{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HMBPAZV7VSLZH223Z42B6VFYPJ","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":"8a186e7fc13fc280c7c8af644a5d95ba79d61d78aa5d8ee682db8c05810883bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2016-03-24T09:32:49Z","title_canon_sha256":"4f7cd36ea1ecc410578a9f21a3e27916094941732350fbe9e3304445245d3862"},"schema_version":"1.0","source":{"id":"1603.07496","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.07496","created_at":"2026-05-18T01:18:20Z"},{"alias_kind":"arxiv_version","alias_value":"1603.07496v1","created_at":"2026-05-18T01:18:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07496","created_at":"2026-05-18T01:18:20Z"},{"alias_kind":"pith_short_12","alias_value":"HMBPAZV7VSLZ","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HMBPAZV7VSLZH223","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HMBPAZV7","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:33e12aecad4d40b5608f1365573e68f9db13eb4ba272d1c4ef29436682604bf7","target":"graph","created_at":"2026-05-18T01:18:20Z","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":"In this paper, we discuss the inverse problem for a mixed Li\\'enard type nonlinear oscillator equation $\\ddot{x}+f(x)\\dot{x}^2+g(x)\\dot{x}+h(x)=0$, where $f(x),\\,g(x)$ and $h(x)$ are arbitrary functions of $x$. Very recently, we have reported the Lie point symmetries of this equation. By exploiting the interconnection between Jacobi last multiplier, Lie point symmetries and Prelle-Singer procedure we construct a time independent integral for the case exhibiting maximal symmetry from which we identify the associated conservative non-standard Lagrangian and Hamiltonian functions. The classical d","authors_text":"Ajey K. Tiwari, M. Lakshmanan, M. Senthilvelan, S. N. Pandey, V. K. Chandrasekar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2016-03-24T09:32:49Z","title":"The inverse problem of a mixed Li\\'enard type nonlinear oscillator equation from symmetry perspective"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07496","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":"sha256:634ca88a98109de7c7c6ca23f77c029e449b471dcd2c3f82edbdb1ef4d46ccc0","target":"record","created_at":"2026-05-18T01:18:20Z","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":"8a186e7fc13fc280c7c8af644a5d95ba79d61d78aa5d8ee682db8c05810883bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2016-03-24T09:32:49Z","title_canon_sha256":"4f7cd36ea1ecc410578a9f21a3e27916094941732350fbe9e3304445245d3862"},"schema_version":"1.0","source":{"id":"1603.07496","kind":"arxiv","version":1}},"canonical_sha256":"3b02f066bfac9793eb5bcf341f54b87a70fe7a38200769ff3058b25fd912dba9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b02f066bfac9793eb5bcf341f54b87a70fe7a38200769ff3058b25fd912dba9","first_computed_at":"2026-05-18T01:18:20.735714Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:20.735714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MOFg0twfIHgDtJ1lh1DWa4nCbb/pVpkxaqp2/304VNXmnQhtMq1L/2jNSFsQ8Wg4x9ZI2pqdFs0jL9Kx7ap9AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:20.736451Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.07496","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:634ca88a98109de7c7c6ca23f77c029e449b471dcd2c3f82edbdb1ef4d46ccc0","sha256:33e12aecad4d40b5608f1365573e68f9db13eb4ba272d1c4ef29436682604bf7"],"state_sha256":"e29b53dcc57419d24064b6fb4f49909ec8fd192b6e1b5d0c78edca400cbec57e"}