Not evaluated
Joint metric and connection recovery from one boundary patch (family 365)
The gist
OpenAI claims, in three manuscripts announced on October 6, 2026, results on determining a metric and a unitary connection, on the Calderón problem and on conductivities.
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-365-joint-metric-connection-recovery-one-r1
@misc{discoveria-oai-fam-365-joint-metric-connection-recovery-one-r1,
author = {{DiscoverIA}},
title = {Joint metric and connection recovery from one boundary patch (family 365)},
howpublished = {DiscoverIA registry, entry oai-fam-365-joint-metric-connection-recovery-one},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-365-joint-metric-connection-recovery-one#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 Calderón problem consists in recovering the conductivity inside a body from measurements made at its boundary. If the manuscripts held, the first would give the determination of a metric and a unitary connection from a single boundary patch. The second would give uniqueness for a smooth anisotropic version of the Calderón problem from one boundary patch. The third would give nonuniqueness (several possible answers) for bounded measurable scalar conductivities in three dimensions.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) is supplied by OpenAI itself, with the wording “review: status: unchecked”; no third-party verification is read. It includes only 1 Comparator statement, and the sources read do not say which of the three manuscripts it concerns.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 365.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 · Determination-of-a-metric…link only, reading not recorded
- Repositorygithub.com · Smooth-Anisotropic…link only, reading not recorded
- Repositorygithub.com · Nonuniqueness-for-Bounded…link only, reading not recorded
- Lean proofgithub.com · 365.mdpage read word for word
- Lean proofgithub.com · Conductivity.leanlink only, reading not recorded
Method
Manuscript of October 5, 2026: “Determination of a metric and a unitary connection from one boundary patch”. Manuscript of September 24, 2026: “Smooth Anisotropic Uniqueness in the Calderón Problem from One Boundary Patch”. Manuscript of September 23, 2026: “Nonuniqueness for Bounded Measurable Scalar Conductivities in Three Dimensions”. The claimant supplies lean/docs/365.md and 1 Comparator file: lean/ComparatorChallenges/Conductivity.lean. Section “Partial differential equations”; family present in the sources of formalization.yaml; history.md records 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 (Partial differential equations)
- In openai/math
- family 365, section “Partial differential equations”, 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
- 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 358 of 372, by family number
- Not evaluated : Global smoothness for relativistic Vlasov–Maxwell (family 362)
- Not evaluated : Boltzmann nonuniqueness with exact local conservation (family 363)
- Not evaluated : Kinetic limits and fluctuations over the Boltzmann lifespan (family 364)
- Not evaluated : Joint metric and connection recovery from one boundary patch (family 365)
- Not evaluated : The planar Mumford–Shah regularity conjecture (family 366)
- Not evaluated : The critical dimension for the one-phase Bernoulli problem (family 367)
- Not evaluated : The three-dimensional Ball–Evans approximation problem (family 368)
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