{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:QAP5OG2F2BRBQTQGLBISBPPFYE","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":"51a51fb4445a6a53041a3e0b819f16d7a276b319407f31fd35d5b4a117719f08","cross_cats_sorted":["math-ph","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-03-18T09:05:12Z","title_canon_sha256":"e652191cfecb140e86884360f58ff66f0edb3633038d1b5078d20873dde9376c"},"schema_version":"1.0","source":{"id":"1003.3529","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.3529","created_at":"2026-05-18T04:08:04Z"},{"alias_kind":"arxiv_version","alias_value":"1003.3529v3","created_at":"2026-05-18T04:08:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.3529","created_at":"2026-05-18T04:08:04Z"},{"alias_kind":"pith_short_12","alias_value":"QAP5OG2F2BRB","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"QAP5OG2F2BRBQTQG","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"QAP5OG2F","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:c43b84d7cb5f36488526e90e4337fa9f6669d558b46bf628574070730cb6b1de","target":"graph","created_at":"2026-05-18T04:08:04Z","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 analyze families of non-autonomous systems of first-order ordinary differential equations admitting a common time-dependent superposition rule, i.e., a time-dependent map expressing any solution of each of these systems in terms of a generic set of particular solutions of the system and some constants. We next study relations of these families, called Lie families, with the theory of Lie and quasi-Lie systems and apply our theory to provide common time-dependent superposition rules for certain Lie families.","authors_text":"Janusz Grabowski, Javier de Lucas, Jose F. Carinena","cross_cats":["math-ph","math.DG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-03-18T09:05:12Z","title":"Lie families: theory and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.3529","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":"sha256:976dc7a44c96f4b05bf07f15cbba476f63508753d6f64e109432159e8e7d980c","target":"record","created_at":"2026-05-18T04:08:04Z","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":"51a51fb4445a6a53041a3e0b819f16d7a276b319407f31fd35d5b4a117719f08","cross_cats_sorted":["math-ph","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-03-18T09:05:12Z","title_canon_sha256":"e652191cfecb140e86884360f58ff66f0edb3633038d1b5078d20873dde9376c"},"schema_version":"1.0","source":{"id":"1003.3529","kind":"arxiv","version":3}},"canonical_sha256":"801fd71b45d062184e06585120bde5c125aa6bb9e6d3be9c1747ef2d1f251cff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"801fd71b45d062184e06585120bde5c125aa6bb9e6d3be9c1747ef2d1f251cff","first_computed_at":"2026-05-18T04:08:04.008351Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:04.008351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uw/ya8u2bz8yg73HohAgwHKENZdiEtvRN1v1RxxE8RGOzajtBTy7EkVJo59xyy0PAYakHQg6GGZXadZI6UD4DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:04.009094Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.3529","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:976dc7a44c96f4b05bf07f15cbba476f63508753d6f64e109432159e8e7d980c","sha256:c43b84d7cb5f36488526e90e4337fa9f6669d558b46bf628574070730cb6b1de"],"state_sha256":"7c3f47a344b9bdc00a230be8e81745dfa2d43eff64a1cd165875c11ee3d9c4c7"}