{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1994:VIIOYJVOKLZS4MHUIDD3PQSL7C","short_pith_number":"pith:VIIOYJVO","schema_version":"1.0","canonical_sha256":"aa10ec26ae52f32e30f440c7b7c24bf880445af99fd79f6735a817940ec02790","source":{"kind":"arxiv","id":"hep-th/9407018","version":1},"attestation_state":"computed","paper":{"title":"Geometry of 2d topological field theories","license":"","headline":"","cross_cats":["math.QA"],"primary_cat":"hep-th","authors_text":"Boris Dubrovin","submitted_at":"1994-07-04T22:52:48Z","abstract_excerpt":"These lecture notes are devoted to the theory of equations of associativity describing geometry of moduli spaces of 2D topological field theories. Introduction. Lecture 1. WDVV equations and Frobenius manifolds. {Appendix A.} Polynomial solutions of WDVV. {Appendix B.} Symmetriies of WDVV. Twisted Frobenius manifolds. {Appendix C.} WDVV and Chazy equation. Affine connections on curves with projective structure. Lecture 2. Topological conformal field theories and their moduli. Lecture 3. Spaces of isomonodromy deformations as Frobenius manifolds. {Appendix D.} Geometry of flat pencils of metric"},"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":"hep-th/9407018","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1994-07-04T22:52:48Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"0a0a665b6f29f5b522399656cab7378499d30dfb14c032ec31edd1185e7997c2","abstract_canon_sha256":"ec5bb823d5a1f94288f1f99725af5050c8d96b781d63c917c8b2790610442164"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:08:52.946796Z","signature_b64":"yqoPRiPcB1PAZoRn9+akR070/9Ho/d5hDdTfRoOWouLCUIrWyUSL/qgDUqK1dcZSJGQ7pgf/3ajxnJXo2g1FAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa10ec26ae52f32e30f440c7b7c24bf880445af99fd79f6735a817940ec02790","last_reissued_at":"2026-07-04T15:08:52.946446Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:08:52.946446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometry of 2d topological field theories","license":"","headline":"","cross_cats":["math.QA"],"primary_cat":"hep-th","authors_text":"Boris Dubrovin","submitted_at":"1994-07-04T22:52:48Z","abstract_excerpt":"These lecture notes are devoted to the theory of equations of associativity describing geometry of moduli spaces of 2D topological field theories. Introduction. Lecture 1. WDVV equations and Frobenius manifolds. {Appendix A.} Polynomial solutions of WDVV. {Appendix B.} Symmetriies of WDVV. Twisted Frobenius manifolds. {Appendix C.} WDVV and Chazy equation. Affine connections on curves with projective structure. Lecture 2. Topological conformal field theories and their moduli. Lecture 3. Spaces of isomonodromy deformations as Frobenius manifolds. {Appendix D.} Geometry of flat pencils of metric"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9407018","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/hep-th/9407018/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"hep-th/9407018","created_at":"2026-07-04T15:08:52.946509+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9407018v1","created_at":"2026-07-04T15:08:52.946509+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9407018","created_at":"2026-07-04T15:08:52.946509+00:00"},{"alias_kind":"pith_short_12","alias_value":"VIIOYJVOKLZS","created_at":"2026-07-04T15:08:52.946509+00:00"},{"alias_kind":"pith_short_16","alias_value":"VIIOYJVOKLZS4MHU","created_at":"2026-07-04T15:08:52.946509+00:00"},{"alias_kind":"pith_short_8","alias_value":"VIIOYJVO","created_at":"2026-07-04T15:08:52.946509+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/VIIOYJVOKLZS4MHUIDD3PQSL7C","json":"https://pith.science/pith/VIIOYJVOKLZS4MHUIDD3PQSL7C.json","graph_json":"https://pith.science/api/pith-number/VIIOYJVOKLZS4MHUIDD3PQSL7C/graph.json","events_json":"https://pith.science/api/pith-number/VIIOYJVOKLZS4MHUIDD3PQSL7C/events.json","paper":"https://pith.science/paper/VIIOYJVO"},"agent_actions":{"view_html":"https://pith.science/pith/VIIOYJVOKLZS4MHUIDD3PQSL7C","download_json":"https://pith.science/pith/VIIOYJVOKLZS4MHUIDD3PQSL7C.json","view_paper":"https://pith.science/paper/VIIOYJVO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-th/9407018&json=true","fetch_graph":"https://pith.science/api/pith-number/VIIOYJVOKLZS4MHUIDD3PQSL7C/graph.json","fetch_events":"https://pith.science/api/pith-number/VIIOYJVOKLZS4MHUIDD3PQSL7C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VIIOYJVOKLZS4MHUIDD3PQSL7C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VIIOYJVOKLZS4MHUIDD3PQSL7C/action/storage_attestation","attest_author":"https://pith.science/pith/VIIOYJVOKLZS4MHUIDD3PQSL7C/action/author_attestation","sign_citation":"https://pith.science/pith/VIIOYJVOKLZS4MHUIDD3PQSL7C/action/citation_signature","submit_replication":"https://pith.science/pith/VIIOYJVOKLZS4MHUIDD3PQSL7C/action/replication_record"}},"created_at":"2026-07-04T15:08:52.946509+00:00","updated_at":"2026-07-04T15:08:52.946509+00:00"}