{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:TKW4AXWYIRTQMJCFXWTOZZQW2S","short_pith_number":"pith:TKW4AXWY","schema_version":"1.0","canonical_sha256":"9aadc05ed84467062445bda6ece616d481d7f3a0dac7522d98d59b3faa5617b2","source":{"kind":"arxiv","id":"1605.05018","version":1},"attestation_state":"computed","paper":{"title":"Geometry of webs of algebraic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.DG"],"primary_cat":"math.AG","authors_text":"Jun-Muk Hwang","submitted_at":"2016-05-17T05:06:35Z","abstract_excerpt":"A family of algebraic curves covering a projective variety $X$ is called a web of curves on $X$ if it has only finitely many members through a general point of $X$. A web of curves on $X$ induces a web-structure, in the sense of local differential geometry, in a neighborhood of a general point of $X$. We study how the local differential geometry of the web-structure affects the global algebraic geometry of $X$. Under two geometric assumptions on the web-structure, the pairwise non-integrability condition and the bracket-generating condition, we prove that the local differential geometry determ"},"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":"1605.05018","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-05-17T05:06:35Z","cross_cats_sorted":["math.CV","math.DG"],"title_canon_sha256":"1178600b073b73f9bea69a41cf1916fa72da9a8272875b1a73e269769ae725ca","abstract_canon_sha256":"da2ea8a05c1da88ab9d8faf115da5dda5eab4b464757b7765ea531a49568f7f6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:52.255238Z","signature_b64":"6ajlF+8cUT9qGDaEXJ6tBJB/Pkav0GrGddYrNJYAFv+gwj4n5F1umFGif4WUYqDlLH7VaSRSjTzr/rlRdsMGCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9aadc05ed84467062445bda6ece616d481d7f3a0dac7522d98d59b3faa5617b2","last_reissued_at":"2026-05-18T00:49:52.254861Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:52.254861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometry of webs of algebraic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.DG"],"primary_cat":"math.AG","authors_text":"Jun-Muk Hwang","submitted_at":"2016-05-17T05:06:35Z","abstract_excerpt":"A family of algebraic curves covering a projective variety $X$ is called a web of curves on $X$ if it has only finitely many members through a general point of $X$. A web of curves on $X$ induces a web-structure, in the sense of local differential geometry, in a neighborhood of a general point of $X$. We study how the local differential geometry of the web-structure affects the global algebraic geometry of $X$. Under two geometric assumptions on the web-structure, the pairwise non-integrability condition and the bracket-generating condition, we prove that the local differential geometry determ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05018","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":"1605.05018","created_at":"2026-05-18T00:49:52.254916+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.05018v1","created_at":"2026-05-18T00:49:52.254916+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.05018","created_at":"2026-05-18T00:49:52.254916+00:00"},{"alias_kind":"pith_short_12","alias_value":"TKW4AXWYIRTQ","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_16","alias_value":"TKW4AXWYIRTQMJCF","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_8","alias_value":"TKW4AXWY","created_at":"2026-05-18T12:30:44.179134+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/TKW4AXWYIRTQMJCFXWTOZZQW2S","json":"https://pith.science/pith/TKW4AXWYIRTQMJCFXWTOZZQW2S.json","graph_json":"https://pith.science/api/pith-number/TKW4AXWYIRTQMJCFXWTOZZQW2S/graph.json","events_json":"https://pith.science/api/pith-number/TKW4AXWYIRTQMJCFXWTOZZQW2S/events.json","paper":"https://pith.science/paper/TKW4AXWY"},"agent_actions":{"view_html":"https://pith.science/pith/TKW4AXWYIRTQMJCFXWTOZZQW2S","download_json":"https://pith.science/pith/TKW4AXWYIRTQMJCFXWTOZZQW2S.json","view_paper":"https://pith.science/paper/TKW4AXWY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.05018&json=true","fetch_graph":"https://pith.science/api/pith-number/TKW4AXWYIRTQMJCFXWTOZZQW2S/graph.json","fetch_events":"https://pith.science/api/pith-number/TKW4AXWYIRTQMJCFXWTOZZQW2S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TKW4AXWYIRTQMJCFXWTOZZQW2S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TKW4AXWYIRTQMJCFXWTOZZQW2S/action/storage_attestation","attest_author":"https://pith.science/pith/TKW4AXWYIRTQMJCFXWTOZZQW2S/action/author_attestation","sign_citation":"https://pith.science/pith/TKW4AXWYIRTQMJCFXWTOZZQW2S/action/citation_signature","submit_replication":"https://pith.science/pith/TKW4AXWYIRTQMJCFXWTOZZQW2S/action/replication_record"}},"created_at":"2026-05-18T00:49:52.254916+00:00","updated_at":"2026-05-18T00:49:52.254916+00:00"}