{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:LVU775RHXFC3GU7NPVT2JNQEDM","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":"91d1cc19df37cf75b68ad97f4a69676108f5f8d202c3c95a1790872685d1c5dd","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-12T03:33:58Z","title_canon_sha256":"a150fb2cfe17ef9c2543608fec8b567ef554d563a14c338b86494c5678fce286"},"schema_version":"1.0","source":{"id":"1810.05341","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.05341","created_at":"2026-07-05T01:20:44Z"},{"alias_kind":"arxiv_version","alias_value":"1810.05341v2","created_at":"2026-07-05T01:20:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.05341","created_at":"2026-07-05T01:20:44Z"},{"alias_kind":"pith_short_12","alias_value":"LVU775RHXFC3","created_at":"2026-07-05T01:20:44Z"},{"alias_kind":"pith_short_16","alias_value":"LVU775RHXFC3GU7N","created_at":"2026-07-05T01:20:44Z"},{"alias_kind":"pith_short_8","alias_value":"LVU775RH","created_at":"2026-07-05T01:20:44Z"}],"graph_snapshots":[{"event_id":"sha256:df6f6355e1cc80d0e982e654faba48ff70d67fbd76413f3a5ff91fa77263c13d","target":"graph","created_at":"2026-07-05T01:20:44Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1810.05341/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For a one-dimensional smooth vector field in a neighborhood of an unstable equilibrium, we consider the associated dynamics perturbed by small noise. We give a revealing elementary proof of a result proved earlier using heavy machinery from Malliavin calculus. In particular, we obtain precise vanishing noise asymptotics for the tail of the exit time and for the exit distribution conditioned on atypically long exits.","authors_text":"Yuri Bakhtin, Zsolt Pajor-Gyulai","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-12T03:33:58Z","title":"Tails of exit times from unstable equilibria on the line"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05341","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":"sha256:12157019fbfa0a52f29f339dc142aff16f9168f7529eaf544e0a8fac5db9a9b8","target":"record","created_at":"2026-07-05T01:20:44Z","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":"91d1cc19df37cf75b68ad97f4a69676108f5f8d202c3c95a1790872685d1c5dd","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-12T03:33:58Z","title_canon_sha256":"a150fb2cfe17ef9c2543608fec8b567ef554d563a14c338b86494c5678fce286"},"schema_version":"1.0","source":{"id":"1810.05341","kind":"arxiv","version":2}},"canonical_sha256":"5d69fff627b945b353ed7d67a4b6041b1edd6959351b8a809da749ae87db274e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d69fff627b945b353ed7d67a4b6041b1edd6959351b8a809da749ae87db274e","first_computed_at":"2026-07-05T01:20:44.938863Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:20:44.938863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TCziKMAhY0yECE5/5k9r7mHmTDJ8m7+i6RB1FaqvcvemPq+sQslxbS/5G8H782k/n/1HGOX5l/sNChnGcWhaBg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:20:44.939239Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.05341","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12157019fbfa0a52f29f339dc142aff16f9168f7529eaf544e0a8fac5db9a9b8","sha256:df6f6355e1cc80d0e982e654faba48ff70d67fbd76413f3a5ff91fa77263c13d"],"state_sha256":"7365444ba810ad72142a8037829f92cdbc63925f834452e0e8b696e862f9cb88"}