{"paper":{"title":"Discrete tomography: Magic numbers for $N$-fold symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Christian Huck, Johan Nilsson, Markus Moll","submitted_at":"2014-02-10T15:23:06Z","abstract_excerpt":"We consider the problem of distinguishing convex subsets of $n$-cyclotomic model sets $\\varLambda$ by (discrete parallel) X-rays in prescribed $\\varLambda$-directions. In this context, a `magic number' $m_{\\varLambda}$ has the property that any two convex subsets of $\\varLambda$ can be distinguished by their X-rays in any set of $m_{\\varLambda}$ prescribed $\\varLambda$-directions. Recent calculations suggest that (with one exception in the case $n=4$) the least possible magic number for $n$-cyclotomic model sets might just be $N+1$, where $N=\\operatorname{lcm}(n,2)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2183","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"}