{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:XMRF6LZMOEP4BYDL7TELS7E5OX","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":"1b0cac39922d8398754c8ae4037c18939122fc94e4efb66b5a7c5d9baee9e8cf","cross_cats_sorted":["math.PR","q-bio.NC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-11-14T08:32:00Z","title_canon_sha256":"d1cdc9b87c55e08893e58664a9869d9bccb9f5aebb625953aac32fbb8dbb54ac"},"schema_version":"1.0","source":{"id":"1011.3193","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.3193","created_at":"2026-05-18T04:02:12Z"},{"alias_kind":"arxiv_version","alias_value":"1011.3193v1","created_at":"2026-05-18T04:02:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.3193","created_at":"2026-05-18T04:02:12Z"},{"alias_kind":"pith_short_12","alias_value":"XMRF6LZMOEP4","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"XMRF6LZMOEP4BYDL","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"XMRF6LZM","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:b378db3bfb50da13565bf15b1942cec14d386f399ac7b3a18dc406257129f847","target":"graph","created_at":"2026-05-18T04:02:12Z","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 consider the effect of Gaussian white noise on fast-slow dynamical systems with one fast and two slow variables, containing a folded-node singularity. In the absence of noise, these systems are known to display mixed-mode oscillations, consisting of alternating large- and small-amplitude oscillations. We quantify the effect of noise and obtain critical noise intensities above which the small-amplitude oscillations become hidden by fluctuations. Furthermore we prove that the noise can cause sample paths to jump away from so-called canard solutions with high probability before deterministic o","authors_text":"Barbara Gentz, Christian Kuehn, Nils Berglund","cross_cats":["math.PR","q-bio.NC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-11-14T08:32:00Z","title":"Hunting French Ducks in a Noisy Environment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3193","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":"sha256:41cca79026220618d400fba96c0db6a228a21d5a42009140a9c921b351190904","target":"record","created_at":"2026-05-18T04:02:12Z","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":"1b0cac39922d8398754c8ae4037c18939122fc94e4efb66b5a7c5d9baee9e8cf","cross_cats_sorted":["math.PR","q-bio.NC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-11-14T08:32:00Z","title_canon_sha256":"d1cdc9b87c55e08893e58664a9869d9bccb9f5aebb625953aac32fbb8dbb54ac"},"schema_version":"1.0","source":{"id":"1011.3193","kind":"arxiv","version":1}},"canonical_sha256":"bb225f2f2c711fc0e06bfcc8b97c9d75f2d082f4726e9a44bd68ee13fffcd4f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bb225f2f2c711fc0e06bfcc8b97c9d75f2d082f4726e9a44bd68ee13fffcd4f1","first_computed_at":"2026-05-18T04:02:12.049529Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:12.049529Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+oxPq5pPlMMpM1U5z3Rsp0DC/2z8s+3dMeY2sy4xtVOETFOJf2vFkJFYkrafQvoxoGzUe45wxmd83vnhwUqMBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:12.050287Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.3193","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:41cca79026220618d400fba96c0db6a228a21d5a42009140a9c921b351190904","sha256:b378db3bfb50da13565bf15b1942cec14d386f399ac7b3a18dc406257129f847"],"state_sha256":"04e7ee5641165a9b7cb02f057a8dfed058a2778e3ec8e0cc6b327c3421d63d45"}