{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:C5MLZTDOCYILMHPLESUUANLNH5","short_pith_number":"pith:C5MLZTDO","canonical_record":{"source":{"id":"1102.4664","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-02-23T06:05:08Z","cross_cats_sorted":[],"title_canon_sha256":"13c7b8cbf49f4b65ac7b6fa2246bc2a785b5c1c34ae52d2e784062848c1abb4d","abstract_canon_sha256":"f27629943cd61e92f571930854bf5d517c352441a44bab2fce0fc6b0341031e2"},"schema_version":"1.0"},"canonical_sha256":"1758bccc6e1610b61deb24a940356d3f54ff1d1e6b046887664312816a6cf38d","source":{"kind":"arxiv","id":"1102.4664","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4664","created_at":"2026-05-18T03:40:36Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4664v3","created_at":"2026-05-18T03:40:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4664","created_at":"2026-05-18T03:40:36Z"},{"alias_kind":"pith_short_12","alias_value":"C5MLZTDOCYIL","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"C5MLZTDOCYILMHPL","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"C5MLZTDO","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:C5MLZTDOCYILMHPLESUUANLNH5","target":"record","payload":{"canonical_record":{"source":{"id":"1102.4664","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-02-23T06:05:08Z","cross_cats_sorted":[],"title_canon_sha256":"13c7b8cbf49f4b65ac7b6fa2246bc2a785b5c1c34ae52d2e784062848c1abb4d","abstract_canon_sha256":"f27629943cd61e92f571930854bf5d517c352441a44bab2fce0fc6b0341031e2"},"schema_version":"1.0"},"canonical_sha256":"1758bccc6e1610b61deb24a940356d3f54ff1d1e6b046887664312816a6cf38d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:36.884536Z","signature_b64":"EF3LcBv5ucgrBhsglBHamlZSmA3J9xMuWu1TK2Sc8VxDv9x+MCemKOMCWysPqlizKbMTOJei4XuHgMXezAjOBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1758bccc6e1610b61deb24a940356d3f54ff1d1e6b046887664312816a6cf38d","last_reissued_at":"2026-05-18T03:40:36.883638Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:36.883638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.4664","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:40:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kp+Ll6aV6NgHcS9Qhu88USdQyw0yk6eouJ3wsqqmTkIY8UmV+ECUveTxYNOlHK7rR31CXf5xcFE7iwFbUa3uDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T08:33:09.842109Z"},"content_sha256":"66c12570b5ab73b46ce96b9f1fc6ea013184c73c2717be3b29b2543df0affa50","schema_version":"1.0","event_id":"sha256:66c12570b5ab73b46ce96b9f1fc6ea013184c73c2717be3b29b2543df0affa50"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:C5MLZTDOCYILMHPLESUUANLNH5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Toric Degenerations of Fano Threefolds Giving Weak Landau-Ginzburg Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jacob Lewis, Nathan Owen Ilten, Victor Przyjalkowski","submitted_at":"2011-02-23T06:05:08Z","abstract_excerpt":"We show that every rank one smooth Fano threefold has a weak Landau-Ginzburg model coming from a toric degeneration. The fibers of these Landau-Ginzburg models can be compactified to K3 surfaces with Picard lattice of rank 19. We also show that any smooth Fano variety of arbitrary dimension which is a complete intersection of Cartier divisors in weighted projective space has a very weak Landau-Ginzburg model coming from a toric degeneration."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4664","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:40:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oSfo+cpOfO4p92k3gg2QcJAZBtHzeohrfOY//feodm8zM5CvsDLT5WssZDJ2TFyYJapNezi6ET9WH3yDlQqPAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T08:33:09.842468Z"},"content_sha256":"78a01e3b45d5c6fe5980f9ee45e36cf45c1eef903b483556a66e8d781376862c","schema_version":"1.0","event_id":"sha256:78a01e3b45d5c6fe5980f9ee45e36cf45c1eef903b483556a66e8d781376862c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C5MLZTDOCYILMHPLESUUANLNH5/bundle.json","state_url":"https://pith.science/pith/C5MLZTDOCYILMHPLESUUANLNH5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C5MLZTDOCYILMHPLESUUANLNH5/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":"2026-05-28T08:33:09Z","links":{"resolver":"https://pith.science/pith/C5MLZTDOCYILMHPLESUUANLNH5","bundle":"https://pith.science/pith/C5MLZTDOCYILMHPLESUUANLNH5/bundle.json","state":"https://pith.science/pith/C5MLZTDOCYILMHPLESUUANLNH5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C5MLZTDOCYILMHPLESUUANLNH5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:C5MLZTDOCYILMHPLESUUANLNH5","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":"f27629943cd61e92f571930854bf5d517c352441a44bab2fce0fc6b0341031e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-02-23T06:05:08Z","title_canon_sha256":"13c7b8cbf49f4b65ac7b6fa2246bc2a785b5c1c34ae52d2e784062848c1abb4d"},"schema_version":"1.0","source":{"id":"1102.4664","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4664","created_at":"2026-05-18T03:40:36Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4664v3","created_at":"2026-05-18T03:40:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4664","created_at":"2026-05-18T03:40:36Z"},{"alias_kind":"pith_short_12","alias_value":"C5MLZTDOCYIL","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"C5MLZTDOCYILMHPL","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"C5MLZTDO","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:78a01e3b45d5c6fe5980f9ee45e36cf45c1eef903b483556a66e8d781376862c","target":"graph","created_at":"2026-05-18T03:40:36Z","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":"We show that every rank one smooth Fano threefold has a weak Landau-Ginzburg model coming from a toric degeneration. The fibers of these Landau-Ginzburg models can be compactified to K3 surfaces with Picard lattice of rank 19. We also show that any smooth Fano variety of arbitrary dimension which is a complete intersection of Cartier divisors in weighted projective space has a very weak Landau-Ginzburg model coming from a toric degeneration.","authors_text":"Jacob Lewis, Nathan Owen Ilten, Victor Przyjalkowski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-02-23T06:05:08Z","title":"Toric Degenerations of Fano Threefolds Giving Weak Landau-Ginzburg Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4664","kind":"arxiv","version":3},"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":"sha256:66c12570b5ab73b46ce96b9f1fc6ea013184c73c2717be3b29b2543df0affa50","target":"record","created_at":"2026-05-18T03:40:36Z","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":"f27629943cd61e92f571930854bf5d517c352441a44bab2fce0fc6b0341031e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-02-23T06:05:08Z","title_canon_sha256":"13c7b8cbf49f4b65ac7b6fa2246bc2a785b5c1c34ae52d2e784062848c1abb4d"},"schema_version":"1.0","source":{"id":"1102.4664","kind":"arxiv","version":3}},"canonical_sha256":"1758bccc6e1610b61deb24a940356d3f54ff1d1e6b046887664312816a6cf38d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1758bccc6e1610b61deb24a940356d3f54ff1d1e6b046887664312816a6cf38d","first_computed_at":"2026-05-18T03:40:36.883638Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:36.883638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EF3LcBv5ucgrBhsglBHamlZSmA3J9xMuWu1TK2Sc8VxDv9x+MCemKOMCWysPqlizKbMTOJei4XuHgMXezAjOBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:36.884536Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.4664","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:66c12570b5ab73b46ce96b9f1fc6ea013184c73c2717be3b29b2543df0affa50","sha256:78a01e3b45d5c6fe5980f9ee45e36cf45c1eef903b483556a66e8d781376862c"],"state_sha256":"d52f9cb863d5336d619927410a4573081af61a0668c0b2377e36ec4ffa19a8f9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xGiAwdklR30n10y+LKWBKxWcypRKCotmEqj6wRPIkm00UcI94UA8ziuoX+7TnxGZh0jdjbRP/J2krQsKe6C0Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T08:33:09.844416Z","bundle_sha256":"d525e8a5c36a9f4f531167b8751eaa8705d53a0a88942660872fc141d850416c"}}