{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2003:77STRWHLEV2PZEP3FDGSV5KXUL","short_pith_number":"pith:77STRWHL","schema_version":"1.0","canonical_sha256":"ffe538d8eb2574fc91fb28cd2af557a2c880e0f8fcb515246c22c03a35f28ea9","source":{"kind":"arxiv","id":"math/0305283","version":6},"attestation_state":"computed","paper":{"title":"The Szemeredi-Trotter Theorem in the Complex Plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Csaba D. Toth","submitted_at":"2003-05-20T00:29:27Z","abstract_excerpt":"It is shown that $n$ points and $e$ lines in the complex Euclidean plane ${\\mathbb C}^2$ determine $O(n^{2/3}e^{2/3}+n+e)$ point-line incidences. This bound is the best possible, and it generalizes the celebrated theorem by Szemer\\'edi and Trotter about point-line incidences in the real Euclidean plane ${\\mathbb R}^2$."},"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":"math/0305283","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2003-05-20T00:29:27Z","cross_cats_sorted":[],"title_canon_sha256":"13464691713d7b340beda06d8d39009472c0375a4bdb59a68c8d41bcf9dafca5","abstract_canon_sha256":"9b5161ab88df4da342f5ffe94a967ee0ee29ddb0ffbad3cf985ee11f54a1069a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:06.101727Z","signature_b64":"flD/f6uDVJ6abrsCMFIwSCQ52ygj5VsJDfxd+Gsd+r3ElyNUBkn3ZJFy8TZ5Z+7SYJMvtolsRXKCHqDWHxJTAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ffe538d8eb2574fc91fb28cd2af557a2c880e0f8fcb515246c22c03a35f28ea9","last_reissued_at":"2026-05-18T01:37:06.101072Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:06.101072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Szemeredi-Trotter Theorem in the Complex Plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Csaba D. Toth","submitted_at":"2003-05-20T00:29:27Z","abstract_excerpt":"It is shown that $n$ points and $e$ lines in the complex Euclidean plane ${\\mathbb C}^2$ determine $O(n^{2/3}e^{2/3}+n+e)$ point-line incidences. This bound is the best possible, and it generalizes the celebrated theorem by Szemer\\'edi and Trotter about point-line incidences in the real Euclidean plane ${\\mathbb R}^2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0305283","kind":"arxiv","version":6},"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":"math/0305283","created_at":"2026-05-18T01:37:06.101170+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0305283v6","created_at":"2026-05-18T01:37:06.101170+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0305283","created_at":"2026-05-18T01:37:06.101170+00:00"},{"alias_kind":"pith_short_12","alias_value":"77STRWHLEV2P","created_at":"2026-05-18T12:25:51.375804+00:00"},{"alias_kind":"pith_short_16","alias_value":"77STRWHLEV2PZEP3","created_at":"2026-05-18T12:25:51.375804+00:00"},{"alias_kind":"pith_short_8","alias_value":"77STRWHL","created_at":"2026-05-18T12:25:51.375804+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/77STRWHLEV2PZEP3FDGSV5KXUL","json":"https://pith.science/pith/77STRWHLEV2PZEP3FDGSV5KXUL.json","graph_json":"https://pith.science/api/pith-number/77STRWHLEV2PZEP3FDGSV5KXUL/graph.json","events_json":"https://pith.science/api/pith-number/77STRWHLEV2PZEP3FDGSV5KXUL/events.json","paper":"https://pith.science/paper/77STRWHL"},"agent_actions":{"view_html":"https://pith.science/pith/77STRWHLEV2PZEP3FDGSV5KXUL","download_json":"https://pith.science/pith/77STRWHLEV2PZEP3FDGSV5KXUL.json","view_paper":"https://pith.science/paper/77STRWHL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0305283&json=true","fetch_graph":"https://pith.science/api/pith-number/77STRWHLEV2PZEP3FDGSV5KXUL/graph.json","fetch_events":"https://pith.science/api/pith-number/77STRWHLEV2PZEP3FDGSV5KXUL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/77STRWHLEV2PZEP3FDGSV5KXUL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/77STRWHLEV2PZEP3FDGSV5KXUL/action/storage_attestation","attest_author":"https://pith.science/pith/77STRWHLEV2PZEP3FDGSV5KXUL/action/author_attestation","sign_citation":"https://pith.science/pith/77STRWHLEV2PZEP3FDGSV5KXUL/action/citation_signature","submit_replication":"https://pith.science/pith/77STRWHLEV2PZEP3FDGSV5KXUL/action/replication_record"}},"created_at":"2026-05-18T01:37:06.101170+00:00","updated_at":"2026-05-18T01:37:06.101170+00:00"}