{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:T2P2H3IXYIQIYTP7WOLM4O2UOX","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":"c816e41b1a7f4c98f18131301a8d1b913e4954610536b951435da1a64d35b304","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-03-20T13:10:49Z","title_canon_sha256":"a3192ee8278a8b2ad15d7d5345bc5debcf7aae20b6c668680d81b3a47212dfa8"},"schema_version":"1.0","source":{"id":"1803.07404","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.07404","created_at":"2026-05-17T23:59:32Z"},{"alias_kind":"arxiv_version","alias_value":"1803.07404v1","created_at":"2026-05-17T23:59:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.07404","created_at":"2026-05-17T23:59:32Z"},{"alias_kind":"pith_short_12","alias_value":"T2P2H3IXYIQI","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"T2P2H3IXYIQIYTP7","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"T2P2H3IX","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:e0699627a01c06d72c5108dd7cc371b86cf8a533a9452862042f14aec6edb1de","target":"graph","created_at":"2026-05-17T23:59:32Z","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":"Based on a recently developed procedure to construct Poisson-Hopf deformations of Lie-Hamilton systems, a novel unified approach to nonequivalent deformations of Lie-Hamilton systems on the real plane with a Vessiot-Guldberg Lie algebra isomorphic to $\\mathfrak{sl}(2)$ is proposed. This, in particular, allows us to define a notion of Poisson-Hopf systems in dependence of a parameterized family of Poisson algebra representations. Such an approach is explicitly illustrated by applying it to the three non-diffeomorphic classes of $\\mathfrak{sl}(2)$ Lie-Hamilton systems. Our results cover deformat","authors_text":"Angel Ballesteros, Eduardo Fernandez-Saiz, Francisco J. Herranz, Javier de Lucas, Rutwig Campoamor-Stursberg","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-03-20T13:10:49Z","title":"A unified approach to Poisson-Hopf deformations of Lie-Hamilton systems based on sl(2)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.07404","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":"sha256:792b1ad48cba906b7993ef6a6e25da66fc82eadfa5efb53cab03c0277c86b824","target":"record","created_at":"2026-05-17T23:59:32Z","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":"c816e41b1a7f4c98f18131301a8d1b913e4954610536b951435da1a64d35b304","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-03-20T13:10:49Z","title_canon_sha256":"a3192ee8278a8b2ad15d7d5345bc5debcf7aae20b6c668680d81b3a47212dfa8"},"schema_version":"1.0","source":{"id":"1803.07404","kind":"arxiv","version":1}},"canonical_sha256":"9e9fa3ed17c2208c4dffb396ce3b5475f77942f63d37791cfeb46b2db2e5aecd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e9fa3ed17c2208c4dffb396ce3b5475f77942f63d37791cfeb46b2db2e5aecd","first_computed_at":"2026-05-17T23:59:32.925458Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:32.925458Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RvrggDbwB2m+mlJRdhjJmchQmB7v/NsWlsflJS1JBPinPsMwtpz7FCutCXnu/F1Hvt6Sgo6cynbqaz0s0lRuDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:32.926039Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.07404","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:792b1ad48cba906b7993ef6a6e25da66fc82eadfa5efb53cab03c0277c86b824","sha256:e0699627a01c06d72c5108dd7cc371b86cf8a533a9452862042f14aec6edb1de"],"state_sha256":"e4890742f5a05576b28c9377d706293e0a46f94050e807e09f5fb8940bef8ea8"}