{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:MB7T66OEXSQJ7NLDDQGTJ7GLL3","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":"727658aa6d471905d46d8477d6ceb190ed0077f3699bcd226eb4d5e7982e5593","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.SG","submitted_at":"2007-01-07T17:24:32Z","title_canon_sha256":"304458143c0c7b61074f32d64bdec38d44532e4c7efbd2f7d769c5fb31b2c202"},"schema_version":"1.0","source":{"id":"math/0701209","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0701209","created_at":"2026-05-18T03:39:14Z"},{"alias_kind":"arxiv_version","alias_value":"math/0701209v3","created_at":"2026-05-18T03:39:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0701209","created_at":"2026-05-18T03:39:14Z"},{"alias_kind":"pith_short_12","alias_value":"MB7T66OEXSQJ","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"MB7T66OEXSQJ7NLD","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"MB7T66OE","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:a9f64df6b0639e3f93a0acafdc5614fcd9a0979ed0adf433d2b952914ab30fd2","target":"graph","created_at":"2026-05-18T03:39:14Z","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 derive a formula for the the modular class of a Lie algebroid with a regular twisted Poisson structure in terms of a canonical Lie algebroid representation of the image of the Poisson map. We use this formula to compute the modular classes of Lie algebras with a twisted triangular r-matrix. The special case of r-matrices associated to Frobenius Lie algebras is also studied.","authors_text":"Milen Yakimov, Yvette Kosmann-Schwarzbach","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"math.SG","submitted_at":"2007-01-07T17:24:32Z","title":"Modular classes of regular twisted Poisson structures on Lie algebroids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0701209","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:a1be873b0f765d1886a838b69d9947603c6eef3f93671e9ccf6dab5e97c28725","target":"record","created_at":"2026-05-18T03:39:14Z","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":"727658aa6d471905d46d8477d6ceb190ed0077f3699bcd226eb4d5e7982e5593","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.SG","submitted_at":"2007-01-07T17:24:32Z","title_canon_sha256":"304458143c0c7b61074f32d64bdec38d44532e4c7efbd2f7d769c5fb31b2c202"},"schema_version":"1.0","source":{"id":"math/0701209","kind":"arxiv","version":3}},"canonical_sha256":"607f3f79c4bca09fb5631c0d34fccb5eee780f8a063e9a6131ee5fc1e55b4379","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"607f3f79c4bca09fb5631c0d34fccb5eee780f8a063e9a6131ee5fc1e55b4379","first_computed_at":"2026-05-18T03:39:14.950609Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:14.950609Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v++VuICXO16nIBwP3LDjf7iPvfX/5b9wrVtAuc5L3C2G7FTx74MG99Erx9jRBYjB7kFKwoHc+U+67C3bURa6CA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:14.951274Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0701209","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1be873b0f765d1886a838b69d9947603c6eef3f93671e9ccf6dab5e97c28725","sha256:a9f64df6b0639e3f93a0acafdc5614fcd9a0979ed0adf433d2b952914ab30fd2"],"state_sha256":"cc60fb6d0139772533dc4c5935aa630540cc96ee593677d5ab2a2058a0974c01"}