{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FMD5CBGHYC3HS2NX4DR6J4743H","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":"e459acae6c562d762f2e6e8f9681602032c4ec993e15c92f71a92880bf736158","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-04-09T19:07:39Z","title_canon_sha256":"391f3844305ce8156bf08f40d44d5bba85887dae631d02dbc531ea7622bc7637"},"schema_version":"1.0","source":{"id":"1504.02425","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.02425","created_at":"2026-05-17T23:42:49Z"},{"alias_kind":"arxiv_version","alias_value":"1504.02425v2","created_at":"2026-05-17T23:42:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.02425","created_at":"2026-05-17T23:42:49Z"},{"alias_kind":"pith_short_12","alias_value":"FMD5CBGHYC3H","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FMD5CBGHYC3HS2NX","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FMD5CBGH","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:5994063544b5b14171fc078f6957018b1dfd92e5f1283cbe151e99201aba5a4c","target":"graph","created_at":"2026-05-17T23:42:49Z","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 introduce the concept of sliding Shilnikov orbits for $3$D Filippov systems. In short, such an orbit is a piecewise smooth closed curve, composed by Filippov trajectories, which slides on the switching surface and connects a Filippov equilibrium to itself, namely a pseudo saddle-focus. A version of the Shilnikov's Theorem is provided for such systems. Particularly, we show that sliding Shilnikov orbits occur in generic one-parameter families of Filippov systems, and that arbitrarily close to a sliding Shilnikov orbit there exist countably infinitely many sliding periodic orbit","authors_text":"Douglas D. Novaes, Marco A. Teixeira","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-04-09T19:07:39Z","title":"Shilnikov problem in Filippov dynamical systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02425","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":"sha256:1bdc86b2faf939aa3d0f51f36dcd004dae7256b2c51a67a432075312483ad577","target":"record","created_at":"2026-05-17T23:42:49Z","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":"e459acae6c562d762f2e6e8f9681602032c4ec993e15c92f71a92880bf736158","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-04-09T19:07:39Z","title_canon_sha256":"391f3844305ce8156bf08f40d44d5bba85887dae631d02dbc531ea7622bc7637"},"schema_version":"1.0","source":{"id":"1504.02425","kind":"arxiv","version":2}},"canonical_sha256":"2b07d104c7c0b67969b7e0e3e4f3fcd9ef0a4d372dd01d8a719c7cee984d3f7d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b07d104c7c0b67969b7e0e3e4f3fcd9ef0a4d372dd01d8a719c7cee984d3f7d","first_computed_at":"2026-05-17T23:42:49.945763Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:49.945763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4rG3i5JNUioMe4j5/FyccbWhCkE0ThyzIwvGkrGepHwRzlAjlBmasBq10t6VU2sM4DX7LUlon/GWX/KXhAqIAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:49.946229Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.02425","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1bdc86b2faf939aa3d0f51f36dcd004dae7256b2c51a67a432075312483ad577","sha256:5994063544b5b14171fc078f6957018b1dfd92e5f1283cbe151e99201aba5a4c"],"state_sha256":"b16b12f6404c7967655110b89cc2540eeefb1d6e4c964a820cbfed19857291d1"}