{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7VLJHF22QWWJRQII5H2GNXBJOS","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":"cc6d92f855ba8cd2b4d739687095dece9d3c40fc0e7c901d65428c6e1b72d1fa","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-16T12:15:12Z","title_canon_sha256":"11bbfa6534416c4e40a81edb896eefc7f4b2a5e17e93ab536c07a701e04408f7"},"schema_version":"1.0","source":{"id":"1307.4255","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.4255","created_at":"2026-05-18T01:31:53Z"},{"alias_kind":"arxiv_version","alias_value":"1307.4255v3","created_at":"2026-05-18T01:31:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.4255","created_at":"2026-05-18T01:31:53Z"},{"alias_kind":"pith_short_12","alias_value":"7VLJHF22QWWJ","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"7VLJHF22QWWJRQII","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"7VLJHF22","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:c65fd16d92ae0f7e6f855afbd190d8542c04d0976b5897c199398087004da054","target":"graph","created_at":"2026-05-18T01:31:53Z","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 certain one dimensional ordinary stochastic differential equations driven by additive Brownian motion of variance $\\varepsilon ^2$. When $\\varepsilon =0$ such equations have an unstable non-hyperbolic fixed point and the drift near such a point has a power law behavior. For $\\varepsilon >0$ small, the fixed point property disappears, but it is replaced by a random escape or transit time which diverges as $\\varepsilon \\searrow0$. We show that this random time, under suitable (easily guessed) rescaling, converges to a limit random variable that essentially depends only on the power e","authors_text":"Giambattista Giacomin, Mathieu Merle","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-16T12:15:12Z","title":"Weak noise and non-hyperbolic unstable fixed points: Sharp estimates on transit and exit times"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4255","kind":"arxiv","version":3},"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":"sha256:373c6c78a1db529f9650fceb281793b4657263de67fa7b639382bd805f261206","target":"record","created_at":"2026-05-18T01:31:53Z","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":"cc6d92f855ba8cd2b4d739687095dece9d3c40fc0e7c901d65428c6e1b72d1fa","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-16T12:15:12Z","title_canon_sha256":"11bbfa6534416c4e40a81edb896eefc7f4b2a5e17e93ab536c07a701e04408f7"},"schema_version":"1.0","source":{"id":"1307.4255","kind":"arxiv","version":3}},"canonical_sha256":"fd5693975a85ac98c108e9f466dc29748baf2596cc2f53a4ff3c9818ae050ef2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd5693975a85ac98c108e9f466dc29748baf2596cc2f53a4ff3c9818ae050ef2","first_computed_at":"2026-05-18T01:31:53.526001Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:53.526001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mPCw4JqlPvMQeIXP071L3iBY5TwYBT/lNHBnmVJwurd9bSbBksaYTmlUwq4ZUPLFpRRa5jBcKuAfHDCYD0+IDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:53.526655Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.4255","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:373c6c78a1db529f9650fceb281793b4657263de67fa7b639382bd805f261206","sha256:c65fd16d92ae0f7e6f855afbd190d8542c04d0976b5897c199398087004da054"],"state_sha256":"a2f4285782621d9836fcaa2b80b471f2de47e69d1e66c12dd3ed71f41044fc6c"}