Smooth anisotropic uniqueness in the Calderón problem from one boundary patch

OpenAI

For compact connected smooth manifolds of dimension at least three, the manuscript claims that equal density-valued energy Dirichlet-to-Neumann forms measured on any nonempty proper relatively open boundary patch determine two smooth metrics up to a smooth diffeomorphism fixing that patch.

Sources for this record

What was already known

Prior anisotropic recovery results cited in the manuscript required real analyticity, Einstein structure, or other geometric restrictions.

AI involvement AI-led

OpenAI identifies the manuscript as an internal-model product and is the credited author. No named human check or explanation of the continuation argument is documented.

The credited author is the AI institution OpenAI and the repository describes the manuscripts as internal-model products.

Importance Major

Arbitrary-patch uniqueness for smooth anisotropic metrics would settle a central inverse-boundary question.

Limitations

The claimed full proof has no documented completed human check, matching formalization, or exact certificate; the smooth and arbitrary-patch scope remains unverified.

Technical verification Reported

A complete proof is presented, but no completed human check, matching Lean formalization, or exact computational certificate for this theorem is documented in the reviewed release. A proof's availability alone is not a check.

Human understanding Few

The paper gives a mathematical explanation but does not identify a person's understanding of the central continuation and globalization argument; Few is the documentation default.

Correction and publication history

2026-10-18 · publication

If correct, arbitrary-patch uniqueness for smooth anisotropic metrics would settle a central inverse-boundary question.

Read this published revision