{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:CEO2QMT2F4WTC72EJURX4MD7GH","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":"62c9042c55ca719067277e08420d6567b3b15cfed3f54f682c07ac59e384b246","cross_cats_sorted":["math.SG"],"license":"","primary_cat":"math.DG","submitted_at":"2005-08-25T17:58:55Z","title_canon_sha256":"dad624e5e460a2ee1f177265b1836924b17b8c199ebf24e2cb352be11e0f807a"},"schema_version":"1.0","source":{"id":"math/0508515","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0508515","created_at":"2026-07-04T14:40:20Z"},{"alias_kind":"arxiv_version","alias_value":"math/0508515v1","created_at":"2026-07-04T14:40:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0508515","created_at":"2026-07-04T14:40:20Z"},{"alias_kind":"pith_short_12","alias_value":"CEO2QMT2F4WT","created_at":"2026-07-04T14:40:20Z"},{"alias_kind":"pith_short_16","alias_value":"CEO2QMT2F4WTC72E","created_at":"2026-07-04T14:40:20Z"},{"alias_kind":"pith_short_8","alias_value":"CEO2QMT2","created_at":"2026-07-04T14:40:20Z"}],"graph_snapshots":[{"event_id":"sha256:537031ef982e139af28873095563eccae0d26d4a16b3c189a97f909fb34d23b6","target":"graph","created_at":"2026-07-04T14:40:20Z","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/0508515/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the relative modular classes of Lie algebroids, and we determine their relationship with the modular classes of Lie algebroids with a twisted Poisson structure.","authors_text":"Alan Weinstein, Yvette Kosmann-Schwarzbach","cross_cats":["math.SG"],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2005-08-25T17:58:55Z","title":"Relative modular classes of Lie algebroids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0508515","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":"sha256:3a9c8f2dbbfbb24df8c9f1f44a373c91927e855f3829a99307b4f27de66dc24e","target":"record","created_at":"2026-07-04T14:40:20Z","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":"62c9042c55ca719067277e08420d6567b3b15cfed3f54f682c07ac59e384b246","cross_cats_sorted":["math.SG"],"license":"","primary_cat":"math.DG","submitted_at":"2005-08-25T17:58:55Z","title_canon_sha256":"dad624e5e460a2ee1f177265b1836924b17b8c199ebf24e2cb352be11e0f807a"},"schema_version":"1.0","source":{"id":"math/0508515","kind":"arxiv","version":1}},"canonical_sha256":"111da8327a2f2d317f444d237e307f31c63b526420989f038b6ce466d6179848","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"111da8327a2f2d317f444d237e307f31c63b526420989f038b6ce466d6179848","first_computed_at":"2026-07-04T14:40:20.292393Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:40:20.292393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tJ+baJ3HBTUK7kQRMljD/zhRH6E6FP3s/5uc9FbzR/VswFwc9YvdBELNKbuGTDaChWB53T2EH8RCWckHdtVJCA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:40:20.292760Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0508515","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a9c8f2dbbfbb24df8c9f1f44a373c91927e855f3829a99307b4f27de66dc24e","sha256:537031ef982e139af28873095563eccae0d26d4a16b3c189a97f909fb34d23b6"],"state_sha256":"17201a7082bce00c2879e0d76176b20f4da9e1bff317fc9a861d44ff4dc86e9b"}