{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:RM2T2MLKJJ7XGQH7HPOUFB52MA","short_pith_number":"pith:RM2T2MLK","canonical_record":{"source":{"id":"1904.00604","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.DS","submitted_at":"2019-04-01T07:23:30Z","cross_cats_sorted":[],"title_canon_sha256":"bacb019e04d89e096930cd5e1c5b21bd2ef2902d90d7dfa4303b95129882fb16","abstract_canon_sha256":"fea0015ec987c443307de62d27d22834bc84a6f119e03556f6c67c33bb5c4738"},"schema_version":"1.0"},"canonical_sha256":"8b353d316a4a7f7340ff3bdd4287ba60023b2f4767006cc2cad5711a1879db2f","source":{"kind":"arxiv","id":"1904.00604","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.00604","created_at":"2026-05-17T23:49:38Z"},{"alias_kind":"arxiv_version","alias_value":"1904.00604v2","created_at":"2026-05-17T23:49:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.00604","created_at":"2026-05-17T23:49:38Z"},{"alias_kind":"pith_short_12","alias_value":"RM2T2MLKJJ7X","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"RM2T2MLKJJ7XGQH7","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"RM2T2MLK","created_at":"2026-05-18T12:33:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:RM2T2MLKJJ7XGQH7HPOUFB52MA","target":"record","payload":{"canonical_record":{"source":{"id":"1904.00604","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.DS","submitted_at":"2019-04-01T07:23:30Z","cross_cats_sorted":[],"title_canon_sha256":"bacb019e04d89e096930cd5e1c5b21bd2ef2902d90d7dfa4303b95129882fb16","abstract_canon_sha256":"fea0015ec987c443307de62d27d22834bc84a6f119e03556f6c67c33bb5c4738"},"schema_version":"1.0"},"canonical_sha256":"8b353d316a4a7f7340ff3bdd4287ba60023b2f4767006cc2cad5711a1879db2f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:38.182831Z","signature_b64":"rgMvQtd/FDGOuTnu62XRA3va7/goh/HityZlJWdf6+q9VFhdIyR8R4rQr8YXhcV5XHahIy2EVExzRKi/woW8DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8b353d316a4a7f7340ff3bdd4287ba60023b2f4767006cc2cad5711a1879db2f","last_reissued_at":"2026-05-17T23:49:38.182075Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:38.182075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.00604","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:49:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xY0+GSCU60bbcUI5ysQjrHFzopTnFZdxAMdl+GF03Q/mqRbnYaDGVmtfV7EQrpgwuU7UtlAFN33j+cMwYZmOCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T07:33:16.468546Z"},"content_sha256":"7b7dfce1946dafa47a94237acd0ecf59434577dbe7095bc202da4c976b521012","schema_version":"1.0","event_id":"sha256:7b7dfce1946dafa47a94237acd0ecf59434577dbe7095bc202da4c976b521012"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:RM2T2MLKJJ7XGQH7HPOUFB52MA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reduction of Kinetic Equations to Li\\'enard-Levinson-Smith Form: Counting Limit Cycles","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Deb Shankar Ray, Gautam Gangopadhyay, Sandip Saha","submitted_at":"2019-04-01T07:23:30Z","abstract_excerpt":"We have presented an unified scheme to express a class of system of equations in two variables into a Li\\'enard-Levinson-Smith (LLS) oscillator form. We have derived the condition for limit cycle with special reference to Rayleigh and Li\\'enard systems for arbitrary polynomial functions of damping and restoring force. Krylov-Boguliubov (K-B) method is implemented to determine the maximum number of limit cycles admissible for a LLS oscillator atleast in the weak damping limit. Scheme is illustrated by a number of model systems with single cycle as well as the multiple cycle cases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.00604","kind":"arxiv","version":2},"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":"2026-05-17T23:49:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W+/nu4Ooz0h9NwIC/PVFGvbQ79NBDECGyrDlkK8E77WVoewdTJ7Rbu9Y2/In4xmKPIvLDFTZ2BfPjVZXTsB/CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T07:33:16.468891Z"},"content_sha256":"0a58be85d21a9961887438aca860648de9d80ce55d27df600e77da31d02a0e20","schema_version":"1.0","event_id":"sha256:0a58be85d21a9961887438aca860648de9d80ce55d27df600e77da31d02a0e20"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RM2T2MLKJJ7XGQH7HPOUFB52MA/bundle.json","state_url":"https://pith.science/pith/RM2T2MLKJJ7XGQH7HPOUFB52MA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RM2T2MLKJJ7XGQH7HPOUFB52MA/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":"2026-06-02T07:33:16Z","links":{"resolver":"https://pith.science/pith/RM2T2MLKJJ7XGQH7HPOUFB52MA","bundle":"https://pith.science/pith/RM2T2MLKJJ7XGQH7HPOUFB52MA/bundle.json","state":"https://pith.science/pith/RM2T2MLKJJ7XGQH7HPOUFB52MA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RM2T2MLKJJ7XGQH7HPOUFB52MA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:RM2T2MLKJJ7XGQH7HPOUFB52MA","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":"fea0015ec987c443307de62d27d22834bc84a6f119e03556f6c67c33bb5c4738","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.DS","submitted_at":"2019-04-01T07:23:30Z","title_canon_sha256":"bacb019e04d89e096930cd5e1c5b21bd2ef2902d90d7dfa4303b95129882fb16"},"schema_version":"1.0","source":{"id":"1904.00604","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.00604","created_at":"2026-05-17T23:49:38Z"},{"alias_kind":"arxiv_version","alias_value":"1904.00604v2","created_at":"2026-05-17T23:49:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.00604","created_at":"2026-05-17T23:49:38Z"},{"alias_kind":"pith_short_12","alias_value":"RM2T2MLKJJ7X","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"RM2T2MLKJJ7XGQH7","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"RM2T2MLK","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:0a58be85d21a9961887438aca860648de9d80ce55d27df600e77da31d02a0e20","target":"graph","created_at":"2026-05-17T23:49:38Z","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":"We have presented an unified scheme to express a class of system of equations in two variables into a Li\\'enard-Levinson-Smith (LLS) oscillator form. We have derived the condition for limit cycle with special reference to Rayleigh and Li\\'enard systems for arbitrary polynomial functions of damping and restoring force. Krylov-Boguliubov (K-B) method is implemented to determine the maximum number of limit cycles admissible for a LLS oscillator atleast in the weak damping limit. Scheme is illustrated by a number of model systems with single cycle as well as the multiple cycle cases.","authors_text":"Deb Shankar Ray, Gautam Gangopadhyay, Sandip Saha","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.DS","submitted_at":"2019-04-01T07:23:30Z","title":"Reduction of Kinetic Equations to Li\\'enard-Levinson-Smith Form: Counting Limit Cycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.00604","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":"sha256:7b7dfce1946dafa47a94237acd0ecf59434577dbe7095bc202da4c976b521012","target":"record","created_at":"2026-05-17T23:49:38Z","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":"fea0015ec987c443307de62d27d22834bc84a6f119e03556f6c67c33bb5c4738","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.DS","submitted_at":"2019-04-01T07:23:30Z","title_canon_sha256":"bacb019e04d89e096930cd5e1c5b21bd2ef2902d90d7dfa4303b95129882fb16"},"schema_version":"1.0","source":{"id":"1904.00604","kind":"arxiv","version":2}},"canonical_sha256":"8b353d316a4a7f7340ff3bdd4287ba60023b2f4767006cc2cad5711a1879db2f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b353d316a4a7f7340ff3bdd4287ba60023b2f4767006cc2cad5711a1879db2f","first_computed_at":"2026-05-17T23:49:38.182075Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:38.182075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rgMvQtd/FDGOuTnu62XRA3va7/goh/HityZlJWdf6+q9VFhdIyR8R4rQr8YXhcV5XHahIy2EVExzRKi/woW8DA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:38.182831Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.00604","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7b7dfce1946dafa47a94237acd0ecf59434577dbe7095bc202da4c976b521012","sha256:0a58be85d21a9961887438aca860648de9d80ce55d27df600e77da31d02a0e20"],"state_sha256":"3b086e963d0a3ed02f834ad93c0a1c5b6918cbad80dce48299822106dd9e1c94"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zxYyrav1ohAqvun4eh9KCRqedtoG2DfAgXvWTo9fYxoh+hkq8P1Shl5GkIvUSwCzZm0ZmArRU1muwnZ5s+eZAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T07:33:16.470877Z","bundle_sha256":"ea350ca1828848c6129a564dc810098bb4bcdbd267691820599c0402f6851259"}}