{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:OCILDZUG2FTGTOITLI3RDMPFTJ","short_pith_number":"pith:OCILDZUG","schema_version":"1.0","canonical_sha256":"7090b1e686d16669b9135a3711b1e59a75ec2a038aec3e6bc055b87494784011","source":{"kind":"arxiv","id":"1403.0098","version":1},"attestation_state":"computed","paper":{"title":"Topological and measure properties of some self-similar sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Artur Bartoszewicz, Emilia Szymonik, Malgorzata Filipczak, Taras Banakh","submitted_at":"2014-03-01T15:43:44Z","abstract_excerpt":"Given a finite subset $\\Sigma\\subset\\mathbb{R}$ and a positive real number $q<1$ we study topological and measure-theoretic properties of the self-similar set $K(\\Sigma;q)=\\big\\{\\sum_{n=0}^\\infty a_nq^n:(a_n)_{n\\in\\omega}\\in\\Sigma^\\omega\\big\\}$, which is the unique compact solution of the equation $K=\\Sigma+qK$. The obtained results are applied to studying partial sumsets $E(x)=\\big\\{\\sum_{n=0}^\\infty x_n\\varepsilon_n:(\\varepsilon_n)_{n\\in\\omega}\\in\\{0,1\\}^\\omega\\big\\}$ of some (multigeometric) sequences $x=(x_n)_{n\\in\\omega}$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1403.0098","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2014-03-01T15:43:44Z","cross_cats_sorted":[],"title_canon_sha256":"4e946a88e4fd433597375178c48666ef3331ad940d3ae8d3fa09d9a3daeca1b1","abstract_canon_sha256":"6f172c8beb9bca6a8ab81e37cc6cc4e3c9ba0a34513855aed65b61f501b5ed7c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:26.589047Z","signature_b64":"VlLui3qsPgYzrcrK11AvxD04icPrYKzgdbWuUMx00hT1+ngcYpNVDZU1PFMt3gsqVhpGv8QIpOc6McIhegDVBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7090b1e686d16669b9135a3711b1e59a75ec2a038aec3e6bc055b87494784011","last_reissued_at":"2026-05-18T01:20:26.588525Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:26.588525Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Topological and measure properties of some self-similar sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Artur Bartoszewicz, Emilia Szymonik, Malgorzata Filipczak, Taras Banakh","submitted_at":"2014-03-01T15:43:44Z","abstract_excerpt":"Given a finite subset $\\Sigma\\subset\\mathbb{R}$ and a positive real number $q<1$ we study topological and measure-theoretic properties of the self-similar set $K(\\Sigma;q)=\\big\\{\\sum_{n=0}^\\infty a_nq^n:(a_n)_{n\\in\\omega}\\in\\Sigma^\\omega\\big\\}$, which is the unique compact solution of the equation $K=\\Sigma+qK$. The obtained results are applied to studying partial sumsets $E(x)=\\big\\{\\sum_{n=0}^\\infty x_n\\varepsilon_n:(\\varepsilon_n)_{n\\in\\omega}\\in\\{0,1\\}^\\omega\\big\\}$ of some (multigeometric) sequences $x=(x_n)_{n\\in\\omega}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0098","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1403.0098","created_at":"2026-05-18T01:20:26.588632+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.0098v1","created_at":"2026-05-18T01:20:26.588632+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.0098","created_at":"2026-05-18T01:20:26.588632+00:00"},{"alias_kind":"pith_short_12","alias_value":"OCILDZUG2FTG","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_16","alias_value":"OCILDZUG2FTGTOIT","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_8","alias_value":"OCILDZUG","created_at":"2026-05-18T12:28:41.024544+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OCILDZUG2FTGTOITLI3RDMPFTJ","json":"https://pith.science/pith/OCILDZUG2FTGTOITLI3RDMPFTJ.json","graph_json":"https://pith.science/api/pith-number/OCILDZUG2FTGTOITLI3RDMPFTJ/graph.json","events_json":"https://pith.science/api/pith-number/OCILDZUG2FTGTOITLI3RDMPFTJ/events.json","paper":"https://pith.science/paper/OCILDZUG"},"agent_actions":{"view_html":"https://pith.science/pith/OCILDZUG2FTGTOITLI3RDMPFTJ","download_json":"https://pith.science/pith/OCILDZUG2FTGTOITLI3RDMPFTJ.json","view_paper":"https://pith.science/paper/OCILDZUG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.0098&json=true","fetch_graph":"https://pith.science/api/pith-number/OCILDZUG2FTGTOITLI3RDMPFTJ/graph.json","fetch_events":"https://pith.science/api/pith-number/OCILDZUG2FTGTOITLI3RDMPFTJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OCILDZUG2FTGTOITLI3RDMPFTJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OCILDZUG2FTGTOITLI3RDMPFTJ/action/storage_attestation","attest_author":"https://pith.science/pith/OCILDZUG2FTGTOITLI3RDMPFTJ/action/author_attestation","sign_citation":"https://pith.science/pith/OCILDZUG2FTGTOITLI3RDMPFTJ/action/citation_signature","submit_replication":"https://pith.science/pith/OCILDZUG2FTGTOITLI3RDMPFTJ/action/replication_record"}},"created_at":"2026-05-18T01:20:26.588632+00:00","updated_at":"2026-05-18T01:20:26.588632+00:00"}