{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XMBQIAXUQEVLNNKPFQLGF2BGVX","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":"6ad0e737d19e98e62f490698981f9318dc2dcdffacc2d0940b640001b28e83b3","cross_cats_sorted":["math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-04-03T12:54:03Z","title_canon_sha256":"7dd7d50f1c58c9c5d7404529e6d09cd387224d6b87f6ce198e40abdaf1aabcb9"},"schema_version":"1.0","source":{"id":"1304.1468","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.1468","created_at":"2026-05-18T03:17:44Z"},{"alias_kind":"arxiv_version","alias_value":"1304.1468v1","created_at":"2026-05-18T03:17:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.1468","created_at":"2026-05-18T03:17:44Z"},{"alias_kind":"pith_short_12","alias_value":"XMBQIAXUQEVL","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XMBQIAXUQEVLNNKP","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XMBQIAXU","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:329330e96c343767244621363c77d285f5f116bfba6f9d6125829a7eeade65e9","target":"graph","created_at":"2026-05-18T03:17:44Z","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":"Using N. Euler's theorem on the integrability of the general anharmonic oscillator equation \\cite{12}, we present three distinct classes of general solutions of the highly nonlinear second order ordinary differential equation $\\frac{d^{2}x}{dt^{2}}+f_{1}\\left(t\\right) \\frac{dx}{dt}+f_{2}\\left(t\\right) x+f_{3}\\left(t\\right) x^{n}=0$. The first exact solution is obtained from a particular solution of the point transformed equation $d^{2}X/dT^{2}+X^{n}\\left(T\\right) =0$, $n\\notin \\left\\{-3,-1,0,1\\right\\} $, which is equivalent to the anharmonic oscillator equation if the coefficients $f_{i}(t)$, ","authors_text":"Francisco S. N. Lobo, M. K. Mak, Tiberiu Harko","cross_cats":["math.MP","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-04-03T12:54:03Z","title":"Integrability cases for the anharmonic oscillator equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1468","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":"sha256:7e88b87e058ddf6e99da671abe31b698c3cfa4129c71d586f1bce619bf9be826","target":"record","created_at":"2026-05-18T03:17:44Z","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":"6ad0e737d19e98e62f490698981f9318dc2dcdffacc2d0940b640001b28e83b3","cross_cats_sorted":["math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-04-03T12:54:03Z","title_canon_sha256":"7dd7d50f1c58c9c5d7404529e6d09cd387224d6b87f6ce198e40abdaf1aabcb9"},"schema_version":"1.0","source":{"id":"1304.1468","kind":"arxiv","version":1}},"canonical_sha256":"bb030402f4812ab6b54f2c1662e826ade0b78c9f7b61c1e3db9dfc30a187044b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bb030402f4812ab6b54f2c1662e826ade0b78c9f7b61c1e3db9dfc30a187044b","first_computed_at":"2026-05-18T03:17:44.296896Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:44.296896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Vak3qTYkzHPBjtnWA/gxLNLmEdGjaHFeGZ6S6a8Oh1GpRmY4bNfKKEhProA0WGsvtAvc0gGFZKA8LEHwSTa+Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:44.297607Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.1468","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e88b87e058ddf6e99da671abe31b698c3cfa4129c71d586f1bce619bf9be826","sha256:329330e96c343767244621363c77d285f5f116bfba6f9d6125829a7eeade65e9"],"state_sha256":"cb55bcb488b0b6498ceb6c4cab14c6b95616fc27c59b801ecbcb849b6de163db"}