{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:OJGAOFSL5MCVPDJEKOXBQVURPX","short_pith_number":"pith:OJGAOFSL","schema_version":"1.0","canonical_sha256":"724c07164beb05578d2453ae1856917dcfffa011fda9d649e2c97ae7dd87a09b","source":{"kind":"arxiv","id":"1208.4008","version":1},"attestation_state":"computed","paper":{"title":"A modular Szemeredi-Trotter theorem for hyperbolas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jean Bourgain","submitted_at":"2012-08-20T13:52:38Z","abstract_excerpt":"We establish a Szemeredi-Trotter type result for hyperbolas in $\\mathbb F_p\\times\\mathbb F_p$"},"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":"1208.4008","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-08-20T13:52:38Z","cross_cats_sorted":[],"title_canon_sha256":"1fcca37f41e80ff7a77450e573aa4e2fd1194deb7a1d5f1ec55ec8eea361be84","abstract_canon_sha256":"99f98b3fc472f4cb76c83fea03c294d71b9c3c94367d8b6c0c98af8df53ea975"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:25.490835Z","signature_b64":"IY9iPY311qbnNnaavAFtU1boUbFRli3eY19ZCDB4jN5CWSbPucgGMSX348pcPdjbhSfWVYGaAsAAGOg2fSx0CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"724c07164beb05578d2453ae1856917dcfffa011fda9d649e2c97ae7dd87a09b","last_reissued_at":"2026-05-18T03:48:25.490359Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:25.490359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A modular Szemeredi-Trotter theorem for hyperbolas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jean Bourgain","submitted_at":"2012-08-20T13:52:38Z","abstract_excerpt":"We establish a Szemeredi-Trotter type result for hyperbolas in $\\mathbb F_p\\times\\mathbb F_p$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.4008","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":"1208.4008","created_at":"2026-05-18T03:48:25.490438+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.4008v1","created_at":"2026-05-18T03:48:25.490438+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.4008","created_at":"2026-05-18T03:48:25.490438+00:00"},{"alias_kind":"pith_short_12","alias_value":"OJGAOFSL5MCV","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"OJGAOFSL5MCVPDJE","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"OJGAOFSL","created_at":"2026-05-18T12:27:16.716162+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/OJGAOFSL5MCVPDJEKOXBQVURPX","json":"https://pith.science/pith/OJGAOFSL5MCVPDJEKOXBQVURPX.json","graph_json":"https://pith.science/api/pith-number/OJGAOFSL5MCVPDJEKOXBQVURPX/graph.json","events_json":"https://pith.science/api/pith-number/OJGAOFSL5MCVPDJEKOXBQVURPX/events.json","paper":"https://pith.science/paper/OJGAOFSL"},"agent_actions":{"view_html":"https://pith.science/pith/OJGAOFSL5MCVPDJEKOXBQVURPX","download_json":"https://pith.science/pith/OJGAOFSL5MCVPDJEKOXBQVURPX.json","view_paper":"https://pith.science/paper/OJGAOFSL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.4008&json=true","fetch_graph":"https://pith.science/api/pith-number/OJGAOFSL5MCVPDJEKOXBQVURPX/graph.json","fetch_events":"https://pith.science/api/pith-number/OJGAOFSL5MCVPDJEKOXBQVURPX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OJGAOFSL5MCVPDJEKOXBQVURPX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OJGAOFSL5MCVPDJEKOXBQVURPX/action/storage_attestation","attest_author":"https://pith.science/pith/OJGAOFSL5MCVPDJEKOXBQVURPX/action/author_attestation","sign_citation":"https://pith.science/pith/OJGAOFSL5MCVPDJEKOXBQVURPX/action/citation_signature","submit_replication":"https://pith.science/pith/OJGAOFSL5MCVPDJEKOXBQVURPX/action/replication_record"}},"created_at":"2026-05-18T03:48:25.490438+00:00","updated_at":"2026-05-18T03:48:25.490438+00:00"}