{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:RN5S25EXRARSNORWNKZ6X6VS4Y","short_pith_number":"pith:RN5S25EX","schema_version":"1.0","canonical_sha256":"8b7b2d7497882326ba366ab3ebfab2e61fe219242c19ab38d6ae76046e97ac63","source":{"kind":"arxiv","id":"1610.07029","version":1},"attestation_state":"computed","paper":{"title":"A characterization of connected self-affine fractals arising from collinear digits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Jun Jason Luo, King-Shun Leung","submitted_at":"2016-10-22T10:27:07Z","abstract_excerpt":"Let $A$ be an expanding integer matrix with characteristic polynomial $f(x)=x^{2}+px+q$, and let $\\mathcal{D}=\\{0,1,\\dots,|q|-2,|q|+m\\}\\mathbf{v}$ be a collinear digit set where $m\\geqslant 0, {\\mathbf v}\\in {\\mathbb Z}^2$. It is well known that there exists a unique self-affine fractal $T$ satisfying $AT=T+\\mathcal{D}$. In this paper, we give a complete characterization on the connected $T$. That generalizes the previous result of $|q|=3$."},"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":"1610.07029","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2016-10-22T10:27:07Z","cross_cats_sorted":[],"title_canon_sha256":"f6bca79879c0401634e92724afd1a989a747a9f24d2f465f0db958ce7a742958","abstract_canon_sha256":"d4d0d3f55156a76c48d40a8b60ebac5bb7a9dc96442f9af966cee4f5d2b05f50"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:35.384827Z","signature_b64":"BMt9a1hYchVCIejK7z3Zj2YL5wFGqWHa7QyrAmalw71rsNrnzcixd1GnRC9mNeQ0no2UIt3GH2Hw2i8gSyCXBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8b7b2d7497882326ba366ab3ebfab2e61fe219242c19ab38d6ae76046e97ac63","last_reissued_at":"2026-05-18T01:01:35.384398Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:35.384398Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A characterization of connected self-affine fractals arising from collinear digits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Jun Jason Luo, King-Shun Leung","submitted_at":"2016-10-22T10:27:07Z","abstract_excerpt":"Let $A$ be an expanding integer matrix with characteristic polynomial $f(x)=x^{2}+px+q$, and let $\\mathcal{D}=\\{0,1,\\dots,|q|-2,|q|+m\\}\\mathbf{v}$ be a collinear digit set where $m\\geqslant 0, {\\mathbf v}\\in {\\mathbb Z}^2$. It is well known that there exists a unique self-affine fractal $T$ satisfying $AT=T+\\mathcal{D}$. In this paper, we give a complete characterization on the connected $T$. That generalizes the previous result of $|q|=3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07029","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":"1610.07029","created_at":"2026-05-18T01:01:35.384470+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.07029v1","created_at":"2026-05-18T01:01:35.384470+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.07029","created_at":"2026-05-18T01:01:35.384470+00:00"},{"alias_kind":"pith_short_12","alias_value":"RN5S25EXRARS","created_at":"2026-05-18T12:30:41.710351+00:00"},{"alias_kind":"pith_short_16","alias_value":"RN5S25EXRARSNORW","created_at":"2026-05-18T12:30:41.710351+00:00"},{"alias_kind":"pith_short_8","alias_value":"RN5S25EX","created_at":"2026-05-18T12:30:41.710351+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/RN5S25EXRARSNORWNKZ6X6VS4Y","json":"https://pith.science/pith/RN5S25EXRARSNORWNKZ6X6VS4Y.json","graph_json":"https://pith.science/api/pith-number/RN5S25EXRARSNORWNKZ6X6VS4Y/graph.json","events_json":"https://pith.science/api/pith-number/RN5S25EXRARSNORWNKZ6X6VS4Y/events.json","paper":"https://pith.science/paper/RN5S25EX"},"agent_actions":{"view_html":"https://pith.science/pith/RN5S25EXRARSNORWNKZ6X6VS4Y","download_json":"https://pith.science/pith/RN5S25EXRARSNORWNKZ6X6VS4Y.json","view_paper":"https://pith.science/paper/RN5S25EX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.07029&json=true","fetch_graph":"https://pith.science/api/pith-number/RN5S25EXRARSNORWNKZ6X6VS4Y/graph.json","fetch_events":"https://pith.science/api/pith-number/RN5S25EXRARSNORWNKZ6X6VS4Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RN5S25EXRARSNORWNKZ6X6VS4Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RN5S25EXRARSNORWNKZ6X6VS4Y/action/storage_attestation","attest_author":"https://pith.science/pith/RN5S25EXRARSNORWNKZ6X6VS4Y/action/author_attestation","sign_citation":"https://pith.science/pith/RN5S25EXRARSNORWNKZ6X6VS4Y/action/citation_signature","submit_replication":"https://pith.science/pith/RN5S25EXRARSNORWNKZ6X6VS4Y/action/replication_record"}},"created_at":"2026-05-18T01:01:35.384470+00:00","updated_at":"2026-05-18T01:01:35.384470+00:00"}