{"paper":{"title":"Solution of a uniqueness problem in the discrete tomography of algebraic Delone sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Christian Huck, Michael Spiess","submitted_at":"2011-01-21T14:44:51Z","abstract_excerpt":"We consider algebraic Delone sets $\\varLambda$ in the Euclidean plane and address the problem of distinguishing convex subsets of $\\varLambda$ by X-rays in prescribed $\\varLambda$-directions, i.e., directions parallel to nonzero interpoint vectors of $\\varLambda$. Here, an X-ray in direction $u$ of a finite set gives the number of points in the set on each line parallel to $u$. It is shown that for any algebraic Delone set $\\varLambda$ there are four prescribed $\\varLambda$-directions such that any two convex subsets of $\\varLambda$ can be distinguished by the corresponding X-rays. We further "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4149","kind":"arxiv","version":1},"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"}