{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:YSLPVQPOKTBFS7CPZ5OINNJJ65","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":"230ae321b524d7ed133ef73f32feb60c0ec0d2a80d8ca10a96b53782af20a248","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-12-09T15:56:48Z","title_canon_sha256":"7f08de70b1d53e5171f57de13420f51ac21d2f86c7042ad85ebf9bec1b5ea47e"},"schema_version":"1.0","source":{"id":"1112.2129","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.2129","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"arxiv_version","alias_value":"1112.2129v2","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.2129","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"pith_short_12","alias_value":"YSLPVQPOKTBF","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YSLPVQPOKTBFS7CP","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YSLPVQPO","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:6bbca52b0c98c50d31a17cfc1d211e9620df58015242a4ee510809fd1170fdee","target":"graph","created_at":"2026-05-18T02:51:42Z","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":"Using the damped pendulum system we introduce the averaging method to study the periodic solutions of a dynamical system with small perturbation. We provide sufficient conditions for the existence of periodic solutions with small amplitude of the non--linear perturbed damped pendulum. The averaging theory provides a useful means to study dynamical systems, accessible to Master and PhD students.","authors_text":"Douglas Duarte Novaes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-12-09T15:56:48Z","title":"Perturbed damped pendulum: finding periodic solutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2129","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:d8f34616bf69d49605d39e5b0d2bc4d08c052a4bf71392eb32797d7ae129a64d","target":"record","created_at":"2026-05-18T02:51:42Z","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":"230ae321b524d7ed133ef73f32feb60c0ec0d2a80d8ca10a96b53782af20a248","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-12-09T15:56:48Z","title_canon_sha256":"7f08de70b1d53e5171f57de13420f51ac21d2f86c7042ad85ebf9bec1b5ea47e"},"schema_version":"1.0","source":{"id":"1112.2129","kind":"arxiv","version":2}},"canonical_sha256":"c496fac1ee54c2597c4fcf5c86b529f7600f75f257db2a99a945c87e1108d55b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c496fac1ee54c2597c4fcf5c86b529f7600f75f257db2a99a945c87e1108d55b","first_computed_at":"2026-05-18T02:51:42.671029Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:42.671029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uuZ+2pxHgWAuKntWJessOWq2plPmCzR7l8YqP+6u72DjMY1heznAfm6A8nbbx6eF6uPe4m/gyEx9Oi1j6m1iAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:42.671514Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.2129","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d8f34616bf69d49605d39e5b0d2bc4d08c052a4bf71392eb32797d7ae129a64d","sha256:6bbca52b0c98c50d31a17cfc1d211e9620df58015242a4ee510809fd1170fdee"],"state_sha256":"347ef4922e1c2619636efc514988a0d5724b0e3ad95a8b1d90534e4ada060a63"}