{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:PCLSBN66VHICFQSM4ZQCUZK7FR","short_pith_number":"pith:PCLSBN66","canonical_record":{"source":{"id":"nlin/0210024","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"nlin.PS","submitted_at":"2002-10-14T07:55:41Z","cross_cats_sorted":[],"title_canon_sha256":"2a1d568b32905152cc48d503432d1514bafab2c159ec844054a7a6dbf3555137","abstract_canon_sha256":"5bfc35d1da4efeaecb3862c91b284794dd8aead1a4ac42386f4003448ccbebc1"},"schema_version":"1.0"},"canonical_sha256":"789720b7dea9d022c24ce6602a655f2c7d0eec71dacd0f48910abf18762e17a2","source":{"kind":"arxiv","id":"nlin/0210024","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0210024","created_at":"2026-05-18T01:38:19Z"},{"alias_kind":"arxiv_version","alias_value":"nlin/0210024v1","created_at":"2026-05-18T01:38:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0210024","created_at":"2026-05-18T01:38:19Z"},{"alias_kind":"pith_short_12","alias_value":"PCLSBN66VHIC","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"PCLSBN66VHICFQSM","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"PCLSBN66","created_at":"2026-05-18T12:25:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:PCLSBN66VHICFQSM4ZQCUZK7FR","target":"record","payload":{"canonical_record":{"source":{"id":"nlin/0210024","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"nlin.PS","submitted_at":"2002-10-14T07:55:41Z","cross_cats_sorted":[],"title_canon_sha256":"2a1d568b32905152cc48d503432d1514bafab2c159ec844054a7a6dbf3555137","abstract_canon_sha256":"5bfc35d1da4efeaecb3862c91b284794dd8aead1a4ac42386f4003448ccbebc1"},"schema_version":"1.0"},"canonical_sha256":"789720b7dea9d022c24ce6602a655f2c7d0eec71dacd0f48910abf18762e17a2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:19.664607Z","signature_b64":"fF2SiKD8qe40T68omI7/rft2imIdP082ILpJUlnPoARkab4s/dutDlmtTWOzpgndPOOrqDTVUxhq6aKFk9QoCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"789720b7dea9d022c24ce6602a655f2c7d0eec71dacd0f48910abf18762e17a2","last_reissued_at":"2026-05-18T01:38:19.663961Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:19.663961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"nlin/0210024","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":"2026-05-18T01:38:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EwvK+F4X2/SusWthiUaOwVhqKCyPbJEaBh6itrb+Y3qgYI2q5oVGlMZH+tuXvskH+5AxXSX4C/wnvlyf1wwXCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T12:23:38.235045Z"},"content_sha256":"6c7b3e469ec2911ec873f569bd532c446ed01cff6ec39c326e10a086e2161096","schema_version":"1.0","event_id":"sha256:6c7b3e469ec2911ec873f569bd532c446ed01cff6ec39c326e10a086e2161096"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:PCLSBN66VHICFQSM4ZQCUZK7FR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Number and Amplitude of Limit Cycles emerging from {\\it Topologically Equivalent} Perturbed Centers","license":"","headline":"","cross_cats":[],"primary_cat":"nlin.PS","authors_text":"Jose-Luis Lopez, Ricardo Lopez-Ruiz","submitted_at":"2002-10-14T07:55:41Z","abstract_excerpt":"We consider three examples of weekly perturbed centers which do not have {\\it geometrical equivalence}: a linear center, a degenerate center and a non-hamiltonian center. In each case the number and amplitude of the limit cycles emerging from the period annulus are calculated following the same strategy: we reduce of all of them to locally equivalent perturbed integrable systems of the form: $dH(x,y)+\\epsilon(f(x,y)dy-g(x,y)dx)=0$, with $H(x,y)={1/2}(x^2+y^2)$. This reduction allows us to find the Melnikov function, $M(h)=\\int_{H=h}fdy-gdx$, associated to each particular problem. We obtain the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0210024","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":"2026-05-18T01:38:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tpQ3kiIF9n1wKHZshdCn0ixn6DIhqDwi1+sLfBy7pFUatxvFRAxHqgYdZ/sGuDOOdULn6gxWEYe7r9sP5r7pBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T12:23:38.235405Z"},"content_sha256":"81ccd2597ecafbd5fe90363b75957f90a77e96f9db5ccff24790a7b076cd59b0","schema_version":"1.0","event_id":"sha256:81ccd2597ecafbd5fe90363b75957f90a77e96f9db5ccff24790a7b076cd59b0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PCLSBN66VHICFQSM4ZQCUZK7FR/bundle.json","state_url":"https://pith.science/pith/PCLSBN66VHICFQSM4ZQCUZK7FR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PCLSBN66VHICFQSM4ZQCUZK7FR/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":"2026-06-23T12:23:38Z","links":{"resolver":"https://pith.science/pith/PCLSBN66VHICFQSM4ZQCUZK7FR","bundle":"https://pith.science/pith/PCLSBN66VHICFQSM4ZQCUZK7FR/bundle.json","state":"https://pith.science/pith/PCLSBN66VHICFQSM4ZQCUZK7FR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PCLSBN66VHICFQSM4ZQCUZK7FR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:PCLSBN66VHICFQSM4ZQCUZK7FR","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":"5bfc35d1da4efeaecb3862c91b284794dd8aead1a4ac42386f4003448ccbebc1","cross_cats_sorted":[],"license":"","primary_cat":"nlin.PS","submitted_at":"2002-10-14T07:55:41Z","title_canon_sha256":"2a1d568b32905152cc48d503432d1514bafab2c159ec844054a7a6dbf3555137"},"schema_version":"1.0","source":{"id":"nlin/0210024","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0210024","created_at":"2026-05-18T01:38:19Z"},{"alias_kind":"arxiv_version","alias_value":"nlin/0210024v1","created_at":"2026-05-18T01:38:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0210024","created_at":"2026-05-18T01:38:19Z"},{"alias_kind":"pith_short_12","alias_value":"PCLSBN66VHIC","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"PCLSBN66VHICFQSM","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"PCLSBN66","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:81ccd2597ecafbd5fe90363b75957f90a77e96f9db5ccff24790a7b076cd59b0","target":"graph","created_at":"2026-05-18T01:38:19Z","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 consider three examples of weekly perturbed centers which do not have {\\it geometrical equivalence}: a linear center, a degenerate center and a non-hamiltonian center. In each case the number and amplitude of the limit cycles emerging from the period annulus are calculated following the same strategy: we reduce of all of them to locally equivalent perturbed integrable systems of the form: $dH(x,y)+\\epsilon(f(x,y)dy-g(x,y)dx)=0$, with $H(x,y)={1/2}(x^2+y^2)$. This reduction allows us to find the Melnikov function, $M(h)=\\int_{H=h}fdy-gdx$, associated to each particular problem. We obtain the","authors_text":"Jose-Luis Lopez, Ricardo Lopez-Ruiz","cross_cats":[],"headline":"","license":"","primary_cat":"nlin.PS","submitted_at":"2002-10-14T07:55:41Z","title":"Number and Amplitude of Limit Cycles emerging from {\\it Topologically Equivalent} Perturbed Centers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0210024","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":"sha256:6c7b3e469ec2911ec873f569bd532c446ed01cff6ec39c326e10a086e2161096","target":"record","created_at":"2026-05-18T01:38:19Z","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":"5bfc35d1da4efeaecb3862c91b284794dd8aead1a4ac42386f4003448ccbebc1","cross_cats_sorted":[],"license":"","primary_cat":"nlin.PS","submitted_at":"2002-10-14T07:55:41Z","title_canon_sha256":"2a1d568b32905152cc48d503432d1514bafab2c159ec844054a7a6dbf3555137"},"schema_version":"1.0","source":{"id":"nlin/0210024","kind":"arxiv","version":1}},"canonical_sha256":"789720b7dea9d022c24ce6602a655f2c7d0eec71dacd0f48910abf18762e17a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"789720b7dea9d022c24ce6602a655f2c7d0eec71dacd0f48910abf18762e17a2","first_computed_at":"2026-05-18T01:38:19.663961Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:19.663961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fF2SiKD8qe40T68omI7/rft2imIdP082ILpJUlnPoARkab4s/dutDlmtTWOzpgndPOOrqDTVUxhq6aKFk9QoCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:19.664607Z","signed_message":"canonical_sha256_bytes"},"source_id":"nlin/0210024","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c7b3e469ec2911ec873f569bd532c446ed01cff6ec39c326e10a086e2161096","sha256:81ccd2597ecafbd5fe90363b75957f90a77e96f9db5ccff24790a7b076cd59b0"],"state_sha256":"175f956b2050d5fb51b6b35d8f5a0ceec599d80f6b3df7e5144c0d891de03695"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ue+F67q6VMKfunvae4ggnslsLaHS5k6r4JH+4nbQQuSHPUlBrUozu3TzYUZ+K/qzhxiORi7/teOYFzDrEDDfBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T12:23:38.237686Z","bundle_sha256":"86f835a1f2d016f8574d745741291ba796e3d422a2b538ac28d5c43c479e857c"}}