{"paper":{"title":"p-adic path set fractals and arithmetic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Jeffrey C. Lagarias, William Abram","submitted_at":"2012-10-09T03:31:44Z","abstract_excerpt":"This paper considers a class C(Z_p) of closed sets of the p-adic integers obtained by graph-directed constructions analogous to those of Mauldin and Williams over the real numbers. These sets are characterized as collections of those p-adic integers whose p-adic expansions are describeed by paths in the graph of a finite automaton issuing from a distinguished initial vertex. This paper shows that this class of sets is closed under the arithmetic operations of addition and multiplication by p-integral rational numbers. In addition the Minkowski sum (under p-adic addition) of two set in the clas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2478","kind":"arxiv","version":4},"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"}