{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:IDCK372Z37PTQXRLIDKXSZPV7N","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":"12173626618eabe99add333732170972a7747d0e9588cb04bcb8d3788f9c8823","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-07-29T11:48:49Z","title_canon_sha256":"2ef231b0574f74b83ab28bf389250b5e89f9ebd8db660173dbdd1cfc9989eaf2"},"schema_version":"1.0","source":{"id":"1407.7703","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.7703","created_at":"2026-05-18T02:46:21Z"},{"alias_kind":"arxiv_version","alias_value":"1407.7703v1","created_at":"2026-05-18T02:46:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.7703","created_at":"2026-05-18T02:46:21Z"},{"alias_kind":"pith_short_12","alias_value":"IDCK372Z37PT","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IDCK372Z37PTQXRL","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IDCK372Z","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:10343a10b8fc7485ea517ba303b02834f15d50a4d369cd667ce4614a388f8fd8","target":"graph","created_at":"2026-05-18T02:46:21Z","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 analyze canard explosions in delayed differential equations with a one-dimensional slow manifold. This study is applied to explore the dynamics of the van der Pol slow-fast system with delayed self-coupling. In the absence of delays, this system provides a canonical example of a canard explosion. We show that as the delay is increased a family of `classical' canard explosions ends as a Bogdanov-Takens bifurcation occurs at the folds points of the S-shaped critical manifold.","authors_text":"Jonathan D. Touboul, Maciej Krupa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-07-29T11:48:49Z","title":"Canard explosion in delayed equations with multiple timescales"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7703","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:afd8cab3b576c3f67cc83ea83c13cf8af5d8f14c897a21815fb1c0b7c79cbc0b","target":"record","created_at":"2026-05-18T02:46:21Z","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":"12173626618eabe99add333732170972a7747d0e9588cb04bcb8d3788f9c8823","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-07-29T11:48:49Z","title_canon_sha256":"2ef231b0574f74b83ab28bf389250b5e89f9ebd8db660173dbdd1cfc9989eaf2"},"schema_version":"1.0","source":{"id":"1407.7703","kind":"arxiv","version":1}},"canonical_sha256":"40c4adff59dfdf385e2b40d57965f5fb5fe5674dbf669ec6124c1a3489d7970b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40c4adff59dfdf385e2b40d57965f5fb5fe5674dbf669ec6124c1a3489d7970b","first_computed_at":"2026-05-18T02:46:21.997191Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:46:21.997191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"McCWOqKPfeJz/F36anrYLfgjIyc9u+xclfFDOgqcC67tfrJ5VxRFNIwdWJN7PUxkHExCL9Cqv2KhmK678Fj5DA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:46:21.997613Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.7703","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:afd8cab3b576c3f67cc83ea83c13cf8af5d8f14c897a21815fb1c0b7c79cbc0b","sha256:10343a10b8fc7485ea517ba303b02834f15d50a4d369cd667ce4614a388f8fd8"],"state_sha256":"b3bb5a0e63df7d8af3c02b5580f8245f2f82b5ea199a97fdab0c03c71c15f694"}