{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:BIM4JMFXA7JS3QDQ7H7773VCGI","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":"9f1ccca9ad23ee0e2927024d9e7bcf251a030d6af3054818798666fba2657599","cross_cats_sorted":["math.RA"],"license":"","primary_cat":"math.AC","submitted_at":"2007-10-21T06:28:49Z","title_canon_sha256":"da1e72252270d27a366671261ab523dfb3a4448a9bbfeb03a8a3b2cbab9aa068"},"schema_version":"1.0","source":{"id":"0710.3908","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.3908","created_at":"2026-07-04T15:11:45Z"},{"alias_kind":"arxiv_version","alias_value":"0710.3908v2","created_at":"2026-07-04T15:11:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.3908","created_at":"2026-07-04T15:11:45Z"},{"alias_kind":"pith_short_12","alias_value":"BIM4JMFXA7JS","created_at":"2026-07-04T15:11:45Z"},{"alias_kind":"pith_short_16","alias_value":"BIM4JMFXA7JS3QDQ","created_at":"2026-07-04T15:11:45Z"},{"alias_kind":"pith_short_8","alias_value":"BIM4JMFX","created_at":"2026-07-04T15:11:45Z"}],"graph_snapshots":[{"event_id":"sha256:e628ef80bad8b93bc2ac2987c87e23608ffccf5b3abda6ef484c9ed208709587","target":"graph","created_at":"2026-07-04T15:11:45Z","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/0710.3908/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study Lie Rinehart bialgebras, the algebraic generalization of Lie bialgebroids. More precisely, we analyze the structure of Lie Rinehart bialgebras for crossed products induced by actions of Lie algebras on K[t].","authors_text":"D.-S. Zhong, Z. Chen, Z.-J. Liu","cross_cats":["math.RA"],"headline":"","license":"","primary_cat":"math.AC","submitted_at":"2007-10-21T06:28:49Z","title":"Lie Rinehart Bialgebras for Crossed Products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.3908","kind":"arxiv","version":2},"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:ede0442fbd1c22e29373e1ac6f460d5ced957d5e9fa42569cb8af8cd53510ada","target":"record","created_at":"2026-07-04T15:11:45Z","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":"9f1ccca9ad23ee0e2927024d9e7bcf251a030d6af3054818798666fba2657599","cross_cats_sorted":["math.RA"],"license":"","primary_cat":"math.AC","submitted_at":"2007-10-21T06:28:49Z","title_canon_sha256":"da1e72252270d27a366671261ab523dfb3a4448a9bbfeb03a8a3b2cbab9aa068"},"schema_version":"1.0","source":{"id":"0710.3908","kind":"arxiv","version":2}},"canonical_sha256":"0a19c4b0b707d32dc070f9ffffeea2320343b47a3ff723411193cefc6b75319d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a19c4b0b707d32dc070f9ffffeea2320343b47a3ff723411193cefc6b75319d","first_computed_at":"2026-07-04T15:11:45.442621Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:11:45.442621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B3EB+byCPTNjAX5pUYZlGQ2Uz2HSZss+pv7tdXOItpDduFk8ksc1VKdsqpVtm+PXkccz4wEl6zcDzPg2kc1JDw==","signature_status":"signed_v1","signed_at":"2026-07-04T15:11:45.443023Z","signed_message":"canonical_sha256_bytes"},"source_id":"0710.3908","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ede0442fbd1c22e29373e1ac6f460d5ced957d5e9fa42569cb8af8cd53510ada","sha256:e628ef80bad8b93bc2ac2987c87e23608ffccf5b3abda6ef484c9ed208709587"],"state_sha256":"2316683fb629c42396ee6829c4784824fdd218f34e80e04f192c031ca2beeee0"}