 Lean statements cover the manuscripts, and the sources read do not say of which quantity the bound is the squared logarithm.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 110.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 · Squared-logarithmic…link only, reading not recorded
- Repositorygithub.com · Uniform-computation-of…link only, reading not recorded
- Lean proofgithub.com · 110.mdpage read word for word
- Lean proofgithub.com · KServer.leanlink only, reading not recorded
- Lean proofgithub.com · UniformKServer.leanlink only, reading not recorded
Method
The openai/math repository contains two manuscripts dated September 24, 2026. The first is titled “Squared-logarithmic randomized k-server on arbitrary metrics”, the second “Uniform computation of the squared-logarithmic k-server bound”. The file lean/docs/110.md describes the scope of the Lean formalisation, with 2 Comparator statements. The family is not among the sources of formalization.yaml, 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: “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
- Theoretical computer science
- In openai/math
- family 110, section “Theoretical computer science”, 2 manuscripts dated Sep 24, 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
- 6 : 1 read word for word, 5 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 107 of 372, by family number
- Not evaluated : Matrix multiplication exponent at most 9/4 (family 107)
- Not evaluated : A cubic permanent–determinant lower bound (family 108)
- Not evaluated : Integer multiplication below n log n (family 109)
- Not evaluated : Optimal-order randomized k-server on arbitrary metrics (family 110)
- Not evaluated : One-sample matroid prophet inequalities against an almighty adversary (family 111)
- Not evaluated : Beyond the square-root exponent for depth-three circuits (family 112)
- Not evaluated : Approximate counting and the perfect-matching entropy conjecture (family 113)
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