{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:ZQQPV5VYG6JP5A3K5JGQJT7PEW","short_pith_number":"pith:ZQQPV5VY","schema_version":"1.0","canonical_sha256":"cc20faf6b83792fe836aea4d04cfef25bbd94daf5a6110f8fdb3d32f43bf71ab","source":{"kind":"arxiv","id":"1301.3567","version":4},"attestation_state":"computed","paper":{"title":"Integrable equations with Ermakov-Pinney nonlinearities and Chiellini damping","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Haret C. Rosu, Stefan C. Mancas","submitted_at":"2013-01-16T03:14:53Z","abstract_excerpt":"We introduce a special type of dissipative Ermakov-Pinney equations of the form v_{\\zeta \\zeta}+g(v)v_{\\zeta}+h(v)=0, where h(v)=h_0(v)+cv^{-3} and the nonlinear dissipation g(v) is based on the corresponding Chiellini integrable Abel equation. When h_0(v) is a linear function, h_0(v)=\\lambda^2v, general solutions are obtained following the Abel equation route. Based on particular solutions, we also provide general solutions containing a factor with the phase of the Milne type. In addition, the same kinds of general solutions are constructed for the cases of higher-order Reid nonlinearities. T"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1301.3567","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-01-16T03:14:53Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"5eb28837a90a73440c4b9ae91653cbf442e67b5679de64c8f5086ed0257c3aa2","abstract_canon_sha256":"dccb052199d02cf72528494e563b6616eaf1cd76ceb93c9ee4eafc789513c547"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:34.415547Z","signature_b64":"ISF1uNID9qgSsUaJEEsstYemUb+qPMNLxHlXHZ32enGAUTcvzQAXMqSRISSHKQxiB/B1xM4WI5IJV/U0B4zOCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc20faf6b83792fe836aea4d04cfef25bbd94daf5a6110f8fdb3d32f43bf71ab","last_reissued_at":"2026-05-18T02:25:34.415031Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:34.415031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Integrable equations with Ermakov-Pinney nonlinearities and Chiellini damping","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Haret C. Rosu, Stefan C. Mancas","submitted_at":"2013-01-16T03:14:53Z","abstract_excerpt":"We introduce a special type of dissipative Ermakov-Pinney equations of the form v_{\\zeta \\zeta}+g(v)v_{\\zeta}+h(v)=0, where h(v)=h_0(v)+cv^{-3} and the nonlinear dissipation g(v) is based on the corresponding Chiellini integrable Abel equation. When h_0(v) is a linear function, h_0(v)=\\lambda^2v, general solutions are obtained following the Abel equation route. Based on particular solutions, we also provide general solutions containing a factor with the phase of the Milne type. In addition, the same kinds of general solutions are constructed for the cases of higher-order Reid nonlinearities. T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3567","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1301.3567","created_at":"2026-05-18T02:25:34.415100+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.3567v4","created_at":"2026-05-18T02:25:34.415100+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.3567","created_at":"2026-05-18T02:25:34.415100+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZQQPV5VYG6JP","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZQQPV5VYG6JP5A3K","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZQQPV5VY","created_at":"2026-05-18T12:28:09.283467+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZQQPV5VYG6JP5A3K5JGQJT7PEW","json":"https://pith.science/pith/ZQQPV5VYG6JP5A3K5JGQJT7PEW.json","graph_json":"https://pith.science/api/pith-number/ZQQPV5VYG6JP5A3K5JGQJT7PEW/graph.json","events_json":"https://pith.science/api/pith-number/ZQQPV5VYG6JP5A3K5JGQJT7PEW/events.json","paper":"https://pith.science/paper/ZQQPV5VY"},"agent_actions":{"view_html":"https://pith.science/pith/ZQQPV5VYG6JP5A3K5JGQJT7PEW","download_json":"https://pith.science/pith/ZQQPV5VYG6JP5A3K5JGQJT7PEW.json","view_paper":"https://pith.science/paper/ZQQPV5VY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.3567&json=true","fetch_graph":"https://pith.science/api/pith-number/ZQQPV5VYG6JP5A3K5JGQJT7PEW/graph.json","fetch_events":"https://pith.science/api/pith-number/ZQQPV5VYG6JP5A3K5JGQJT7PEW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZQQPV5VYG6JP5A3K5JGQJT7PEW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZQQPV5VYG6JP5A3K5JGQJT7PEW/action/storage_attestation","attest_author":"https://pith.science/pith/ZQQPV5VYG6JP5A3K5JGQJT7PEW/action/author_attestation","sign_citation":"https://pith.science/pith/ZQQPV5VYG6JP5A3K5JGQJT7PEW/action/citation_signature","submit_replication":"https://pith.science/pith/ZQQPV5VYG6JP5A3K5JGQJT7PEW/action/replication_record"}},"created_at":"2026-05-18T02:25:34.415100+00:00","updated_at":"2026-05-18T02:25:34.415100+00:00"}