{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:AI3EN4LN3SF74UYD7ZIUM7DPOH","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":"b884bb63254eacccf0d9b0e6097c36aec89ff238b629a15e4e80b2de9ad23604","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-08-30T14:58:43Z","title_canon_sha256":"6c389f0e40a3d985f5740beb7e0d1da1f938b5de350813938ff780aeed89ebfc"},"schema_version":"1.0","source":{"id":"1808.10334","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.10334","created_at":"2026-05-18T00:01:37Z"},{"alias_kind":"arxiv_version","alias_value":"1808.10334v2","created_at":"2026-05-18T00:01:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.10334","created_at":"2026-05-18T00:01:37Z"},{"alias_kind":"pith_short_12","alias_value":"AI3EN4LN3SF7","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"AI3EN4LN3SF74UYD","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"AI3EN4LN","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:25902b1808cfa6fdf1b7a83d63695c2bf981dd72c47dd2ec00d0288bd2b13938","target":"graph","created_at":"2026-05-18T00:01:37Z","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 work we consider two-dimensional critical manifolds in planar fast-slow systems near fold and so-called canard (=`duck') points. These higher-dimension, and lower-codimension, situation is directly motivated by the case of hysteresis operators limiting onto fast-slow systems as well as by systems with constraints. We use geometric desingularization via blow-up to investigate two situations for the slow flow: generic fold (or jump) points, and canards in one-parameter families. We directly prove that the fold case is analogous to the classical fold involving a one-dimensional critical m","authors_text":"Christian Kuehn, Christian M\\\"unch","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-08-30T14:58:43Z","title":"Duck Traps: Two-dimensional Critical Manifolds in Planar Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.10334","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":"sha256:9f2af8b292aac050e6678d262322b837be09777bc54ed58c3fd205129b626c13","target":"record","created_at":"2026-05-18T00:01:37Z","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":"b884bb63254eacccf0d9b0e6097c36aec89ff238b629a15e4e80b2de9ad23604","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-08-30T14:58:43Z","title_canon_sha256":"6c389f0e40a3d985f5740beb7e0d1da1f938b5de350813938ff780aeed89ebfc"},"schema_version":"1.0","source":{"id":"1808.10334","kind":"arxiv","version":2}},"canonical_sha256":"023646f16ddc8bfe5303fe51467c6f71fad528273dcc85cc986afcbaff86d086","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"023646f16ddc8bfe5303fe51467c6f71fad528273dcc85cc986afcbaff86d086","first_computed_at":"2026-05-18T00:01:37.811136Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:37.811136Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sTNs/yOlhUgw9DtlcaUlURWYXRWVzM6oYzWkSFtVUelrKs8lu5KASiK3rOPcrSDkzlK2iEHapS4rHhedBUTtBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:37.811690Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.10334","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f2af8b292aac050e6678d262322b837be09777bc54ed58c3fd205129b626c13","sha256:25902b1808cfa6fdf1b7a83d63695c2bf981dd72c47dd2ec00d0288bd2b13938"],"state_sha256":"ab752217f24def86693779c743fb67a1f111cb120ebc543c885b46b248d805d3"}