{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6YOY2IUDX4R3RV5T2ED6FXPBXX","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":"5df317a99916ebfa972cfd322e41bc6d460b23965b756cbea2b699160867fd9f","cross_cats_sorted":["math.AT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-12-31T17:38:35Z","title_canon_sha256":"29711f1a8f69bfe5d9f71c9d7615100c46b68f1940d5299cbeb3edc1aa3dac03"},"schema_version":"1.0","source":{"id":"1812.11913","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.11913","created_at":"2026-05-17T23:57:10Z"},{"alias_kind":"arxiv_version","alias_value":"1812.11913v1","created_at":"2026-05-17T23:57:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.11913","created_at":"2026-05-17T23:57:10Z"},{"alias_kind":"pith_short_12","alias_value":"6YOY2IUDX4R3","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6YOY2IUDX4R3RV5T","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6YOY2IUD","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:632faaf2d39a5c3a1f3231d8c106917402c6aa9e157153b91c642cd77c792821","target":"graph","created_at":"2026-05-17T23:57:10Z","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 a Calabi-Yau structure of dimension $d$ on a smooth dg category $C$ induces a symplectic form of degree $2-d$ on the moduli space of objects $M_{C}$. We show moreover that a relative Calabi-Yau structure on a dg functor $C \\to D$ compatible with the absolute Calabi-Yau structure on $C$ induces a Lagrangian structure on the corresponding map of moduli $M_{D} \\to M_{C}$.","authors_text":"Christopher Brav, Tobias Dyckerhoff","cross_cats":["math.AT","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-12-31T17:38:35Z","title":"Relative Calabi-Yau structures II: Shifted Lagrangians in the moduli of objects"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.11913","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":"sha256:93ee35abd9b650e75b992c70699f4876f21e8b49681e36fef36a72f7dbbe93ec","target":"record","created_at":"2026-05-17T23:57:10Z","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":"5df317a99916ebfa972cfd322e41bc6d460b23965b756cbea2b699160867fd9f","cross_cats_sorted":["math.AT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-12-31T17:38:35Z","title_canon_sha256":"29711f1a8f69bfe5d9f71c9d7615100c46b68f1940d5299cbeb3edc1aa3dac03"},"schema_version":"1.0","source":{"id":"1812.11913","kind":"arxiv","version":1}},"canonical_sha256":"f61d8d2283bf23b8d7b3d107e2dde1bdff4cf8ffa61bd87b09d55d40b3fca5c9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f61d8d2283bf23b8d7b3d107e2dde1bdff4cf8ffa61bd87b09d55d40b3fca5c9","first_computed_at":"2026-05-17T23:57:10.787253Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:10.787253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DndMOVMwJaH6IRqF4Mg0Xff8AcUlbmrFF+J7PKioOfmVPrM/mrS0VsVQCWf9haQe2O3B/q0OgDt/LRiXs9ISAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:10.787647Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.11913","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:93ee35abd9b650e75b992c70699f4876f21e8b49681e36fef36a72f7dbbe93ec","sha256:632faaf2d39a5c3a1f3231d8c106917402c6aa9e157153b91c642cd77c792821"],"state_sha256":"b7e21a1684ab574b05ead6ad4f325173eeed39f266aa329aa0b2a3142c000c42"}