Source authenticated

Schiffer's Conjecture and the Pompeiu Problem

Also refutes the 1929 Pompeiu problem: Corollary 1.2 applies Williams' classical 1976 equivalence to the same constructed domains, so this is one construction settling both, not two separate results.

Exact FrontierDelta

disproved→disproved

Scope and record

Occurred: Oct 29, 2026

Delta type: REGISTRY REVISION

Assumptions: VibeMathed verification: lean-verified. Publication: preprint. AI contribution: ai-assisted. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: Schiffer's Conjecture and the Pompeiu Problem · Schiffer's Conjecture

Confidence: Not scored

Registry verification: lean verified · preprint · resolved

Open the source record ↗

Attribution

VibeMathed
registry · event recorded by

GPT-5.6
model · ai model contributor · maker attribution ambiguous: OpenAI, Anthropic

Claude Opus 4.8
model · ai model contributor · maker attribution ambiguous: OpenAI, Anthropic

Claude Fable 5
model · ai model contributor · maker attribution ambiguous: OpenAI, Anthropic

Gonzalo Cao-Labora
human · human collaborator

Jaume de Dios Pont
human · human collaborator

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: Schiffer's Conjecture and the Pompeiu Problem

specialist registry · passed

A day-old preprint. The paper states that a Lean4 verification of the proof was written by GPT 5.6, available at https://github.com/jaumededios/Schiffer. It solves the Pompeiu Problem challenge provided by https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/Wikipedia/PompeiuProblem.lean

Source ↗

Lean formalization of Theorem 1.1 and Corollary 1.2

lean artifact · passed

lean-proof link supplied by the VibeMathed registry.

Source ↗

Schiffer's Conjecture and the Pompeiu Problem

preprint · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

Source ↗

Pompeiu problem Wikipedia article

witness · pending

wikipedia link supplied by the VibeMathed registry.

Source ↗

Artifacts and verifiers

Lean formalization of Theorem 1.1 and Corollary 1.2

lean artifact · passed

Artifact ↗

Compute record

No linked compute attempts recorded.

Lineage and corrections

Corrects Schiffer's Conjecture and the Pompeiu Problem →

Supersedes Schiffer's Conjecture and the Pompeiu Problem →

Also refutes the 1929 Pompeiu problem: Corollary 1.2 applies Williams' classical 1976 equivalence to the same constructed domains, so this is one construction settling both, not two separate results. parent of this event

This event attributed to GPT-5.6

Schiffer's Conjecture and the Pompeiu Problem parent of this event

This event attributed to Jaume de Dios Pont

Pompeiu problem Wikipedia article evidence for this event

VibeMathed record: Schiffer's Conjecture and the Pompeiu Problem evidence for this event

Schiffer's Conjecture and the Pompeiu Problem evidence for this event

This event attributed to Gonzalo Cao-Labora

Lean formalization of Theorem 1.1 and Corollary 1.2 evidence for this event

This event attributed to Claude Opus 4.8

This event attributed to Claude Fable 5

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