Not evaluated
The sharp distortion of edit distance into ℓ_1 (family 099)
The gist
On October 6, 2026, OpenAI announced, with an unreleased internal model, three manuscripts on edit distance in l1, one of which announces bounds that match up to constants in the exponent.
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-099-sharp-distortion-edit-distance-l-1-r1
@misc{discoveria-oai-fam-099-sharp-distortion-edit-distance-l-1-r1,
author = {{DiscoverIA}},
title = {The sharp distortion of edit distance into ℓ_1 (family 099)},
howpublished = {DiscoverIA registry, entry oai-fam-099-sharp-distortion-edit-distance-l-1},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-099-sharp-distortion-edit-distance-l-1#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
The edit distance between two words is the minimum number of insertions, deletions and replacements of letters needed to turn one into the other. Embedding it into l1 means representing it by a sum of coordinate differences, with some distortion. If the first manuscript held, the distortion needed would be pinned down by bounds that match up to constants in the exponent.
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 4 Lean statements cover the three manuscripts.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 099.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 · Edit-Distance-in-l1…link only, reading not recorded
- Repositorygithub.com · Finite-Circle…link only, reading not recorded
- Repositorygithub.com · Tree-Constructions-for…link only, reading not recorded
- Lean proofgithub.com · 099.mdpage read word for word
- Lean proofgithub.com · BinaryEditLower.leanlink only, reading not recorded
- Lean proofgithub.com · EditDistance.leanlink only, reading not recorded
- Lean proofgithub.com · FiniteCircle.leanlink only, reading not recorded
- Lean proofgithub.com · TreeEdit.leanlink only, reading not recorded
Method
The openai/math repository contains three manuscripts dated September 27, 2026. The first is titled “Edit Distance in l1: Matching Bounds up to Constants in the Exponent”. The second is titled “Finite-Circle Obstructions, Binary Codes, and Histogram Embeddings for Edit Distance”. The third is titled “Tree Constructions for the l1 Distortion of Binary Edit Distance”. The file lean/docs/099.md describes the scope of the Lean formalisation, with 4 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
- Mathematics (Convex and metric geometry)
- In openai/math
- family 099, section “Convex and metric geometry”, 3 manuscripts dated Sep 27, 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
- 9 : 1 read word for word, 8 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 96 of 372, by family number
- Not evaluated : The Gaussian propeller conjecture (family 096)
- Not evaluated : The Euclidean Steinitz–Bergström conjecture (family 097)
- Not evaluated : A negative answer to the Lang–Plaut problem (family 098)
- Not evaluated : The sharp distortion of edit distance into ℓ_1 (family 099)
- Not evaluated : A counterexample to Bang's cylinder-covering bound (family 100)
- Not evaluated : The sharp simplex conjecture for isotropic constants (family 101)
- Not evaluated : Claimed proof of the Unique Games Conjecture (family 102)
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