{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4DBSJTFC4TMCNPNEJLBG5QBSV6","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"47568b5d7259f4e6fcc0ad22ae4684c640ab9c27c0ff2898535cdf846b6f71e4","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-04-04T15:48:57Z","title_canon_sha256":"049fbd9f7f093473d62dd5b69387d588d47b7cc1e655831d628eac2d1fca8ea6"},"schema_version":"1.0","source":{"id":"1604.00920","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.00920","created_at":"2026-05-18T01:17:47Z"},{"alias_kind":"arxiv_version","alias_value":"1604.00920v1","created_at":"2026-05-18T01:17:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.00920","created_at":"2026-05-18T01:17:47Z"},{"alias_kind":"pith_short_12","alias_value":"4DBSJTFC4TMC","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4DBSJTFC4TMCNPNE","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4DBSJTFC","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:6b3753231b99485b9967e3711b8dafb0c6e578c58b0d4f150aa94c10850d0a67","target":"graph","created_at":"2026-05-18T01:17:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Aaron Levin, Yu Yasufuku","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-04-04T15:48:57Z","title":"Integral points and orbits of endomorphisms on the projective plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00920","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:bd1ad11210830ec2593ba63c66ca7bbf76f94c04e8d43c9b19b489960006b048","target":"record","created_at":"2026-05-18T01:17:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"47568b5d7259f4e6fcc0ad22ae4684c640ab9c27c0ff2898535cdf846b6f71e4","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-04-04T15:48:57Z","title_canon_sha256":"049fbd9f7f093473d62dd5b69387d588d47b7cc1e655831d628eac2d1fca8ea6"},"schema_version":"1.0","source":{"id":"1604.00920","kind":"arxiv","version":1}},"canonical_sha256":"e0c324cca2e4d826bda44ac26ec032af9af80e308f2ff3e50a03915ddfdbdf84","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e0c324cca2e4d826bda44ac26ec032af9af80e308f2ff3e50a03915ddfdbdf84","first_computed_at":"2026-05-18T01:17:47.805001Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:47.805001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"boHtgAZgBNvmA/ljoCQHE6lLOsaVya5vS2dXFQYI0fSc6JvvZhmN5ppJucFzhGIuYz8uXG57scYrF4cQp1sKDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:47.805773Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.00920","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd1ad11210830ec2593ba63c66ca7bbf76f94c04e8d43c9b19b489960006b048","sha256:6b3753231b99485b9967e3711b8dafb0c6e578c58b0d4f150aa94c10850d0a67"],"state_sha256":"21737af5fa70a216fcc66f94904c7a097654cf24c5fbd29baf18e8ddc433d51f"}