{"paper":{"title":"The Broken Ray Transform in $n$ Dimensions with Flat Reflecting Boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mark Hubenthal","submitted_at":"2013-10-27T01:19:05Z","abstract_excerpt":"We study the broken ray transform on $n$-dimensional Euclidean domains where the reflecting parts of the boundary are flat and establish injectivity and stability under certain conditions. Given a subset $E$ of the boundary $\\partial \\Omega$ such that $\\partial \\Omega \\setminus E$ is itself flat (contained in a union of hyperplanes), we measure the attenuation of all broken rays starting and ending at $E$ with the standard optical reflection rule applied to $\\partial \\Omega \\setminus E$. By localizing the measurement operator around broken rays which reflect off a fixed sequence of flat hyperp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7156","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}