{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:C3YRNNDPIRZOCXCHVW7SI6XINC","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":"84312ad1e2e14c0f699df628f296c9c4229d9a5e46f0ceb89c1ac27004378671","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2008-08-07T07:04:54Z","title_canon_sha256":"d2bcd5f49646a3bec65edacb8db1958846ab6e0ed15b09b1924a8e5af5bf5531"},"schema_version":"1.0","source":{"id":"0808.0969","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0808.0969","created_at":"2026-05-18T02:15:43Z"},{"alias_kind":"arxiv_version","alias_value":"0808.0969v2","created_at":"2026-05-18T02:15:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.0969","created_at":"2026-05-18T02:15:43Z"},{"alias_kind":"pith_short_12","alias_value":"C3YRNNDPIRZO","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"C3YRNNDPIRZOCXCH","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"C3YRNNDP","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:41271bb4614493d97dbb8a52010c4218546810573462ec07a6343e1ac8110091","target":"graph","created_at":"2026-05-18T02:15:43Z","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":"Linearization of coupled second order nonlinear ordinary differential equations (SNODEs) is one of the open and challenging problems in the theory of differential equations. In this paper we describe a simple and straightforward method to derive linearizing transformations for a class of two coupled SNODEs. Our procedure gives several new types of linearizing transformations of both invertible and non-invertible kinds. In both the cases we provide algorithms to derive the general solution of the given SNODE. We illustrate the theory with potentially important examples.","authors_text":"M. Lakshmanan, M. Senthilvelan, V. K. Chandrasekar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2008-08-07T07:04:54Z","title":"On the complete integrability and linearization of nonlinear ordinary differential equations - Part V: Linearization of coupled second order equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.0969","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":"sha256:6d9851b105a364b5dc2598e1ae09dc0af3acfd31d3018415a9ba82cd904982f8","target":"record","created_at":"2026-05-18T02:15:43Z","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":"84312ad1e2e14c0f699df628f296c9c4229d9a5e46f0ceb89c1ac27004378671","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2008-08-07T07:04:54Z","title_canon_sha256":"d2bcd5f49646a3bec65edacb8db1958846ab6e0ed15b09b1924a8e5af5bf5531"},"schema_version":"1.0","source":{"id":"0808.0969","kind":"arxiv","version":2}},"canonical_sha256":"16f116b46f4472e15c47adbf247ae8689e3c009908f0f2fb4f5177a5faa9c5eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16f116b46f4472e15c47adbf247ae8689e3c009908f0f2fb4f5177a5faa9c5eb","first_computed_at":"2026-05-18T02:15:43.846997Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:15:43.846997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s2b9nEqJHCn4ox2QGuT6mnur2UHD00FWoC8SWJZiZFkJLz1ByLwrRoNBBXtLVFiJir8EVZ/xq0wyNGJpnG1xAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:15:43.847797Z","signed_message":"canonical_sha256_bytes"},"source_id":"0808.0969","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d9851b105a364b5dc2598e1ae09dc0af3acfd31d3018415a9ba82cd904982f8","sha256:41271bb4614493d97dbb8a52010c4218546810573462ec07a6343e1ac8110091"],"state_sha256":"8accf3609fa07d32d0f51b44a5a09161ac210a4d1cc318d37c99eb7762489585"}