{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:I3XQQAVNIGNOWGQ6VUVCPDHNAB","short_pith_number":"pith:I3XQQAVN","schema_version":"1.0","canonical_sha256":"46ef0802ad419aeb1a1ead2a278ced0062379906c93cfe0bf78c3ca077d5b37d","source":{"kind":"arxiv","id":"1110.3192","version":1},"attestation_state":"computed","paper":{"title":"Intersections of homogeneous Cantor sets and beta-expansions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Derong Kong, Michel Dekking, Wenxia Li","submitted_at":"2011-10-14T12:53:22Z","abstract_excerpt":"Let $\\Gamma_{\\beta,N}$ be the $N$-part homogeneous Cantor set with $\\beta\\in(1/(2N-1),1/N)$. Any string $(j_\\ell)_{\\ell=1}^\\N$ with $j_\\ell\\in\\{0,\\pm 1,...,\\pm(N-1)\\}$ such that $t=\\sum_{\\ell=1}^\\N j_\\ell\\beta^{\\ell-1}(1-\\beta)/(N-1)$ is called a code of $t$. Let $\\mathcal{U}_{\\beta,\\pm N}$ be the set of $t\\in[-1,1]$ having a unique code, and let $\\mathcal{S}_{\\beta,\\pm N}$ be the set of $t\\in\\mathcal{U}_{\\beta,\\pm N}$ which make the intersection $\\Gamma_{\\beta,N}\\cap(\\Gamma_{\\beta,N}+t)$ a self-similar set. We characterize the set $\\mathcal{U}_{\\beta,\\pm N}$ in a geometrical and algebraical w"},"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":"1110.3192","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-10-14T12:53:22Z","cross_cats_sorted":[],"title_canon_sha256":"04c4344e3140a531f08adbf1be28553f2434ac5f441d97f009d947b3c2b1de39","abstract_canon_sha256":"94aeb26f651864adaab95ea959183762ea173fc47344ba623e3e719a1daf5cb9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:57.816909Z","signature_b64":"kQ0JabeRtYZ+WVRu5J1MLnci36j1ZLUhbnIbNyotjXvd4cp/RhepMoA5VsAXRuDueHNDGAGtaxLZe9klINS+CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46ef0802ad419aeb1a1ead2a278ced0062379906c93cfe0bf78c3ca077d5b37d","last_reissued_at":"2026-05-18T04:10:57.816363Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:57.816363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Intersections of homogeneous Cantor sets and beta-expansions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Derong Kong, Michel Dekking, Wenxia Li","submitted_at":"2011-10-14T12:53:22Z","abstract_excerpt":"Let $\\Gamma_{\\beta,N}$ be the $N$-part homogeneous Cantor set with $\\beta\\in(1/(2N-1),1/N)$. Any string $(j_\\ell)_{\\ell=1}^\\N$ with $j_\\ell\\in\\{0,\\pm 1,...,\\pm(N-1)\\}$ such that $t=\\sum_{\\ell=1}^\\N j_\\ell\\beta^{\\ell-1}(1-\\beta)/(N-1)$ is called a code of $t$. Let $\\mathcal{U}_{\\beta,\\pm N}$ be the set of $t\\in[-1,1]$ having a unique code, and let $\\mathcal{S}_{\\beta,\\pm N}$ be the set of $t\\in\\mathcal{U}_{\\beta,\\pm N}$ which make the intersection $\\Gamma_{\\beta,N}\\cap(\\Gamma_{\\beta,N}+t)$ a self-similar set. We characterize the set $\\mathcal{U}_{\\beta,\\pm N}$ in a geometrical and algebraical w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3192","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":"1110.3192","created_at":"2026-05-18T04:10:57.816453+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.3192v1","created_at":"2026-05-18T04:10:57.816453+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3192","created_at":"2026-05-18T04:10:57.816453+00:00"},{"alias_kind":"pith_short_12","alias_value":"I3XQQAVNIGNO","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_16","alias_value":"I3XQQAVNIGNOWGQ6","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_8","alias_value":"I3XQQAVN","created_at":"2026-05-18T12:26:30.835961+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/I3XQQAVNIGNOWGQ6VUVCPDHNAB","json":"https://pith.science/pith/I3XQQAVNIGNOWGQ6VUVCPDHNAB.json","graph_json":"https://pith.science/api/pith-number/I3XQQAVNIGNOWGQ6VUVCPDHNAB/graph.json","events_json":"https://pith.science/api/pith-number/I3XQQAVNIGNOWGQ6VUVCPDHNAB/events.json","paper":"https://pith.science/paper/I3XQQAVN"},"agent_actions":{"view_html":"https://pith.science/pith/I3XQQAVNIGNOWGQ6VUVCPDHNAB","download_json":"https://pith.science/pith/I3XQQAVNIGNOWGQ6VUVCPDHNAB.json","view_paper":"https://pith.science/paper/I3XQQAVN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.3192&json=true","fetch_graph":"https://pith.science/api/pith-number/I3XQQAVNIGNOWGQ6VUVCPDHNAB/graph.json","fetch_events":"https://pith.science/api/pith-number/I3XQQAVNIGNOWGQ6VUVCPDHNAB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I3XQQAVNIGNOWGQ6VUVCPDHNAB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I3XQQAVNIGNOWGQ6VUVCPDHNAB/action/storage_attestation","attest_author":"https://pith.science/pith/I3XQQAVNIGNOWGQ6VUVCPDHNAB/action/author_attestation","sign_citation":"https://pith.science/pith/I3XQQAVNIGNOWGQ6VUVCPDHNAB/action/citation_signature","submit_replication":"https://pith.science/pith/I3XQQAVNIGNOWGQ6VUVCPDHNAB/action/replication_record"}},"created_at":"2026-05-18T04:10:57.816453+00:00","updated_at":"2026-05-18T04:10:57.816453+00:00"}