{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:FYCMAONWUBGXQMSQAYJUUZW2QO","short_pith_number":"pith:FYCMAONW","schema_version":"1.0","canonical_sha256":"2e04c039b6a04d78325006134a66da838f328cdb984920bc8e765d3ed5ea0e7a","source":{"kind":"arxiv","id":"1111.1552","version":3},"attestation_state":"computed","paper":{"title":"13/2 ways of counting curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.SG"],"primary_cat":"math.AG","authors_text":"R. Pandharipande, R. P. Thomas","submitted_at":"2011-11-07T11:47:02Z","abstract_excerpt":"In the past 20 years, compactifications of the families of curves in algebraic varieties X have been studied via stable maps, Hilbert schemes, stable pairs, unramified maps, and stable quotients. Each path leads to a different enumeration of curves. A common thread is the use of a 2-term deformation/obstruction theory to define a virtual fundamental class. The richest geometry occurs when X is a nonsingular projective variety of dimension 3.\n  We survey here the 13/2 principal ways to count curves with special attention to the 3-fold case. The different theories are linked by a web of conjectu"},"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":"1111.1552","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-11-07T11:47:02Z","cross_cats_sorted":["hep-th","math.SG"],"title_canon_sha256":"6c1363ab1a58edf05100e8c959466071358800c5cf152a8bb2d9e60414dbb9ff","abstract_canon_sha256":"33d36bf9dbe74e0c783a9d4506d03c3ec3de764f1ea95ac077d4ecebe674c91e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:24.490787Z","signature_b64":"OpMwsWMfszj+hz3OScK6Ib46PfFt1PxZyaIoPTE37IhD3ABAlk4n1hA4fN7d//JpPmX6Z5iq71D4c9/0SXfFCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e04c039b6a04d78325006134a66da838f328cdb984920bc8e765d3ed5ea0e7a","last_reissued_at":"2026-05-18T01:15:24.490096Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:24.490096Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"13/2 ways of counting curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.SG"],"primary_cat":"math.AG","authors_text":"R. Pandharipande, R. P. Thomas","submitted_at":"2011-11-07T11:47:02Z","abstract_excerpt":"In the past 20 years, compactifications of the families of curves in algebraic varieties X have been studied via stable maps, Hilbert schemes, stable pairs, unramified maps, and stable quotients. Each path leads to a different enumeration of curves. A common thread is the use of a 2-term deformation/obstruction theory to define a virtual fundamental class. The richest geometry occurs when X is a nonsingular projective variety of dimension 3.\n  We survey here the 13/2 principal ways to count curves with special attention to the 3-fold case. The different theories are linked by a web of conjectu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1552","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1111.1552","created_at":"2026-05-18T01:15:24.490206+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.1552v3","created_at":"2026-05-18T01:15:24.490206+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.1552","created_at":"2026-05-18T01:15:24.490206+00:00"},{"alias_kind":"pith_short_12","alias_value":"FYCMAONWUBGX","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_16","alias_value":"FYCMAONWUBGXQMSQ","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_8","alias_value":"FYCMAONW","created_at":"2026-05-18T12:26:28.662955+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2605.19552","citing_title":"Large Order Enumerative Geometry, Black Holes and Black Rings","ref_index":1,"is_internal_anchor":true},{"citing_arxiv_id":"2604.05664","citing_title":"The Pandharipande-Thomas rationality conjecture for superpositive curve classes on projective complex 3-manifolds","ref_index":46,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FYCMAONWUBGXQMSQAYJUUZW2QO","json":"https://pith.science/pith/FYCMAONWUBGXQMSQAYJUUZW2QO.json","graph_json":"https://pith.science/api/pith-number/FYCMAONWUBGXQMSQAYJUUZW2QO/graph.json","events_json":"https://pith.science/api/pith-number/FYCMAONWUBGXQMSQAYJUUZW2QO/events.json","paper":"https://pith.science/paper/FYCMAONW"},"agent_actions":{"view_html":"https://pith.science/pith/FYCMAONWUBGXQMSQAYJUUZW2QO","download_json":"https://pith.science/pith/FYCMAONWUBGXQMSQAYJUUZW2QO.json","view_paper":"https://pith.science/paper/FYCMAONW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.1552&json=true","fetch_graph":"https://pith.science/api/pith-number/FYCMAONWUBGXQMSQAYJUUZW2QO/graph.json","fetch_events":"https://pith.science/api/pith-number/FYCMAONWUBGXQMSQAYJUUZW2QO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FYCMAONWUBGXQMSQAYJUUZW2QO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FYCMAONWUBGXQMSQAYJUUZW2QO/action/storage_attestation","attest_author":"https://pith.science/pith/FYCMAONWUBGXQMSQAYJUUZW2QO/action/author_attestation","sign_citation":"https://pith.science/pith/FYCMAONWUBGXQMSQAYJUUZW2QO/action/citation_signature","submit_replication":"https://pith.science/pith/FYCMAONWUBGXQMSQAYJUUZW2QO/action/replication_record"}},"created_at":"2026-05-18T01:15:24.490206+00:00","updated_at":"2026-05-18T01:15:24.490206+00:00"}