{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:4T3ZAE5J3U3GPEIT6MFVASCHAO","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":"29c837456cb8eb9f14f1687dc746109d3856d06b7a9fcbb105e4f42108efc136","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-18T16:59:58Z","title_canon_sha256":"6fd7ef6ef70fc8766da5573d3fca505814828bb633d593c967f049c7214ebd3f"},"schema_version":"1.0","source":{"id":"1402.4402","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.4402","created_at":"2026-05-18T02:48:17Z"},{"alias_kind":"arxiv_version","alias_value":"1402.4402v2","created_at":"2026-05-18T02:48:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.4402","created_at":"2026-05-18T02:48:17Z"},{"alias_kind":"pith_short_12","alias_value":"4T3ZAE5J3U3G","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4T3ZAE5J3U3GPEIT","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4T3ZAE5J","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:de04d8c5d5501b8307adf986584c374b8025dca46c0621df84cde7cd8d3ebc00","target":"graph","created_at":"2026-05-18T02:48:17Z","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":"Reid's m'th-order generalized Ermakov systems of nonlinear coupling constant alpha are equivalent to an integrable Emden-Fowler equation. The standard Ermakov-Lewis invariant is discussed from this perspective, and a closed formula for the invariant is obtained for the higher-order Reid systems (m\\geq 3). We also discuss the parametric solutions of these systems of equations through the integration of the Emden-Fowler equation and present an example of a dynamical system for which the invariant is equivalent to the total energy","authors_text":"Haret C Rosu, Stefan C Mancas","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-18T16:59:58Z","title":"Ermakov-Lewis Invariants and Reid Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.4402","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":"sha256:158f07b0d9e852a6d31c5238c027a73c880e1985b3e7ffb99dfd394c06559e1e","target":"record","created_at":"2026-05-18T02:48:17Z","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":"29c837456cb8eb9f14f1687dc746109d3856d06b7a9fcbb105e4f42108efc136","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-18T16:59:58Z","title_canon_sha256":"6fd7ef6ef70fc8766da5573d3fca505814828bb633d593c967f049c7214ebd3f"},"schema_version":"1.0","source":{"id":"1402.4402","kind":"arxiv","version":2}},"canonical_sha256":"e4f79013a9dd36679113f30b50484703a755df28eebc9709acb31e426bb94751","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4f79013a9dd36679113f30b50484703a755df28eebc9709acb31e426bb94751","first_computed_at":"2026-05-18T02:48:17.241917Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:17.241917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gm4PmRWyBOK/KxycM+D3EKJv5hQpd6fX6ePfPdHwl6kkDTVegu4/1eMVi8RoazGx4y8GBGp31auG16r9D40uCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:17.242329Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.4402","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:158f07b0d9e852a6d31c5238c027a73c880e1985b3e7ffb99dfd394c06559e1e","sha256:de04d8c5d5501b8307adf986584c374b8025dca46c0621df84cde7cd8d3ebc00"],"state_sha256":"57f44b2f918e577cf23104fb29176b6d32a41632c9a92e420eb874992b78b747"}