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The C∞C^\infty Carathéodory Conjecture on Umbilic Points

Only the smooth case falls. Hamburger's real-analytic theorem is untouched, and the counterexample is explicitly a C∞C^\infty object, so the conjecture's classical analytic form remains true. The gap between the two is the whole content of the result.

Exact FrontierDelta

Prior state unknown→disproved

Scope and record

Occurred: Aug 19, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: lean-checked. Publication: announcement. AI contribution: ai-assisted. Editorial metadata: CC BY 4.0; linked content retains its own rights.

Canonical aliases: The $C^\infty$ Carathéodory Conjecture on Umbilic Points · Carathéodory conjecture (smooth)

Confidence: Not scored

Registry verification: lean checked · announcement · candidate

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Attribution

VibeMathed
registry · event recorded by

Levent Alpöge
human · human collaborator

John-Paul Smith
human · human collaborator

Claude
model · ai model contributor · Anthropic

Codex
model · ai model contributor · OpenAI

Artifacts and verifiers

Lean proof, sorry-free at the pinned commit

lean artifact · pending

Artifact ↗
Lean statement of the smooth and analytic conjectures

formal registration · pending

Artifact ↗

Compute record

No linked compute attempts recorded.

Lineage and corrections

This event attributed to Levent Alpöge

This event attributed to John-Paul Smith

This event attributed to Claude

This event attributed to Codex

The C∞C^\infty Carathéodory Conjecture on Umbilic Points parent of this event

Only the smooth case falls. Hamburger's real-analytic theorem is untouched, and the counterexample is explicitly a C∞C^\infty object, so the conjecture's classical analytic form remains true. The gap between the two is the whole content of the result. parent of this event

Ghomi, Open Problems in Geometry of Curves and Surfaces (Problem 8.1) evidence for this event

VibeMathed record: The C∞C^\infty Carathéodory Conjecture on Umbilic Points evidence for this event

Lean proof, sorry-free at the pinned commit evidence for this event

The C∞C^\infty Carathéodory Conjecture on Umbilic Points evidence for this event

The informal proof accompanying the formalization evidence for this event

Lean statement of the smooth and analytic conjectures evidence for this event

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The $C^\infty$ Carathéodory Conjecture on Umbilic Points — Mathematical Frontier Network