{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:32Y6N6C6BWTBUUZIZ7L57VDK7P","short_pith_number":"pith:32Y6N6C6","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"},"canonical_sha256":"deb1e6f85e0da61a5328cfd7dfd46afbe1ca0e958a4aa719a5f1b3472efe4de8","source":{"kind":"arxiv","id":"1812.11748","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.11748","created_at":"2026-05-17T23:57:11Z"},{"alias_kind":"arxiv_version","alias_value":"1812.11748v1","created_at":"2026-05-17T23:57:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.11748","created_at":"2026-05-17T23:57:11Z"},{"alias_kind":"pith_short_12","alias_value":"32Y6N6C6BWTB","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"32Y6N6C6BWTBUUZI","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"32Y6N6C6","created_at":"2026-05-18T12:32:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:32Y6N6C6BWTBUUZIZ7L57VDK7P","target":"record","payload":{"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"},"canonical_sha256":"deb1e6f85e0da61a5328cfd7dfd46afbe1ca0e958a4aa719a5f1b3472efe4de8","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"},"source_kind":"arxiv","source_id":"1812.11748","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:57:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eBDUMrNIpBWsghyBL2o6qxfm4v5K1ch++AXVpCtomqjFVyZbG6wC7jzzUzMymq9feGItvCMjNpNaSlhxlXOuCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T19:23:22.004388Z"},"content_sha256":"a5598d4611f1a9da34f62055224b72eff401434493c50e5fa34829ecd625ab0a","schema_version":"1.0","event_id":"sha256:a5598d4611f1a9da34f62055224b72eff401434493c50e5fa34829ecd625ab0a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:32Y6N6C6BWTBUUZIZ7L57VDK7P","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:57:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DectzSjMRQSA/osxdFQN3Cxh1yZx2ZbGzvOEzcP68z1agHLJNEiQDZnktPmAys9RD1fswu3J41lM8skC8UppDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T19:23:22.004740Z"},"content_sha256":"c929fb46807cd112212ec7d556ee98dbaa8edaa05571ba735f0a9af63778921c","schema_version":"1.0","event_id":"sha256:c929fb46807cd112212ec7d556ee98dbaa8edaa05571ba735f0a9af63778921c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/32Y6N6C6BWTBUUZIZ7L57VDK7P/bundle.json","state_url":"https://pith.science/pith/32Y6N6C6BWTBUUZIZ7L57VDK7P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/32Y6N6C6BWTBUUZIZ7L57VDK7P/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T19:23:22Z","links":{"resolver":"https://pith.science/pith/32Y6N6C6BWTBUUZIZ7L57VDK7P","bundle":"https://pith.science/pith/32Y6N6C6BWTBUUZIZ7L57VDK7P/bundle.json","state":"https://pith.science/pith/32Y6N6C6BWTBUUZIZ7L57VDK7P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/32Y6N6C6BWTBUUZIZ7L57VDK7P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:32Y6N6C6BWTBUUZIZ7L57VDK7P","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"feef0f8c2e2cb8a39eb1f59d1c112250bf773ff7eda2151c03e980408fd5b944","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2018-12-31T10:21:28Z","title_canon_sha256":"4e7fad73ffa12d95d6bb32fcb7a1dbf28b9e5d6fa16e00a17447db9a480e7e43"},"schema_version":"1.0","source":{"id":"1812.11748","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.11748","created_at":"2026-05-17T23:57:11Z"},{"alias_kind":"arxiv_version","alias_value":"1812.11748v1","created_at":"2026-05-17T23:57:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.11748","created_at":"2026-05-17T23:57:11Z"},{"alias_kind":"pith_short_12","alias_value":"32Y6N6C6BWTB","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"32Y6N6C6BWTBUUZI","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"32Y6N6C6","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:c929fb46807cd112212ec7d556ee98dbaa8edaa05571ba735f0a9af63778921c","target":"graph","created_at":"2026-05-17T23:57:11Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Dingyu Yang, Huijun Fan, Wenfeng Jiang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2018-12-31T10:21:28Z","title":"Fukaya category of Landau-Ginzburg model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.11748","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a5598d4611f1a9da34f62055224b72eff401434493c50e5fa34829ecd625ab0a","target":"record","created_at":"2026-05-17T23:57:11Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"feef0f8c2e2cb8a39eb1f59d1c112250bf773ff7eda2151c03e980408fd5b944","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2018-12-31T10:21:28Z","title_canon_sha256":"4e7fad73ffa12d95d6bb32fcb7a1dbf28b9e5d6fa16e00a17447db9a480e7e43"},"schema_version":"1.0","source":{"id":"1812.11748","kind":"arxiv","version":1}},"canonical_sha256":"deb1e6f85e0da61a5328cfd7dfd46afbe1ca0e958a4aa719a5f1b3472efe4de8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"deb1e6f85e0da61a5328cfd7dfd46afbe1ca0e958a4aa719a5f1b3472efe4de8","first_computed_at":"2026-05-17T23:57:11.202155Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:11.202155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pFbpsejI3KvtyrycmLj1RWLDJNClDrIxxm4MoHWGovCw4E7hvCfnJ2SvZjhQH+6WMnlizOhsjEFNR69jzw4YDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:11.202542Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.11748","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5598d4611f1a9da34f62055224b72eff401434493c50e5fa34829ecd625ab0a","sha256:c929fb46807cd112212ec7d556ee98dbaa8edaa05571ba735f0a9af63778921c"],"state_sha256":"5384d8c115256e19c9d6a09314ae17760929e2be95497ff61950b0da65cbbb39"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3jbWbn68GmW+53sG2ACkgznFKQRN2lQeBh29LwZXtl0yacx3YrGZA/Gf51ivXmdOZqvV8gFCU674WTjI9r5sBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T19:23:22.006779Z","bundle_sha256":"b20addd18a3ea37d96510c00b47acac12c4ba65356760c25a479da0a2226e39a"}}