{"id":"openai-math/Determination-of-a-metric-and-a-unitary-connection-from-one-boundary-patch","pdf":"https://github.com/openai/math/blob/main/preprints/Determination-of-a-metric-and-a-unitary-connection-from-one-boundary-patch-October-5-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Determination-of-a-metric-and-a-unitary-connection-from-one-boundary-patch-October-5-2026","tags":["differential-geometry","inverse-problems","gauge-theory"],"score":0,"title":"Determination of a metric and a unitary connection from one boundary patch","domain":"Partial differential equations","family":"365","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AP","summary":"We prove that zero-frequency boundary measurements on any nonempty open boundary patch determine both a smooth Riemannian metric and a smooth unitary connection on the trivial Hermitian rank-two bundle over a compact connected smooth manifold of dimension at least three with smooth boundary. Both inputs and observations are restricted to the same patch. The metric and connection are determined up to a diffeomorphism and a unitary gauge that restrict to the identity on the measured patch.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-05","reactions":{},"formalized":false,"family_title":"Joint metric and connection recovery from one boundary patch"}