{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:W4ZK3OLNT34P4G4P6IE7X4DRSN","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":"fdbcbc2ed930e3cf9c5c33236b18ef7d44968bc6b77cc9885a6bff69524ef972","cross_cats_sorted":["math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-12-12T17:06:53Z","title_canon_sha256":"1600634b12a56f7fe10ba982fcab9e6f3bb2f1cb26dc07b5cb225d690ac3ba20"},"schema_version":"1.0","source":{"id":"1112.2623","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.2623","created_at":"2026-05-18T03:56:10Z"},{"alias_kind":"arxiv_version","alias_value":"1112.2623v2","created_at":"2026-05-18T03:56:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.2623","created_at":"2026-05-18T03:56:10Z"},{"alias_kind":"pith_short_12","alias_value":"W4ZK3OLNT34P","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"W4ZK3OLNT34P4G4P","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"W4ZK3OLN","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:c1284fcde1c0d16dd611c69310c7dc55a33b5edf9bb13279e6417fcd49baf156","target":"graph","created_at":"2026-05-18T03:56:10Z","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":"All possible Poisson-Lie (PL) structures on the 3D real Lie group generated by a dilation and two commuting translations are obtained. Its classification is fully performed by relating these PL groups with the corresponding Lie bialgebra structures on the corresponding \"book\" Lie algebra. By construction, all these Poisson structures are quadratic Poisson-Hopf algebras for which the group multiplication is a Poisson map. In contrast to the case of simple Lie groups, it turns out that most of the PL structures on the book group are non-coboundary ones. Moreover, from the viewpoint of Poisson dy","authors_text":"Alfonso Blasco, Angel Ballesteros, Fabio Musso","cross_cats":["math.MP","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-12-12T17:06:53Z","title":"Non-coboundary Poisson-Lie structures on the book group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2623","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:d2faa7fad749195e5f2237465eccdd3f835597478f356c99b617196dba2cd610","target":"record","created_at":"2026-05-18T03:56:10Z","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":"fdbcbc2ed930e3cf9c5c33236b18ef7d44968bc6b77cc9885a6bff69524ef972","cross_cats_sorted":["math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-12-12T17:06:53Z","title_canon_sha256":"1600634b12a56f7fe10ba982fcab9e6f3bb2f1cb26dc07b5cb225d690ac3ba20"},"schema_version":"1.0","source":{"id":"1112.2623","kind":"arxiv","version":2}},"canonical_sha256":"b732adb96d9ef8fe1b8ff209fbf0719370f4b73603abe7b895aeabcd4516b189","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b732adb96d9ef8fe1b8ff209fbf0719370f4b73603abe7b895aeabcd4516b189","first_computed_at":"2026-05-18T03:56:10.466220Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:10.466220Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ge+wb73jElZ3b/iK+rRsTMC30GQJkTRT+nt71SI3ZZQzFb6x7nRT6Rvis0KyjU42M1NUBDmKObh7MiyXNkHvAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:10.466876Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.2623","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d2faa7fad749195e5f2237465eccdd3f835597478f356c99b617196dba2cd610","sha256:c1284fcde1c0d16dd611c69310c7dc55a33b5edf9bb13279e6417fcd49baf156"],"state_sha256":"8f44592dfb4ade1255c0bd55f85154992abb5ab276dc0b89dab3fb6aef13f5cf"}