{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:Y7ORQFBEJ436YVMCCAZ7WJOUMA","short_pith_number":"pith:Y7ORQFBE","canonical_record":{"source":{"id":"1302.0350","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2013-02-02T06:47:57Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"cdf1c15c42444b2f5087acb9a0176a487f8f9ca3bebf3b2cf9934dff15e7a0a7","abstract_canon_sha256":"bee63c6c56ff105924d97dc9849ff5ec47034e7bd9b60e72e75c0721acdfd1d4"},"schema_version":"1.0"},"canonical_sha256":"c7dd1814244f37ec55821033fb25d4602d9704fed4a04f8898261d7b3df85270","source":{"kind":"arxiv","id":"1302.0350","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.0350","created_at":"2026-05-18T01:51:51Z"},{"alias_kind":"arxiv_version","alias_value":"1302.0350v1","created_at":"2026-05-18T01:51:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0350","created_at":"2026-05-18T01:51:51Z"},{"alias_kind":"pith_short_12","alias_value":"Y7ORQFBEJ436","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"Y7ORQFBEJ436YVMC","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"Y7ORQFBE","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:Y7ORQFBEJ436YVMCCAZ7WJOUMA","target":"record","payload":{"canonical_record":{"source":{"id":"1302.0350","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2013-02-02T06:47:57Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"cdf1c15c42444b2f5087acb9a0176a487f8f9ca3bebf3b2cf9934dff15e7a0a7","abstract_canon_sha256":"bee63c6c56ff105924d97dc9849ff5ec47034e7bd9b60e72e75c0721acdfd1d4"},"schema_version":"1.0"},"canonical_sha256":"c7dd1814244f37ec55821033fb25d4602d9704fed4a04f8898261d7b3df85270","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:51:51.175977Z","signature_b64":"GwWCrRMnuJ5gx3F6SEJr0tWmcIOby1BbrM5E0EdajiABGZ/4uMz5aeSAkzSnFXA6799XIDSSqMkUgsK86CAPDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c7dd1814244f37ec55821033fb25d4602d9704fed4a04f8898261d7b3df85270","last_reissued_at":"2026-05-18T01:51:51.175451Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:51:51.175451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.0350","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":"2026-05-18T01:51:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XA2vE1uAlyDzUmi5Fb7XTSaymUJlKFtE5yzHjG4J+HiUsa0CvZqm/ZpEmf6a5OIXZUrmoFTuIdt/WndGwSoSCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T20:05:02.359377Z"},"content_sha256":"4a53a6981fb6119ce667fa127532189ca6beb7b0e5090e2c93767442e2e3a95f","schema_version":"1.0","event_id":"sha256:4a53a6981fb6119ce667fa127532189ca6beb7b0e5090e2c93767442e2e3a95f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:Y7ORQFBEJ436YVMCCAZ7WJOUMA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classification of Lie point symmetries for quadratic Li$\\acute{\\textbf{e}}$nard type equation $\\ddot{x}+f(x)\\dot{x}^2+g(x)=0$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.SI","authors_text":"Ajey K. Tiwari, M. Lakshmanan, M. Senthilvelan, S. N. Pandey","submitted_at":"2013-02-02T06:47:57Z","abstract_excerpt":"In this paper we carry out a complete classification of the Lie point symmetry groups associated with the quadratic Li$\\acute{e}$nard type equation, $\\ddot {x} + f(x){\\dot {x}}^{2} + g(x)= 0$, where $f(x)$ and $g(x)$ are arbitrary functions of $x$. The symmetry analysis gets divided into two cases, $(i)$ the maximal (eight parameter) symmetry group and $(ii)$ non-maximal (three, two and one parameter) symmetry groups. We identify the most general form of the quadratic Li$\\acute{e}$nard equation in each of these cases. In the case of eight parameter symmetry group, the identified general equati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0350","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":"2026-05-18T01:51:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JK31KYeYRZSR4nQsWZq48w6cDJo4qBykH19pD+o5Gki+9d+QotrDfNBO9eoLNA3meUd8Zm/FIQENYGmD84TmCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T20:05:02.359734Z"},"content_sha256":"97c3975a5d8ac32071bc107d7279f911480b2c2bf68027e88007ff2816eec177","schema_version":"1.0","event_id":"sha256:97c3975a5d8ac32071bc107d7279f911480b2c2bf68027e88007ff2816eec177"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y7ORQFBEJ436YVMCCAZ7WJOUMA/bundle.json","state_url":"https://pith.science/pith/Y7ORQFBEJ436YVMCCAZ7WJOUMA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y7ORQFBEJ436YVMCCAZ7WJOUMA/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":"2026-06-23T20:05:02Z","links":{"resolver":"https://pith.science/pith/Y7ORQFBEJ436YVMCCAZ7WJOUMA","bundle":"https://pith.science/pith/Y7ORQFBEJ436YVMCCAZ7WJOUMA/bundle.json","state":"https://pith.science/pith/Y7ORQFBEJ436YVMCCAZ7WJOUMA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y7ORQFBEJ436YVMCCAZ7WJOUMA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Y7ORQFBEJ436YVMCCAZ7WJOUMA","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":"bee63c6c56ff105924d97dc9849ff5ec47034e7bd9b60e72e75c0721acdfd1d4","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2013-02-02T06:47:57Z","title_canon_sha256":"cdf1c15c42444b2f5087acb9a0176a487f8f9ca3bebf3b2cf9934dff15e7a0a7"},"schema_version":"1.0","source":{"id":"1302.0350","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.0350","created_at":"2026-05-18T01:51:51Z"},{"alias_kind":"arxiv_version","alias_value":"1302.0350v1","created_at":"2026-05-18T01:51:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0350","created_at":"2026-05-18T01:51:51Z"},{"alias_kind":"pith_short_12","alias_value":"Y7ORQFBEJ436","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"Y7ORQFBEJ436YVMC","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"Y7ORQFBE","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:97c3975a5d8ac32071bc107d7279f911480b2c2bf68027e88007ff2816eec177","target":"graph","created_at":"2026-05-18T01:51:51Z","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 carry out a complete classification of the Lie point symmetry groups associated with the quadratic Li$\\acute{e}$nard type equation, $\\ddot {x} + f(x){\\dot {x}}^{2} + g(x)= 0$, where $f(x)$ and $g(x)$ are arbitrary functions of $x$. The symmetry analysis gets divided into two cases, $(i)$ the maximal (eight parameter) symmetry group and $(ii)$ non-maximal (three, two and one parameter) symmetry groups. We identify the most general form of the quadratic Li$\\acute{e}$nard equation in each of these cases. In the case of eight parameter symmetry group, the identified general equati","authors_text":"Ajey K. Tiwari, M. Lakshmanan, M. Senthilvelan, S. N. Pandey","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2013-02-02T06:47:57Z","title":"Classification of Lie point symmetries for quadratic Li$\\acute{\\textbf{e}}$nard type equation $\\ddot{x}+f(x)\\dot{x}^2+g(x)=0$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0350","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":"sha256:4a53a6981fb6119ce667fa127532189ca6beb7b0e5090e2c93767442e2e3a95f","target":"record","created_at":"2026-05-18T01:51:51Z","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":"bee63c6c56ff105924d97dc9849ff5ec47034e7bd9b60e72e75c0721acdfd1d4","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2013-02-02T06:47:57Z","title_canon_sha256":"cdf1c15c42444b2f5087acb9a0176a487f8f9ca3bebf3b2cf9934dff15e7a0a7"},"schema_version":"1.0","source":{"id":"1302.0350","kind":"arxiv","version":1}},"canonical_sha256":"c7dd1814244f37ec55821033fb25d4602d9704fed4a04f8898261d7b3df85270","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c7dd1814244f37ec55821033fb25d4602d9704fed4a04f8898261d7b3df85270","first_computed_at":"2026-05-18T01:51:51.175451Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:51:51.175451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GwWCrRMnuJ5gx3F6SEJr0tWmcIOby1BbrM5E0EdajiABGZ/4uMz5aeSAkzSnFXA6799XIDSSqMkUgsK86CAPDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:51:51.175977Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.0350","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a53a6981fb6119ce667fa127532189ca6beb7b0e5090e2c93767442e2e3a95f","sha256:97c3975a5d8ac32071bc107d7279f911480b2c2bf68027e88007ff2816eec177"],"state_sha256":"cb6be092067333411f90d2507b996d7eae04eaca7494ab3b42024b3d38b3585c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YbQ8GC8Uep0vMwbzWagiWdYLbbNIKrsjDD2F77h+o4H4RuJaTzFHxcpvAyzMsb9lWF/O7wn5bkTwQh64l6s3Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T20:05:02.361737Z","bundle_sha256":"9f02e9690915d15f9edd10fe0994e2594b2d481b5264481c47ca2944ff413e6d"}}