{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:E5ZKMBL5RAOV6GEAH4TIVFUUBQ","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":"cff6ce265c9f12ca5fd7aa3a0c3592d79726daa7fe02928edcd1f84aef2a7fd5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-09-25T20:17:56Z","title_canon_sha256":"96e08d69e5cc19e8cbfbe5f9c6104caead29345e2af2b0c0eb4f1a8f50079f73"},"schema_version":"1.0","source":{"id":"1909.11746","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.11746","created_at":"2026-07-05T00:21:15Z"},{"alias_kind":"arxiv_version","alias_value":"1909.11746v2","created_at":"2026-07-05T00:21:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.11746","created_at":"2026-07-05T00:21:15Z"},{"alias_kind":"pith_short_12","alias_value":"E5ZKMBL5RAOV","created_at":"2026-07-05T00:21:15Z"},{"alias_kind":"pith_short_16","alias_value":"E5ZKMBL5RAOV6GEA","created_at":"2026-07-05T00:21:15Z"},{"alias_kind":"pith_short_8","alias_value":"E5ZKMBL5","created_at":"2026-07-05T00:21:15Z"}],"graph_snapshots":[{"event_id":"sha256:d871ec8cbb8a9525465b879e54ba5a6b4589f3f5e5ee40fb2953f27405a98932","target":"graph","created_at":"2026-07-05T00:21:15Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1909.11746/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we describe a novel type of relaxation oscillations occurring in a model of substrate-depletion oscillators. Using geometric singular perturbation theory, with blow-up as a key technical tool, we show that the oscillations in this planar model are produced by a complicated interplay between two stable nodes and a discontinuity set in the singular limit $\\varepsilon\\rightarrow 0$. This interplay produces a new mechanism for producing relaxation-type oscillations, which we also describe in a more general setting.","authors_text":"Kristian Uldall Kristiansen, Peter Szmolyan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-09-25T20:17:56Z","title":"Relaxation oscillations in substrate-depletion oscillators close to the nonsmooth limit"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.11746","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":"sha256:2964462f10a67dd37e2912c84d03b47730686516d177a3940a386423a0c4492b","target":"record","created_at":"2026-07-05T00:21:15Z","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":"cff6ce265c9f12ca5fd7aa3a0c3592d79726daa7fe02928edcd1f84aef2a7fd5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-09-25T20:17:56Z","title_canon_sha256":"96e08d69e5cc19e8cbfbe5f9c6104caead29345e2af2b0c0eb4f1a8f50079f73"},"schema_version":"1.0","source":{"id":"1909.11746","kind":"arxiv","version":2}},"canonical_sha256":"2772a6057d881d5f18803f268a96940c0109489fec0cdd879901bb5f415b2e5a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2772a6057d881d5f18803f268a96940c0109489fec0cdd879901bb5f415b2e5a","first_computed_at":"2026-07-05T00:21:15.030791Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:21:15.030791Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G4ymbMXqxqCinXHRXXpcLHueAoOEJbewHiHVaViFu33At3m4JNbXYNcovLa4w2jB5pmEjKWIy7Rb+Hy2mrjfDg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:21:15.031301Z","signed_message":"canonical_sha256_bytes"},"source_id":"1909.11746","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2964462f10a67dd37e2912c84d03b47730686516d177a3940a386423a0c4492b","sha256:d871ec8cbb8a9525465b879e54ba5a6b4589f3f5e5ee40fb2953f27405a98932"],"state_sha256":"dcfa6d9da5944ff9b7a688508286b4eb877b852fce2ed725d23eb0146d26577f"}