{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:4DBSJTFC4TMCNPNEJLBG5QBSV6","short_pith_number":"pith:4DBSJTFC","schema_version":"1.0","canonical_sha256":"e0c324cca2e4d826bda44ac26ec032af9af80e308f2ff3e50a03915ddfdbdf84","source":{"kind":"arxiv","id":"1604.00920","version":1},"attestation_state":"computed","paper":{"title":"Integral points and orbits of endomorphisms on the projective plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Aaron Levin, Yu Yasufuku","submitted_at":"2016-04-04T15:48:57Z","abstract_excerpt":"We analyze when integral points on the complement of a finite union of curves in $\\mathbb{P}^2$ are potentially dense. We divide the analysis of these affine surfaces based on their logarithmic Kodaira dimension $\\bar{\\kappa}$. When $\\bar{\\kappa} = -\\infty$, we completely characterize the potential density of integral points in terms of the number of irreducible components on the surface at infinity and the number of multiple members in a pencil naturally associated to the surface. When integral points are not potentially dense, we show that they lie on finitely many effectively computable cur"},"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":"1604.00920","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-04-04T15:48:57Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"049fbd9f7f093473d62dd5b69387d588d47b7cc1e655831d628eac2d1fca8ea6","abstract_canon_sha256":"47568b5d7259f4e6fcc0ad22ae4684c640ab9c27c0ff2898535cdf846b6f71e4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:47.805773Z","signature_b64":"boHtgAZgBNvmA/ljoCQHE6lLOsaVya5vS2dXFQYI0fSc6JvvZhmN5ppJucFzhGIuYz8uXG57scYrF4cQp1sKDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0c324cca2e4d826bda44ac26ec032af9af80e308f2ff3e50a03915ddfdbdf84","last_reissued_at":"2026-05-18T01:17:47.805001Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:47.805001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Integral points and orbits of endomorphisms on the projective plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Aaron Levin, Yu Yasufuku","submitted_at":"2016-04-04T15:48:57Z","abstract_excerpt":"We analyze when integral points on the complement of a finite union of curves in $\\mathbb{P}^2$ are potentially dense. We divide the analysis of these affine surfaces based on their logarithmic Kodaira dimension $\\bar{\\kappa}$. When $\\bar{\\kappa} = -\\infty$, we completely characterize the potential density of integral points in terms of the number of irreducible components on the surface at infinity and the number of multiple members in a pencil naturally associated to the surface. When integral points are not potentially dense, we show that they lie on finitely many effectively computable cur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00920","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":"1604.00920","created_at":"2026-05-18T01:17:47.805127+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.00920v1","created_at":"2026-05-18T01:17:47.805127+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.00920","created_at":"2026-05-18T01:17:47.805127+00:00"},{"alias_kind":"pith_short_12","alias_value":"4DBSJTFC4TMC","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_16","alias_value":"4DBSJTFC4TMCNPNE","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_8","alias_value":"4DBSJTFC","created_at":"2026-05-18T12:29:58.707656+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/4DBSJTFC4TMCNPNEJLBG5QBSV6","json":"https://pith.science/pith/4DBSJTFC4TMCNPNEJLBG5QBSV6.json","graph_json":"https://pith.science/api/pith-number/4DBSJTFC4TMCNPNEJLBG5QBSV6/graph.json","events_json":"https://pith.science/api/pith-number/4DBSJTFC4TMCNPNEJLBG5QBSV6/events.json","paper":"https://pith.science/paper/4DBSJTFC"},"agent_actions":{"view_html":"https://pith.science/pith/4DBSJTFC4TMCNPNEJLBG5QBSV6","download_json":"https://pith.science/pith/4DBSJTFC4TMCNPNEJLBG5QBSV6.json","view_paper":"https://pith.science/paper/4DBSJTFC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.00920&json=true","fetch_graph":"https://pith.science/api/pith-number/4DBSJTFC4TMCNPNEJLBG5QBSV6/graph.json","fetch_events":"https://pith.science/api/pith-number/4DBSJTFC4TMCNPNEJLBG5QBSV6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4DBSJTFC4TMCNPNEJLBG5QBSV6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4DBSJTFC4TMCNPNEJLBG5QBSV6/action/storage_attestation","attest_author":"https://pith.science/pith/4DBSJTFC4TMCNPNEJLBG5QBSV6/action/author_attestation","sign_citation":"https://pith.science/pith/4DBSJTFC4TMCNPNEJLBG5QBSV6/action/citation_signature","submit_replication":"https://pith.science/pith/4DBSJTFC4TMCNPNEJLBG5QBSV6/action/replication_record"}},"created_at":"2026-05-18T01:17:47.805127+00:00","updated_at":"2026-05-18T01:17:47.805127+00:00"}