{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:WFUZJ6SDK2TYVF2YJHFVXN24PN","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":"7432e33d9cfbcb89896ab6bdbb27f1b270741b8af4d9ecbe06f718c11fa6ed2a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-11-30T19:15:30Z","title_canon_sha256":"aaf87d9410b58b0b7c89a277fd904cf3c76492392f607b974e2c832704d501a8"},"schema_version":"1.0","source":{"id":"1412.0263","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.0263","created_at":"2026-05-18T01:21:13Z"},{"alias_kind":"arxiv_version","alias_value":"1412.0263v2","created_at":"2026-05-18T01:21:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.0263","created_at":"2026-05-18T01:21:13Z"},{"alias_kind":"pith_short_12","alias_value":"WFUZJ6SDK2TY","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WFUZJ6SDK2TYVF2Y","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WFUZJ6SD","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:c8575919c6acfec13c2209d5dc7d4bdb051c80fe531aff86ab8ace79762ab990","target":"graph","created_at":"2026-05-18T01:21:13Z","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":"Classical canard explosion results in smooth systems require the vector field to be at least $C^3$, since canard cycles are created as the result of a Hopf bifurcation. The work on canards in nonsmooth, planar systems is recent and has thus far been restricted to piecewise-linear or piecewise-smooth Van der Pol systems, where an extremum of the critical manifold arises from the nonsmoothness. In both of these cases, a canard (or canard-like) explosion is created through a nonsmooth bifurcation as the slow nullcline passes through a corner of the critical manifold. Additionally, it is possible ","authors_text":"Andrew Roberts","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-11-30T19:15:30Z","title":"Canard explosion and relaxation oscillation in planar, piecewise-smooth, continuous systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0263","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:fff7fa24baf1127cc1c5e0db498b6428594bd65a01da1fbad5e384c7ed04a2ff","target":"record","created_at":"2026-05-18T01:21:13Z","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":"7432e33d9cfbcb89896ab6bdbb27f1b270741b8af4d9ecbe06f718c11fa6ed2a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-11-30T19:15:30Z","title_canon_sha256":"aaf87d9410b58b0b7c89a277fd904cf3c76492392f607b974e2c832704d501a8"},"schema_version":"1.0","source":{"id":"1412.0263","kind":"arxiv","version":2}},"canonical_sha256":"b16994fa4356a78a975849cb5bb75c7b4231559e557ad36145494a7ef6085944","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b16994fa4356a78a975849cb5bb75c7b4231559e557ad36145494a7ef6085944","first_computed_at":"2026-05-18T01:21:13.655234Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:13.655234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1Syycj3g8+nGBRobzdxtaRVK7bNv9OfBy1qZ2twyA4+pXwtAzPjXndtdCJ/Q63OuFYw82uuh17DEcv/+7VMzAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:13.655920Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.0263","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fff7fa24baf1127cc1c5e0db498b6428594bd65a01da1fbad5e384c7ed04a2ff","sha256:c8575919c6acfec13c2209d5dc7d4bdb051c80fe531aff86ab8ace79762ab990"],"state_sha256":"a4b18a2b40c3f427d2424cd641c6b9125ae117ba5386e4a51003b6493028490b"}