{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:WCFRWRE3GHAUQZDG2N6WT4KLDY","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":"0fce26c4be8292635a7f78985f3afea589891dd2e8388511a4656c5d7896742f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-18T21:14:19Z","title_canon_sha256":"db7b07ffe5a1e32f9b471321422b39567ed8a642abb5a5ec3da3c109f27ed362"},"schema_version":"1.0","source":{"id":"1403.3029","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.3029","created_at":"2026-05-18T01:12:50Z"},{"alias_kind":"arxiv_version","alias_value":"1403.3029v4","created_at":"2026-05-18T01:12:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.3029","created_at":"2026-05-18T01:12:50Z"},{"alias_kind":"pith_short_12","alias_value":"WCFRWRE3GHAU","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WCFRWRE3GHAUQZDG","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WCFRWRE3","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:c1dadc7bc0945e19b59df738a450797151aefe7c66a223f9ca5bda5d979aaaa3","target":"graph","created_at":"2026-05-18T01:12:50Z","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":"The characteristic equation for a linear delay differential equation (DDE) has countably infinite roots on the complex plane. This paper considers linear DDEs that are on the verge of instability, i.e. a pair of roots of the characteristic equation lie on the imaginary axis of the complex plane, and all other roots have negative real parts. It is shown that, when small noise perturbations are present, the probability law of the dynamics can be approximated by the probability law of a one dimensional stochastic differential equation (SDE) without delay. This is advantageous because equations wi","authors_text":"Nishanth Lingala, N. Sri Namachchivaya","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-18T21:14:19Z","title":"Perturbations of linear delay differential equations at the verge of instability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3029","kind":"arxiv","version":4},"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":"sha256:6e58af51753f3d37f407c8f6b3da31d9add17f9c0fd2bd211db392f4e7279ce9","target":"record","created_at":"2026-05-18T01:12:50Z","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":"0fce26c4be8292635a7f78985f3afea589891dd2e8388511a4656c5d7896742f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-18T21:14:19Z","title_canon_sha256":"db7b07ffe5a1e32f9b471321422b39567ed8a642abb5a5ec3da3c109f27ed362"},"schema_version":"1.0","source":{"id":"1403.3029","kind":"arxiv","version":4}},"canonical_sha256":"b08b1b449b31c1486466d37d69f14b1e141d00f7cf9e1f8b28d33aa28faf984e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b08b1b449b31c1486466d37d69f14b1e141d00f7cf9e1f8b28d33aa28faf984e","first_computed_at":"2026-05-18T01:12:50.175294Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:50.175294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"crd7+V6RtU8+QBdqNyzzr8njqJLey2CX32R/6IRDKyYrsUt8cQwGIR7x9wCkzQTwYT9MvUSyi+uqsiH+lhV2Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:50.175687Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.3029","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e58af51753f3d37f407c8f6b3da31d9add17f9c0fd2bd211db392f4e7279ce9","sha256:c1dadc7bc0945e19b59df738a450797151aefe7c66a223f9ca5bda5d979aaaa3"],"state_sha256":"a00f08ad24d9474339ef327a4a63e4f57a4a86709181ce8300c54e9fa4e6ad7b"}