{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:P6S7DXIDHE3TYIBIQ5ES2EBGUR","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":"bf3a47023d15c716292d5b7466ece5f1c4034797eac8c67241f8e04b2a98501c","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-04-27T11:18:08Z","title_canon_sha256":"b889b4326eaf49faabb0c03f5ce082ae8a6697d2eda73d6f299367c92b567f9f"},"schema_version":"1.0","source":{"id":"1804.10444","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.10444","created_at":"2026-05-18T00:17:20Z"},{"alias_kind":"arxiv_version","alias_value":"1804.10444v1","created_at":"2026-05-18T00:17:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.10444","created_at":"2026-05-18T00:17:20Z"},{"alias_kind":"pith_short_12","alias_value":"P6S7DXIDHE3T","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"P6S7DXIDHE3TYIBI","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"P6S7DXID","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:8f4dd0c0dfa6fd8c80aa3c752db6a594f508969820eba5b70d87a12645c4e6ee","target":"graph","created_at":"2026-05-18T00:17:20Z","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":"The purpose of this short note is to present two existence results concerning symplectic and lagrangian structures in the derived setting, in situations where the constructions of [Ca] and [PTVV] do not apply. For this we show that symplectic structures can be constructed out of Calabi-Yau structures on sheaves of dg-categories, or out of \\emph{orientations} on sheaves of rigid dg-categories. These results follow from two main theorems: the HKR theorem and the cyclotomic aspect of traces in rigid infty-categories.","authors_text":"Bertrand To\\\"en","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-04-27T11:18:08Z","title":"Structures symplectiques et de Poisson sur les champs en cat\\'egories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10444","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":"sha256:69fe956ea3a30a2e420bc35f2f3cc0ae53513ca40a620e2e777181574cb6679e","target":"record","created_at":"2026-05-18T00:17:20Z","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":"bf3a47023d15c716292d5b7466ece5f1c4034797eac8c67241f8e04b2a98501c","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-04-27T11:18:08Z","title_canon_sha256":"b889b4326eaf49faabb0c03f5ce082ae8a6697d2eda73d6f299367c92b567f9f"},"schema_version":"1.0","source":{"id":"1804.10444","kind":"arxiv","version":1}},"canonical_sha256":"7fa5f1dd0339373c202887492d1026a44a75529feeae24e63876a5a093ec67b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7fa5f1dd0339373c202887492d1026a44a75529feeae24e63876a5a093ec67b5","first_computed_at":"2026-05-18T00:17:20.739217Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:20.739217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lGLRa+JSpLiEwuY+3LSZ/FrAmuhdSaznFIPHeQ/9ARhxvc61QOC41DMM5sqtVFxCxdHVSi5438gGJY7Q6FOIAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:20.739841Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.10444","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69fe956ea3a30a2e420bc35f2f3cc0ae53513ca40a620e2e777181574cb6679e","sha256:8f4dd0c0dfa6fd8c80aa3c752db6a594f508969820eba5b70d87a12645c4e6ee"],"state_sha256":"9adc89e8d6b721c874299924db6a8ac002a40a8f3d2dc13536ce5dbb33edc702"}