{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:32Y6N6C6BWTBUUZIZ7L57VDK7P","short_pith_number":"pith:32Y6N6C6","schema_version":"1.0","canonical_sha256":"deb1e6f85e0da61a5328cfd7dfd46afbe1ca0e958a4aa719a5f1b3472efe4de8","source":{"kind":"arxiv","id":"1812.11748","version":1},"attestation_state":"computed","paper":{"title":"Fukaya category of Landau-Ginzburg model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Dingyu Yang, Huijun Fan, Wenfeng Jiang","submitted_at":"2018-12-31T10:21:28Z","abstract_excerpt":"This article introduces and provides the mathematical foundation of the open string Floer theory of Landau-Ginzburg model viaWitten equation. We introduce the concept of regular tame exact Landau-Ginzburg system on a noncompact Kaehler manifold, and define the notion of Landau-Ginzburg branes, as the objects of the Fukaya category. The study on Witten equation in our context provides the construction of the Fukaya category of Landau-Ginzburg model which was conjectured to be existed in Gaiotto-Moore-Witten's work [22] and Kapranov-Kontsevich-Soibelman's work [30]. This is the first paper in th"},"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":"1812.11748","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2018-12-31T10:21:28Z","cross_cats_sorted":[],"title_canon_sha256":"4e7fad73ffa12d95d6bb32fcb7a1dbf28b9e5d6fa16e00a17447db9a480e7e43","abstract_canon_sha256":"feef0f8c2e2cb8a39eb1f59d1c112250bf773ff7eda2151c03e980408fd5b944"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:11.202542Z","signature_b64":"pFbpsejI3KvtyrycmLj1RWLDJNClDrIxxm4MoHWGovCw4E7hvCfnJ2SvZjhQH+6WMnlizOhsjEFNR69jzw4YDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"deb1e6f85e0da61a5328cfd7dfd46afbe1ca0e958a4aa719a5f1b3472efe4de8","last_reissued_at":"2026-05-17T23:57:11.202155Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:11.202155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fukaya category of Landau-Ginzburg model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Dingyu Yang, Huijun Fan, Wenfeng Jiang","submitted_at":"2018-12-31T10:21:28Z","abstract_excerpt":"This article introduces and provides the mathematical foundation of the open string Floer theory of Landau-Ginzburg model viaWitten equation. We introduce the concept of regular tame exact Landau-Ginzburg system on a noncompact Kaehler manifold, and define the notion of Landau-Ginzburg branes, as the objects of the Fukaya category. The study on Witten equation in our context provides the construction of the Fukaya category of Landau-Ginzburg model which was conjectured to be existed in Gaiotto-Moore-Witten's work [22] and Kapranov-Kontsevich-Soibelman's work [30]. This is the first paper in th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.11748","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":"1812.11748","created_at":"2026-05-17T23:57:11.202215+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.11748v1","created_at":"2026-05-17T23:57:11.202215+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.11748","created_at":"2026-05-17T23:57:11.202215+00:00"},{"alias_kind":"pith_short_12","alias_value":"32Y6N6C6BWTB","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_16","alias_value":"32Y6N6C6BWTBUUZI","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_8","alias_value":"32Y6N6C6","created_at":"2026-05-18T12:32:02.567920+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/32Y6N6C6BWTBUUZIZ7L57VDK7P","json":"https://pith.science/pith/32Y6N6C6BWTBUUZIZ7L57VDK7P.json","graph_json":"https://pith.science/api/pith-number/32Y6N6C6BWTBUUZIZ7L57VDK7P/graph.json","events_json":"https://pith.science/api/pith-number/32Y6N6C6BWTBUUZIZ7L57VDK7P/events.json","paper":"https://pith.science/paper/32Y6N6C6"},"agent_actions":{"view_html":"https://pith.science/pith/32Y6N6C6BWTBUUZIZ7L57VDK7P","download_json":"https://pith.science/pith/32Y6N6C6BWTBUUZIZ7L57VDK7P.json","view_paper":"https://pith.science/paper/32Y6N6C6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.11748&json=true","fetch_graph":"https://pith.science/api/pith-number/32Y6N6C6BWTBUUZIZ7L57VDK7P/graph.json","fetch_events":"https://pith.science/api/pith-number/32Y6N6C6BWTBUUZIZ7L57VDK7P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/32Y6N6C6BWTBUUZIZ7L57VDK7P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/32Y6N6C6BWTBUUZIZ7L57VDK7P/action/storage_attestation","attest_author":"https://pith.science/pith/32Y6N6C6BWTBUUZIZ7L57VDK7P/action/author_attestation","sign_citation":"https://pith.science/pith/32Y6N6C6BWTBUUZIZ7L57VDK7P/action/citation_signature","submit_replication":"https://pith.science/pith/32Y6N6C6BWTBUUZIZ7L57VDK7P/action/replication_record"}},"created_at":"2026-05-17T23:57:11.202215+00:00","updated_at":"2026-05-17T23:57:11.202215+00:00"}