{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:QASXECAIBEJUW6DH4D5X4OPFLL","short_pith_number":"pith:QASXECAI","schema_version":"1.0","canonical_sha256":"802572080809134b7867e0fb7e39e55adf28ed07c735add2b21b098c893f35df","source":{"kind":"arxiv","id":"1610.01560","version":2},"attestation_state":"computed","paper":{"title":"Incidences with curves and surfaces in three dimensions, with applications to distinct and repeated distances","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CO","authors_text":"Micha Sharir, Noam Solomon","submitted_at":"2016-10-05T18:34:26Z","abstract_excerpt":"We study a wide spectrum of incidence problems involving points and curves or points and surfaces in $\\mathbb R^3$. The current (and in fact the only viable) approach to such problems, pioneered by Guth and Katz [2010,2015], requires a variety of tools from algebraic geometry, most notably (i) the polynomial partitioning technique, and (ii) the study of algebraic surfaces that are ruled by lines or, in more recent studies [Guth-Zahl 2016], by algebraic curves of some constant degree. By exploiting and refining these tools, we obtain new and improved bounds for numerous incidence problems in $\\"},"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":"1610.01560","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-05T18:34:26Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"ea6c396d0eec93c826817984bb6cb963a615678a9486568e640a2604f4c54294","abstract_canon_sha256":"fec21b3f05f1ba5f1355a83e53697d1c776b8cd88636c9ded4018b6e0c51cca6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:25.938444Z","signature_b64":"aY1QdLENGauA3wY45nI9scI8SqGWSf6iGd4H58xjWBoWVj4fEe54a7doLefSgRENBXlQ4PbbqYt826tJMNg9BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"802572080809134b7867e0fb7e39e55adf28ed07c735add2b21b098c893f35df","last_reissued_at":"2026-05-18T00:45:25.937889Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:25.937889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Incidences with curves and surfaces in three dimensions, with applications to distinct and repeated distances","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CO","authors_text":"Micha Sharir, Noam Solomon","submitted_at":"2016-10-05T18:34:26Z","abstract_excerpt":"We study a wide spectrum of incidence problems involving points and curves or points and surfaces in $\\mathbb R^3$. The current (and in fact the only viable) approach to such problems, pioneered by Guth and Katz [2010,2015], requires a variety of tools from algebraic geometry, most notably (i) the polynomial partitioning technique, and (ii) the study of algebraic surfaces that are ruled by lines or, in more recent studies [Guth-Zahl 2016], by algebraic curves of some constant degree. By exploiting and refining these tools, we obtain new and improved bounds for numerous incidence problems in $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01560","kind":"arxiv","version":2},"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":"1610.01560","created_at":"2026-05-18T00:45:25.937987+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.01560v2","created_at":"2026-05-18T00:45:25.937987+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.01560","created_at":"2026-05-18T00:45:25.937987+00:00"},{"alias_kind":"pith_short_12","alias_value":"QASXECAIBEJU","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_16","alias_value":"QASXECAIBEJUW6DH","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_8","alias_value":"QASXECAI","created_at":"2026-05-18T12:30:39.010887+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/QASXECAIBEJUW6DH4D5X4OPFLL","json":"https://pith.science/pith/QASXECAIBEJUW6DH4D5X4OPFLL.json","graph_json":"https://pith.science/api/pith-number/QASXECAIBEJUW6DH4D5X4OPFLL/graph.json","events_json":"https://pith.science/api/pith-number/QASXECAIBEJUW6DH4D5X4OPFLL/events.json","paper":"https://pith.science/paper/QASXECAI"},"agent_actions":{"view_html":"https://pith.science/pith/QASXECAIBEJUW6DH4D5X4OPFLL","download_json":"https://pith.science/pith/QASXECAIBEJUW6DH4D5X4OPFLL.json","view_paper":"https://pith.science/paper/QASXECAI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.01560&json=true","fetch_graph":"https://pith.science/api/pith-number/QASXECAIBEJUW6DH4D5X4OPFLL/graph.json","fetch_events":"https://pith.science/api/pith-number/QASXECAIBEJUW6DH4D5X4OPFLL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QASXECAIBEJUW6DH4D5X4OPFLL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QASXECAIBEJUW6DH4D5X4OPFLL/action/storage_attestation","attest_author":"https://pith.science/pith/QASXECAIBEJUW6DH4D5X4OPFLL/action/author_attestation","sign_citation":"https://pith.science/pith/QASXECAIBEJUW6DH4D5X4OPFLL/action/citation_signature","submit_replication":"https://pith.science/pith/QASXECAIBEJUW6DH4D5X4OPFLL/action/replication_record"}},"created_at":"2026-05-18T00:45:25.937987+00:00","updated_at":"2026-05-18T00:45:25.937987+00:00"}