{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:TZFT76NHKJH3GBVZQW7YTZAJD4","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":"adc20c557170b9d1222030c38627d3cc996f57e8b5c30d34c9692cd8fa52b75e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-10-27T17:14:47Z","title_canon_sha256":"5ba0f54cd3ce650fb797cc0a334b34ee8e0962a28475361d23c7c4326d4f748a"},"schema_version":"1.0","source":{"id":"1810.11679","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.11679","created_at":"2026-05-17T23:50:44Z"},{"alias_kind":"arxiv_version","alias_value":"1810.11679v2","created_at":"2026-05-17T23:50:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.11679","created_at":"2026-05-17T23:50:44Z"},{"alias_kind":"pith_short_12","alias_value":"TZFT76NHKJH3","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"TZFT76NHKJH3GBVZ","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"TZFT76NH","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:91ae92639c521192d6021e15c081133c351a316f78496b553c5fde4ff686ac3b","target":"graph","created_at":"2026-05-17T23:50:44Z","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 scalar delay differential equation $$ \\dot{x}(t)=-x(t)+f_{K}(x(t-1)) $$ with a nondecreasing feedback function $f_{K}$ depending on a parameter $K$, and we verify that a saddle-node bifurcation of periodic orbits takes place as $K$ varies.\n  The nonlinearity $f_{K}$ is chosen so that it has two unstable fixed points (hence the dynamical system has two unstable equilibria), and these fixed points remain bounded away from each other as $K$ changes. The generated periodic orbits are of large amplitude in the sense that they oscillate about both unstable fixed points of $f_{K}$.","authors_text":"Gabriella Vas, Szandra Guzsv\\'any","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-10-27T17:14:47Z","title":"Saddle-Node Bifurcation of Periodic Orbits for a Delay Differential Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.11679","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":"sha256:7856d429a7ff5a747745281b1087d971067dc043361ee98434c4228d53169282","target":"record","created_at":"2026-05-17T23:50:44Z","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":"adc20c557170b9d1222030c38627d3cc996f57e8b5c30d34c9692cd8fa52b75e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-10-27T17:14:47Z","title_canon_sha256":"5ba0f54cd3ce650fb797cc0a334b34ee8e0962a28475361d23c7c4326d4f748a"},"schema_version":"1.0","source":{"id":"1810.11679","kind":"arxiv","version":2}},"canonical_sha256":"9e4b3ff9a7524fb306b985bf89e4091f2c725128cb023988e89da2b43e9ae68a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e4b3ff9a7524fb306b985bf89e4091f2c725128cb023988e89da2b43e9ae68a","first_computed_at":"2026-05-17T23:50:44.861970Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:44.861970Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lWz2Nu0+WOs5jisYhn2Zp5QAEIZ6wRERhRRkiMUT9kJfNnlcz/JXaLBxua9bZEK+lzR+EMPmLnxXZuiqYDg3Cw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:44.862530Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.11679","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7856d429a7ff5a747745281b1087d971067dc043361ee98434c4228d53169282","sha256:91ae92639c521192d6021e15c081133c351a316f78496b553c5fde4ff686ac3b"],"state_sha256":"71df412bb7f197bad12d5eeed89a6f780b6a94c9f21491866289fd41c13bf810"}