{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:OJGAOFSL5MCVPDJEKOXBQVURPX","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":"99f98b3fc472f4cb76c83fea03c294d71b9c3c94367d8b6c0c98af8df53ea975","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-08-20T13:52:38Z","title_canon_sha256":"1fcca37f41e80ff7a77450e573aa4e2fd1194deb7a1d5f1ec55ec8eea361be84"},"schema_version":"1.0","source":{"id":"1208.4008","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.4008","created_at":"2026-05-18T03:48:25Z"},{"alias_kind":"arxiv_version","alias_value":"1208.4008v1","created_at":"2026-05-18T03:48:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.4008","created_at":"2026-05-18T03:48:25Z"},{"alias_kind":"pith_short_12","alias_value":"OJGAOFSL5MCV","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OJGAOFSL5MCVPDJE","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OJGAOFSL","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:3b60182b1add5d931e710295fd8ddc7900e7117897853d11767036799031c824","target":"graph","created_at":"2026-05-18T03:48:25Z","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 establish a Szemeredi-Trotter type result for hyperbolas in $\\mathbb F_p\\times\\mathbb F_p$","authors_text":"Jean Bourgain","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-08-20T13:52:38Z","title":"A modular Szemeredi-Trotter theorem for hyperbolas"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.4008","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:ca7c325c9b4d6bcdb1f1d6770ea024c857267e10734a5dbac73f73e87ad6a62c","target":"record","created_at":"2026-05-18T03:48:25Z","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":"99f98b3fc472f4cb76c83fea03c294d71b9c3c94367d8b6c0c98af8df53ea975","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-08-20T13:52:38Z","title_canon_sha256":"1fcca37f41e80ff7a77450e573aa4e2fd1194deb7a1d5f1ec55ec8eea361be84"},"schema_version":"1.0","source":{"id":"1208.4008","kind":"arxiv","version":1}},"canonical_sha256":"724c07164beb05578d2453ae1856917dcfffa011fda9d649e2c97ae7dd87a09b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"724c07164beb05578d2453ae1856917dcfffa011fda9d649e2c97ae7dd87a09b","first_computed_at":"2026-05-18T03:48:25.490359Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:48:25.490359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IY9iPY311qbnNnaavAFtU1boUbFRli3eY19ZCDB4jN5CWSbPucgGMSX348pcPdjbhSfWVYGaAsAAGOg2fSx0CA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:48:25.490835Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.4008","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca7c325c9b4d6bcdb1f1d6770ea024c857267e10734a5dbac73f73e87ad6a62c","sha256:3b60182b1add5d931e710295fd8ddc7900e7117897853d11767036799031c824"],"state_sha256":"63283b325db481582888e84b1b77c7765e1c799c37f29b2b6aaadcf63e12538d"}