{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:JLS3VOGUGPGAKUHWS7CWGTLP2C","short_pith_number":"pith:JLS3VOGU","canonical_record":{"source":{"id":"1611.07362","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-11-22T15:33:22Z","cross_cats_sorted":["cs.CG","math.CO"],"title_canon_sha256":"170d9adcbadaa5a3d81a953cda80d7738a0f92fdb389ea91037beac1b21bd69e","abstract_canon_sha256":"41d14b78167d4acd1ac600cec72d34f1955326f35f638b8843013e0b30f6957b"},"schema_version":"1.0"},"canonical_sha256":"4ae5bab8d433cc0550f697c5634d6fd08bc26bb86c0cdce0dfaee714d8a87961","source":{"kind":"arxiv","id":"1611.07362","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.07362","created_at":"2026-05-18T00:40:24Z"},{"alias_kind":"arxiv_version","alias_value":"1611.07362v3","created_at":"2026-05-18T00:40:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.07362","created_at":"2026-05-18T00:40:24Z"},{"alias_kind":"pith_short_12","alias_value":"JLS3VOGUGPGA","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JLS3VOGUGPGAKUHW","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JLS3VOGU","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:JLS3VOGUGPGAKUHWS7CWGTLP2C","target":"record","payload":{"canonical_record":{"source":{"id":"1611.07362","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-11-22T15:33:22Z","cross_cats_sorted":["cs.CG","math.CO"],"title_canon_sha256":"170d9adcbadaa5a3d81a953cda80d7738a0f92fdb389ea91037beac1b21bd69e","abstract_canon_sha256":"41d14b78167d4acd1ac600cec72d34f1955326f35f638b8843013e0b30f6957b"},"schema_version":"1.0"},"canonical_sha256":"4ae5bab8d433cc0550f697c5634d6fd08bc26bb86c0cdce0dfaee714d8a87961","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:24.111473Z","signature_b64":"VjF2Xty1Qfej5wWR2ka7rirj/etlbU9a19xQHBjUjvaMbwxb3KV4Ps9KXKbxQjOMivVM4Ujdh0OGF9aqBi6jDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ae5bab8d433cc0550f697c5634d6fd08bc26bb86c0cdce0dfaee714d8a87961","last_reissued_at":"2026-05-18T00:40:24.110835Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:24.110835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.07362","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:40:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tme3o2H5dwvKYcAo/Ws23pNFi3bp3yIv+zTmtExXA9ucnHpZoo7AIgD1GVRXQRByeT+M/yRRSiK7vhCDJj2yDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:21:13.184775Z"},"content_sha256":"b2401c908ca680c5659534b6704331ed6c8c9a5f00751c5c212c3cd5a3564ada","schema_version":"1.0","event_id":"sha256:b2401c908ca680c5659534b6704331ed6c8c9a5f00751c5c212c3cd5a3564ada"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:JLS3VOGUGPGAKUHWS7CWGTLP2C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An o-minimal Szemer\\'edi-Trotter theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","math.CO"],"primary_cat":"math.LO","authors_text":"Orit E. Raz, Saugata Basu","submitted_at":"2016-11-22T15:33:22Z","abstract_excerpt":"We prove an analog of the Szemer\\'edi-Trotter theorem in the plane for definable curves and points in any o-minimal structure over an arbitrary real closed field $\\mathrm{R}$. One new ingredient in the proof is an extension of the well known crossing number inequality for graphs to the case of embeddings in any o-minimal structure over an arbitrary real closed field."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07362","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:40:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0QQjwri6VgBqGEckNoyXdiyMM4+PD7SlbYhY4dQS75l52GvUun2GeXo2PPmaS/KrGUkm6HTTSO2a+KmWbHL7Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:21:13.185437Z"},"content_sha256":"9108df93c8b514c515cf98dc9173dc0dedf9be13e9d925823804168afa191bb4","schema_version":"1.0","event_id":"sha256:9108df93c8b514c515cf98dc9173dc0dedf9be13e9d925823804168afa191bb4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JLS3VOGUGPGAKUHWS7CWGTLP2C/bundle.json","state_url":"https://pith.science/pith/JLS3VOGUGPGAKUHWS7CWGTLP2C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JLS3VOGUGPGAKUHWS7CWGTLP2C/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T10:21:13Z","links":{"resolver":"https://pith.science/pith/JLS3VOGUGPGAKUHWS7CWGTLP2C","bundle":"https://pith.science/pith/JLS3VOGUGPGAKUHWS7CWGTLP2C/bundle.json","state":"https://pith.science/pith/JLS3VOGUGPGAKUHWS7CWGTLP2C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JLS3VOGUGPGAKUHWS7CWGTLP2C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JLS3VOGUGPGAKUHWS7CWGTLP2C","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":"41d14b78167d4acd1ac600cec72d34f1955326f35f638b8843013e0b30f6957b","cross_cats_sorted":["cs.CG","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-11-22T15:33:22Z","title_canon_sha256":"170d9adcbadaa5a3d81a953cda80d7738a0f92fdb389ea91037beac1b21bd69e"},"schema_version":"1.0","source":{"id":"1611.07362","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.07362","created_at":"2026-05-18T00:40:24Z"},{"alias_kind":"arxiv_version","alias_value":"1611.07362v3","created_at":"2026-05-18T00:40:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.07362","created_at":"2026-05-18T00:40:24Z"},{"alias_kind":"pith_short_12","alias_value":"JLS3VOGUGPGA","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JLS3VOGUGPGAKUHW","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JLS3VOGU","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:9108df93c8b514c515cf98dc9173dc0dedf9be13e9d925823804168afa191bb4","target":"graph","created_at":"2026-05-18T00:40:24Z","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 prove an analog of the Szemer\\'edi-Trotter theorem in the plane for definable curves and points in any o-minimal structure over an arbitrary real closed field $\\mathrm{R}$. One new ingredient in the proof is an extension of the well known crossing number inequality for graphs to the case of embeddings in any o-minimal structure over an arbitrary real closed field.","authors_text":"Orit E. Raz, Saugata Basu","cross_cats":["cs.CG","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-11-22T15:33:22Z","title":"An o-minimal Szemer\\'edi-Trotter theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07362","kind":"arxiv","version":3},"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:b2401c908ca680c5659534b6704331ed6c8c9a5f00751c5c212c3cd5a3564ada","target":"record","created_at":"2026-05-18T00:40:24Z","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":"41d14b78167d4acd1ac600cec72d34f1955326f35f638b8843013e0b30f6957b","cross_cats_sorted":["cs.CG","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-11-22T15:33:22Z","title_canon_sha256":"170d9adcbadaa5a3d81a953cda80d7738a0f92fdb389ea91037beac1b21bd69e"},"schema_version":"1.0","source":{"id":"1611.07362","kind":"arxiv","version":3}},"canonical_sha256":"4ae5bab8d433cc0550f697c5634d6fd08bc26bb86c0cdce0dfaee714d8a87961","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ae5bab8d433cc0550f697c5634d6fd08bc26bb86c0cdce0dfaee714d8a87961","first_computed_at":"2026-05-18T00:40:24.110835Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:24.110835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VjF2Xty1Qfej5wWR2ka7rirj/etlbU9a19xQHBjUjvaMbwxb3KV4Ps9KXKbxQjOMivVM4Ujdh0OGF9aqBi6jDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:24.111473Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.07362","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2401c908ca680c5659534b6704331ed6c8c9a5f00751c5c212c3cd5a3564ada","sha256:9108df93c8b514c515cf98dc9173dc0dedf9be13e9d925823804168afa191bb4"],"state_sha256":"2324a52228d6a5140d27fde0fb3a79b084d31815da58dbc473f145c68a5e19e7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JVtkB4uYPT1s4SfhA6O4/lB/xxS1n6PBis/k29He6vlCjugKp4iEvnWCTf83WsywbWSJ/svwM5+FtiY3UniUDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T10:21:13.188421Z","bundle_sha256":"c12f3c11dea217afa16e5f85bae0967c5805a3cc8a3249c141288f4b90924789"}}