{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:3XXGESLNI26VTVBUG6PYK5S4SD","short_pith_number":"pith:3XXGESLN","canonical_record":{"source":{"id":"1201.5931","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2012-01-28T07:18:52Z","cross_cats_sorted":["math-ph","math.CA","math.MP"],"title_canon_sha256":"01e31198da3da330b8db2c7793acb30a98e6b1718b48fd2f9cef15a052ef8ae8","abstract_canon_sha256":"e6c07955bb3b421c34a6eb41cb62b07639341899d5689f7175d1bd186c5a0bab"},"schema_version":"1.0"},"canonical_sha256":"ddee62496d46bd59d434379f85765c90c2ed45267945d0a3f34734a3bc9568f5","source":{"kind":"arxiv","id":"1201.5931","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.5931","created_at":"2026-05-18T01:58:38Z"},{"alias_kind":"arxiv_version","alias_value":"1201.5931v1","created_at":"2026-05-18T01:58:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.5931","created_at":"2026-05-18T01:58:38Z"},{"alias_kind":"pith_short_12","alias_value":"3XXGESLNI26V","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"3XXGESLNI26VTVBU","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"3XXGESLN","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:3XXGESLNI26VTVBUG6PYK5S4SD","target":"record","payload":{"canonical_record":{"source":{"id":"1201.5931","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2012-01-28T07:18:52Z","cross_cats_sorted":["math-ph","math.CA","math.MP"],"title_canon_sha256":"01e31198da3da330b8db2c7793acb30a98e6b1718b48fd2f9cef15a052ef8ae8","abstract_canon_sha256":"e6c07955bb3b421c34a6eb41cb62b07639341899d5689f7175d1bd186c5a0bab"},"schema_version":"1.0"},"canonical_sha256":"ddee62496d46bd59d434379f85765c90c2ed45267945d0a3f34734a3bc9568f5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:58:38.762840Z","signature_b64":"kplSjV/RVCvw3ZYolrL00tfurFbGPEcyQ7dX0G0K43YzWGlbOhGglJ8JAAZuTJg5BAdBXfA/kIHXSgdh2HwSBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ddee62496d46bd59d434379f85765c90c2ed45267945d0a3f34734a3bc9568f5","last_reissued_at":"2026-05-18T01:58:38.762166Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:58:38.762166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.5931","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:58:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9tG1l+lRdNYvURghoaSPBBmR9gXxYFGOeGJzMgCmq8lwCeedl8/zgjdFOzfYaVEkOcWeiUSNKsSAzsNOzlmVDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:28:59.346715Z"},"content_sha256":"7712f7ad09bbf9329e832df090c3ecb3f834b2b655106ac47b7cb29447ac22f1","schema_version":"1.0","event_id":"sha256:7712f7ad09bbf9329e832df090c3ecb3f834b2b655106ac47b7cb29447ac22f1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:3XXGESLNI26VTVBUG6PYK5S4SD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exact solutions of coupled Li\\'enard-type nonlinear systems using factorization technique","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CA","math.MP"],"primary_cat":"nlin.SI","authors_text":"M. Lakshmanan, R. Gladwin Pradeep, Tamaghna Hazra, V. K. Chandrasekar","submitted_at":"2012-01-28T07:18:52Z","abstract_excerpt":"General solutions of nonlinear ordinary differential equations (ODEs) are in general difficult to find although powerful integrability techniques exist in the literature for this purpose. It has been shown that in some scalar cases particular solutions may be found with little effort if it is possible to factorize the equation in terms of first order differential operators. In our present study we use this factorization technique to address the problem of finding solutions of a system of general two-coupled Li\\'enard type nonlinear differential equations. We describe a generic algorithm to ide"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5931","kind":"arxiv","version":1},"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":"2026-05-18T01:58:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zmMn3HCClwVwx5ULRNMOjLZrfHZw0asOJr99LTHutdWU8asTogmC5Gvahx5UzmQyVA4Z+09OOXAUPjN89hE2Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:28:59.347459Z"},"content_sha256":"171146a4d57435ceb60dedb2c4965d84f860d7a6d06c30a49963dcaaed18bcd1","schema_version":"1.0","event_id":"sha256:171146a4d57435ceb60dedb2c4965d84f860d7a6d06c30a49963dcaaed18bcd1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3XXGESLNI26VTVBUG6PYK5S4SD/bundle.json","state_url":"https://pith.science/pith/3XXGESLNI26VTVBUG6PYK5S4SD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3XXGESLNI26VTVBUG6PYK5S4SD/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":"2026-05-31T10:28:59Z","links":{"resolver":"https://pith.science/pith/3XXGESLNI26VTVBUG6PYK5S4SD","bundle":"https://pith.science/pith/3XXGESLNI26VTVBUG6PYK5S4SD/bundle.json","state":"https://pith.science/pith/3XXGESLNI26VTVBUG6PYK5S4SD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3XXGESLNI26VTVBUG6PYK5S4SD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:3XXGESLNI26VTVBUG6PYK5S4SD","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":"e6c07955bb3b421c34a6eb41cb62b07639341899d5689f7175d1bd186c5a0bab","cross_cats_sorted":["math-ph","math.CA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2012-01-28T07:18:52Z","title_canon_sha256":"01e31198da3da330b8db2c7793acb30a98e6b1718b48fd2f9cef15a052ef8ae8"},"schema_version":"1.0","source":{"id":"1201.5931","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.5931","created_at":"2026-05-18T01:58:38Z"},{"alias_kind":"arxiv_version","alias_value":"1201.5931v1","created_at":"2026-05-18T01:58:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.5931","created_at":"2026-05-18T01:58:38Z"},{"alias_kind":"pith_short_12","alias_value":"3XXGESLNI26V","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"3XXGESLNI26VTVBU","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"3XXGESLN","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:171146a4d57435ceb60dedb2c4965d84f860d7a6d06c30a49963dcaaed18bcd1","target":"graph","created_at":"2026-05-18T01:58:38Z","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":"General solutions of nonlinear ordinary differential equations (ODEs) are in general difficult to find although powerful integrability techniques exist in the literature for this purpose. It has been shown that in some scalar cases particular solutions may be found with little effort if it is possible to factorize the equation in terms of first order differential operators. In our present study we use this factorization technique to address the problem of finding solutions of a system of general two-coupled Li\\'enard type nonlinear differential equations. We describe a generic algorithm to ide","authors_text":"M. Lakshmanan, R. Gladwin Pradeep, Tamaghna Hazra, V. K. Chandrasekar","cross_cats":["math-ph","math.CA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2012-01-28T07:18:52Z","title":"Exact solutions of coupled Li\\'enard-type nonlinear systems using factorization technique"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5931","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":"sha256:7712f7ad09bbf9329e832df090c3ecb3f834b2b655106ac47b7cb29447ac22f1","target":"record","created_at":"2026-05-18T01:58:38Z","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":"e6c07955bb3b421c34a6eb41cb62b07639341899d5689f7175d1bd186c5a0bab","cross_cats_sorted":["math-ph","math.CA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2012-01-28T07:18:52Z","title_canon_sha256":"01e31198da3da330b8db2c7793acb30a98e6b1718b48fd2f9cef15a052ef8ae8"},"schema_version":"1.0","source":{"id":"1201.5931","kind":"arxiv","version":1}},"canonical_sha256":"ddee62496d46bd59d434379f85765c90c2ed45267945d0a3f34734a3bc9568f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ddee62496d46bd59d434379f85765c90c2ed45267945d0a3f34734a3bc9568f5","first_computed_at":"2026-05-18T01:58:38.762166Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:58:38.762166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kplSjV/RVCvw3ZYolrL00tfurFbGPEcyQ7dX0G0K43YzWGlbOhGglJ8JAAZuTJg5BAdBXfA/kIHXSgdh2HwSBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:58:38.762840Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.5931","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7712f7ad09bbf9329e832df090c3ecb3f834b2b655106ac47b7cb29447ac22f1","sha256:171146a4d57435ceb60dedb2c4965d84f860d7a6d06c30a49963dcaaed18bcd1"],"state_sha256":"4ec164816bd4c1aedbf885b039d2fda02cf8bc28a082dd9a45bd6b5ac8d8575b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jQojlA3fUmwdawO2OD7wvhEhivFP+uLLIpE3A8ADL+MZPRJM+bthbYvJutaOZeKG3Mz72hWcmpD6UaEmsBg4CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T10:28:59.351299Z","bundle_sha256":"533d6b74849862e9039af0a8876816c04d334fac72dff91fe860228943e27c0a"}}