{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:4LI4LK3YCNG6HZGZXD63M7GFMD","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":"11a97edf147deb430803b4271414f769d63ecb6c7698897c271ad6a3c8118184","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-09-24T21:29:54Z","title_canon_sha256":"d4ef7289f7dfb971093657dd8237eafadb0c02b9702e3e88febdf526bca035f5"},"schema_version":"1.0","source":{"id":"1809.09230","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.09230","created_at":"2026-05-17T23:45:36Z"},{"alias_kind":"arxiv_version","alias_value":"1809.09230v2","created_at":"2026-05-17T23:45:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.09230","created_at":"2026-05-17T23:45:36Z"},{"alias_kind":"pith_short_12","alias_value":"4LI4LK3YCNG6","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4LI4LK3YCNG6HZGZ","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4LI4LK3Y","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:aaa75ebe327638b30a52fb49fbc01e340b018665ece9080d101b94c56d44d273","target":"graph","created_at":"2026-05-17T23:45:36Z","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 is a review of the theory of toric Landau-Ginzburg models - the effective approach to mirror symmetry for Fano varieties. We mainly focus on the cases of dimensions 2 and 3, as well as on the case of complete intersections in weighted projective spaces and Grassmannians. Conjectures that relate invariants of Fano varieties and their Landau--Ginzburg models, such as Katzarkov-Kontsevich-Pantev conjectures, are also studied.","authors_text":"Victor Przyjalkowski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-09-24T21:29:54Z","title":"Toric Landau-Ginzburg models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.09230","kind":"arxiv","version":2},"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":"sha256:8e5944bf99879f2e0858e7d830e6e025294b7f4867767f95730d00795cf5467e","target":"record","created_at":"2026-05-17T23:45:36Z","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":"11a97edf147deb430803b4271414f769d63ecb6c7698897c271ad6a3c8118184","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-09-24T21:29:54Z","title_canon_sha256":"d4ef7289f7dfb971093657dd8237eafadb0c02b9702e3e88febdf526bca035f5"},"schema_version":"1.0","source":{"id":"1809.09230","kind":"arxiv","version":2}},"canonical_sha256":"e2d1c5ab78134de3e4d9b8fdb67cc560f4f395648eceae48fd4d87416f152251","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e2d1c5ab78134de3e4d9b8fdb67cc560f4f395648eceae48fd4d87416f152251","first_computed_at":"2026-05-17T23:45:36.521875Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:36.521875Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TPeb9ufRjfRolwGGo6nNkSmgOQtlp/YqF3S+6lC+qLxbGmJYr8RTC6HWavd3bTzxQblMLNE3XCwnNNfuFgnJCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:36.522589Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.09230","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8e5944bf99879f2e0858e7d830e6e025294b7f4867767f95730d00795cf5467e","sha256:aaa75ebe327638b30a52fb49fbc01e340b018665ece9080d101b94c56d44d273"],"state_sha256":"7f1512951bbf7d2f678e05d6e398dea37540b3e8da1fd62ec89a88a44f91c914"}