{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:UOFG3ED3BCHTDS7NFNTNNSZNRM","short_pith_number":"pith:UOFG3ED3","canonical_record":{"source":{"id":"1001.4631","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-01-26T09:59:38Z","cross_cats_sorted":[],"title_canon_sha256":"708629baf4b53134b3dd65732ab79b118fd9df87b351eb5ccd2dcfec2422bdf8","abstract_canon_sha256":"c5679e6230b5f5dc3342d17d659fbbed84b92ad83097fdc5ee7500a8c0b8cd7d"},"schema_version":"1.0"},"canonical_sha256":"a38a6d907b088f31cbed2b66d6cb2d8b339d84cc20c1eb1cf091917f7276d31d","source":{"kind":"arxiv","id":"1001.4631","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.4631","created_at":"2026-05-18T04:17:04Z"},{"alias_kind":"arxiv_version","alias_value":"1001.4631v3","created_at":"2026-05-18T04:17:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.4631","created_at":"2026-05-18T04:17:04Z"},{"alias_kind":"pith_short_12","alias_value":"UOFG3ED3BCHT","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"UOFG3ED3BCHTDS7N","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"UOFG3ED3","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:UOFG3ED3BCHTDS7NFNTNNSZNRM","target":"record","payload":{"canonical_record":{"source":{"id":"1001.4631","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-01-26T09:59:38Z","cross_cats_sorted":[],"title_canon_sha256":"708629baf4b53134b3dd65732ab79b118fd9df87b351eb5ccd2dcfec2422bdf8","abstract_canon_sha256":"c5679e6230b5f5dc3342d17d659fbbed84b92ad83097fdc5ee7500a8c0b8cd7d"},"schema_version":"1.0"},"canonical_sha256":"a38a6d907b088f31cbed2b66d6cb2d8b339d84cc20c1eb1cf091917f7276d31d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:17:04.619494Z","signature_b64":"PKRjPkJTxOmeiUO7SktfBQ3Z7SVKqMv+vo+uSEyCoHlk3aFuKaU6y4VA94FvYmQW7DrdWV7sJaxIzTQ5WuWbCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a38a6d907b088f31cbed2b66d6cb2d8b339d84cc20c1eb1cf091917f7276d31d","last_reissued_at":"2026-05-18T04:17:04.618920Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:17:04.618920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1001.4631","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:17:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DCWOPv5N/gzOWxegTooqYEa8Cqf0d7cfMzG3zkG1XurLPa3HmS/bTDsVZHajR6Hq0mHcvUST//DuaI9dvwyCDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T23:02:17.999175Z"},"content_sha256":"81e5b806d60a80b464a58ab4182f4091ff9c83db841143fe1c949c137bf2f671","schema_version":"1.0","event_id":"sha256:81e5b806d60a80b464a58ab4182f4091ff9c83db841143fe1c949c137bf2f671"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:UOFG3ED3BCHTDS7NFNTNNSZNRM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Linearizability Criteria for Systems of Two Second-Order Differential Equations by Complex Methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Asghar Qadir, F. M. Mahomed, S. Ali","submitted_at":"2010-01-26T09:59:38Z","abstract_excerpt":"Lie's linearizability criteria for scalar second-order ordinary differential equations had been extended to systems of second-order ordinary differential equations by using geometric methods. These methods not only yield the linearizing transformations but also the solutions of the nonlinear equations. Here complex methods for a scalar ordinary differential equation are used for linearizing systems of two second-order ordinary and partial differential equations, which can use the power of the geometric method for writing the solutions. Illustrative examples of mechanical systems including the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.4631","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:17:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pwnFALJlrW0R/joZK7uUeDn0ehQZj/GPpZyAdONE2CtzNvvW+1ZUEtqTXCw6Z16kDaA5sBL42m+HrApQzZqGBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T23:02:17.999554Z"},"content_sha256":"97b4fcbbc1cb94c4793e113e830512ab781e785aeb589927b5e4a51dfe191f37","schema_version":"1.0","event_id":"sha256:97b4fcbbc1cb94c4793e113e830512ab781e785aeb589927b5e4a51dfe191f37"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UOFG3ED3BCHTDS7NFNTNNSZNRM/bundle.json","state_url":"https://pith.science/pith/UOFG3ED3BCHTDS7NFNTNNSZNRM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UOFG3ED3BCHTDS7NFNTNNSZNRM/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-21T23:02:18Z","links":{"resolver":"https://pith.science/pith/UOFG3ED3BCHTDS7NFNTNNSZNRM","bundle":"https://pith.science/pith/UOFG3ED3BCHTDS7NFNTNNSZNRM/bundle.json","state":"https://pith.science/pith/UOFG3ED3BCHTDS7NFNTNNSZNRM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UOFG3ED3BCHTDS7NFNTNNSZNRM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:UOFG3ED3BCHTDS7NFNTNNSZNRM","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":"c5679e6230b5f5dc3342d17d659fbbed84b92ad83097fdc5ee7500a8c0b8cd7d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-01-26T09:59:38Z","title_canon_sha256":"708629baf4b53134b3dd65732ab79b118fd9df87b351eb5ccd2dcfec2422bdf8"},"schema_version":"1.0","source":{"id":"1001.4631","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.4631","created_at":"2026-05-18T04:17:04Z"},{"alias_kind":"arxiv_version","alias_value":"1001.4631v3","created_at":"2026-05-18T04:17:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.4631","created_at":"2026-05-18T04:17:04Z"},{"alias_kind":"pith_short_12","alias_value":"UOFG3ED3BCHT","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"UOFG3ED3BCHTDS7N","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"UOFG3ED3","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:97b4fcbbc1cb94c4793e113e830512ab781e785aeb589927b5e4a51dfe191f37","target":"graph","created_at":"2026-05-18T04:17:04Z","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":"Lie's linearizability criteria for scalar second-order ordinary differential equations had been extended to systems of second-order ordinary differential equations by using geometric methods. These methods not only yield the linearizing transformations but also the solutions of the nonlinear equations. Here complex methods for a scalar ordinary differential equation are used for linearizing systems of two second-order ordinary and partial differential equations, which can use the power of the geometric method for writing the solutions. Illustrative examples of mechanical systems including the ","authors_text":"Asghar Qadir, F. M. Mahomed, S. Ali","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-01-26T09:59:38Z","title":"Linearizability Criteria for Systems of Two Second-Order Differential Equations by Complex Methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.4631","kind":"arxiv","version":3},"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":"sha256:81e5b806d60a80b464a58ab4182f4091ff9c83db841143fe1c949c137bf2f671","target":"record","created_at":"2026-05-18T04:17:04Z","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":"c5679e6230b5f5dc3342d17d659fbbed84b92ad83097fdc5ee7500a8c0b8cd7d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-01-26T09:59:38Z","title_canon_sha256":"708629baf4b53134b3dd65732ab79b118fd9df87b351eb5ccd2dcfec2422bdf8"},"schema_version":"1.0","source":{"id":"1001.4631","kind":"arxiv","version":3}},"canonical_sha256":"a38a6d907b088f31cbed2b66d6cb2d8b339d84cc20c1eb1cf091917f7276d31d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a38a6d907b088f31cbed2b66d6cb2d8b339d84cc20c1eb1cf091917f7276d31d","first_computed_at":"2026-05-18T04:17:04.618920Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:17:04.618920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PKRjPkJTxOmeiUO7SktfBQ3Z7SVKqMv+vo+uSEyCoHlk3aFuKaU6y4VA94FvYmQW7DrdWV7sJaxIzTQ5WuWbCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:17:04.619494Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.4631","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81e5b806d60a80b464a58ab4182f4091ff9c83db841143fe1c949c137bf2f671","sha256:97b4fcbbc1cb94c4793e113e830512ab781e785aeb589927b5e4a51dfe191f37"],"state_sha256":"9462bdc827a51ae3ebfcb2f8b5f350ee815866d3d51fded1bb478cf736aaf04e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OTMe0+J6zJS2lyn4OgXV9s08GWX8j1etmO5lR888kdbCOwnG6/TSFrAXWfLOPybVxodZHvhxj/XLoNA75/LyAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T23:02:18.002044Z","bundle_sha256":"23577cd51cc785494d53393167b3b522802934947163588dddb563fd93962a76"}}