{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:YI4NCSVYAMXXMW4EEPS3B3NNKA","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":"748cf5617860a91662b1f9a75da86b1b351dff52c694c62c02ebea9988b35794","cross_cats_sorted":["math.SG"],"license":"","primary_cat":"math.DG","submitted_at":"1999-10-15T02:37:12Z","title_canon_sha256":"38cbdbbe4a0fc63c2b9cb816d6709742acf722c35b7713212ff74bca0f9a5c6a"},"schema_version":"1.0","source":{"id":"math/9910078","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9910078","created_at":"2026-07-04T14:41:20Z"},{"alias_kind":"arxiv_version","alias_value":"math/9910078v1","created_at":"2026-07-04T14:41:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9910078","created_at":"2026-07-04T14:41:20Z"},{"alias_kind":"pith_short_12","alias_value":"YI4NCSVYAMXX","created_at":"2026-07-04T14:41:20Z"},{"alias_kind":"pith_short_16","alias_value":"YI4NCSVYAMXXMW4E","created_at":"2026-07-04T14:41:20Z"},{"alias_kind":"pith_short_8","alias_value":"YI4NCSVY","created_at":"2026-07-04T14:41:20Z"}],"graph_snapshots":[{"event_id":"sha256:8818597f086e9dba13f100d55b6ded3bd143ee5eabceb6de6d9cb02e2a832c0d","target":"graph","created_at":"2026-07-04T14:41:20Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/9910078/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this dissertation we study Courant algebroids, objects that first appeared in the work of T. Courant on Dirac structures; they were later studied by Liu, Weinstein and Xu who used Courant algebroids to generalize the notion of the Drinfeld double to Lie bialgebroids. As a first step towards understanding the complicated properties of Courant algebroids, we interpret them by associating to each Courant algebroid a strongly homotopy Lie algebra in a natural way. Next, we propose an alternative construction of the double of a Lie bialgebroid as a homological hamiltonian vector field on an even","authors_text":"Dmitry Roytenberg","cross_cats":["math.SG"],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"1999-10-15T02:37:12Z","title":"Courant algebroids, derived brackets and even symplectic supermanifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9910078","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:c667632e7dcb5707a84bec4725c121ef77e9210c52f8bf8842224c1ad9766b22","target":"record","created_at":"2026-07-04T14:41:20Z","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":"748cf5617860a91662b1f9a75da86b1b351dff52c694c62c02ebea9988b35794","cross_cats_sorted":["math.SG"],"license":"","primary_cat":"math.DG","submitted_at":"1999-10-15T02:37:12Z","title_canon_sha256":"38cbdbbe4a0fc63c2b9cb816d6709742acf722c35b7713212ff74bca0f9a5c6a"},"schema_version":"1.0","source":{"id":"math/9910078","kind":"arxiv","version":1}},"canonical_sha256":"c238d14ab8032f765b8423e5b0edad5010408e01bf896e41c6fcc93a04a40c0d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c238d14ab8032f765b8423e5b0edad5010408e01bf896e41c6fcc93a04a40c0d","first_computed_at":"2026-07-04T14:41:20.656431Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:41:20.656431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z4J4Jk+I7wHFgaz07dwySsdBPj+J/6rxJKAwDZkjdMjfSutJQf7tF6Mzgp82+yU0AUFwxiSEJza3EHFBZ/TgDw==","signature_status":"signed_v1","signed_at":"2026-07-04T14:41:20.656831Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9910078","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c667632e7dcb5707a84bec4725c121ef77e9210c52f8bf8842224c1ad9766b22","sha256:8818597f086e9dba13f100d55b6ded3bd143ee5eabceb6de6d9cb02e2a832c0d"],"state_sha256":"ae38f63b55555afa948ec37c5e6960db099426d949a747d19fb32ab8b88283c0"}