{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:TOTLFV7KNWWV7DVITNOU65HYIG","short_pith_number":"pith:TOTLFV7K","canonical_record":{"source":{"id":"1101.3915","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-01-20T14:36:11Z","cross_cats_sorted":["q-bio.NC"],"title_canon_sha256":"b3a0a40249ff54477285cfab1cc8d0e8e1817f9976bce7c8e29469ac89e776d3","abstract_canon_sha256":"01ce99b69cab8edef7c12c2f54fc50a7c17772fc4a7ee893ac25ddca8936aa74"},"schema_version":"1.0"},"canonical_sha256":"9ba6b2d7ea6dad5f8ea89b5d4f74f841a79b3553af220caeefd34e5b03714ebe","source":{"kind":"arxiv","id":"1101.3915","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.3915","created_at":"2026-05-18T04:09:53Z"},{"alias_kind":"arxiv_version","alias_value":"1101.3915v1","created_at":"2026-05-18T04:09:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.3915","created_at":"2026-05-18T04:09:53Z"},{"alias_kind":"pith_short_12","alias_value":"TOTLFV7KNWWV","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TOTLFV7KNWWV7DVI","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TOTLFV7K","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:TOTLFV7KNWWV7DVITNOU65HYIG","target":"record","payload":{"canonical_record":{"source":{"id":"1101.3915","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-01-20T14:36:11Z","cross_cats_sorted":["q-bio.NC"],"title_canon_sha256":"b3a0a40249ff54477285cfab1cc8d0e8e1817f9976bce7c8e29469ac89e776d3","abstract_canon_sha256":"01ce99b69cab8edef7c12c2f54fc50a7c17772fc4a7ee893ac25ddca8936aa74"},"schema_version":"1.0"},"canonical_sha256":"9ba6b2d7ea6dad5f8ea89b5d4f74f841a79b3553af220caeefd34e5b03714ebe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:53.681957Z","signature_b64":"ga6oaAcIBqZUsbhiDSNqac4Awckh3je2CQcBeEYMXF4Zkk9v//1QYTu59WYzUHXjVpNUWeqwDVb1P9Da0jpXAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ba6b2d7ea6dad5f8ea89b5d4f74f841a79b3553af220caeefd34e5b03714ebe","last_reissued_at":"2026-05-18T04:09:53.681358Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:53.681358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.3915","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:09:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l9Py1gcyEIW96kcjY/oyd6I+16mAX5zYpwV+64t9wEbLulfJnNe8RbJ0j2LNumHtlhZlx1ZPqg+mpP7wdsbjCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T13:31:24.466842Z"},"content_sha256":"f32b8019cb28e3aee387b766a6738a058ed82fca06a258d0c92985547b70e1fe","schema_version":"1.0","event_id":"sha256:f32b8019cb28e3aee387b766a6738a058ed82fca06a258d0c92985547b70e1fe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:TOTLFV7KNWWV7DVITNOU65HYIG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Lower Bound for the First Passage Time Density of the Suprathreshold Ornstein-Uhlenbeck Process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.NC"],"primary_cat":"math.PR","authors_text":"Peter J. Thomas","submitted_at":"2011-01-20T14:36:11Z","abstract_excerpt":"We prove that the first passage time density $\\rho(t)$ for an Ornstein-Uhlenbeck process $X(t)$ obeying $dX=-\\beta X dt + \\sigma dW$ to reach a fixed threshold $\\theta$ from a suprathreshold initial condition $x_0>\\theta>0$ has a lower bound of the form $\\rho(t)>k \\exp\\left[-p e^{6\\beta t}\\right]$ for positive constants $k$ and $p$ for times $t$ exceeding some positive value $u$. We obtain explicit expressions for $k, p$ and $u$ in terms of $\\beta$, $\\sigma$, $x_0$ and $\\theta$, and discuss application of the results to the synchronization of periodically forced stochastic leaky integrate-and-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3915","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:09:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bqOiMO6OKoTDfDerdNB1WIOwHN54GaPqDqZsOS2SEcw6fq4Axk286+PgEu+kuG1u19DdLQwYxpG3ZhTSnz7dCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T13:31:24.467672Z"},"content_sha256":"5b7bb38ff878f71f38a9e9d4db31c4073f23f6ad9139411261955e9ddd19c6b6","schema_version":"1.0","event_id":"sha256:5b7bb38ff878f71f38a9e9d4db31c4073f23f6ad9139411261955e9ddd19c6b6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TOTLFV7KNWWV7DVITNOU65HYIG/bundle.json","state_url":"https://pith.science/pith/TOTLFV7KNWWV7DVITNOU65HYIG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TOTLFV7KNWWV7DVITNOU65HYIG/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-31T13:31:24Z","links":{"resolver":"https://pith.science/pith/TOTLFV7KNWWV7DVITNOU65HYIG","bundle":"https://pith.science/pith/TOTLFV7KNWWV7DVITNOU65HYIG/bundle.json","state":"https://pith.science/pith/TOTLFV7KNWWV7DVITNOU65HYIG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TOTLFV7KNWWV7DVITNOU65HYIG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TOTLFV7KNWWV7DVITNOU65HYIG","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":"01ce99b69cab8edef7c12c2f54fc50a7c17772fc4a7ee893ac25ddca8936aa74","cross_cats_sorted":["q-bio.NC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-01-20T14:36:11Z","title_canon_sha256":"b3a0a40249ff54477285cfab1cc8d0e8e1817f9976bce7c8e29469ac89e776d3"},"schema_version":"1.0","source":{"id":"1101.3915","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.3915","created_at":"2026-05-18T04:09:53Z"},{"alias_kind":"arxiv_version","alias_value":"1101.3915v1","created_at":"2026-05-18T04:09:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.3915","created_at":"2026-05-18T04:09:53Z"},{"alias_kind":"pith_short_12","alias_value":"TOTLFV7KNWWV","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TOTLFV7KNWWV7DVI","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TOTLFV7K","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:5b7bb38ff878f71f38a9e9d4db31c4073f23f6ad9139411261955e9ddd19c6b6","target":"graph","created_at":"2026-05-18T04:09:53Z","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 prove that the first passage time density $\\rho(t)$ for an Ornstein-Uhlenbeck process $X(t)$ obeying $dX=-\\beta X dt + \\sigma dW$ to reach a fixed threshold $\\theta$ from a suprathreshold initial condition $x_0>\\theta>0$ has a lower bound of the form $\\rho(t)>k \\exp\\left[-p e^{6\\beta t}\\right]$ for positive constants $k$ and $p$ for times $t$ exceeding some positive value $u$. We obtain explicit expressions for $k, p$ and $u$ in terms of $\\beta$, $\\sigma$, $x_0$ and $\\theta$, and discuss application of the results to the synchronization of periodically forced stochastic leaky integrate-and-","authors_text":"Peter J. Thomas","cross_cats":["q-bio.NC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-01-20T14:36:11Z","title":"A Lower Bound for the First Passage Time Density of the Suprathreshold Ornstein-Uhlenbeck Process"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3915","kind":"arxiv","version":1},"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:f32b8019cb28e3aee387b766a6738a058ed82fca06a258d0c92985547b70e1fe","target":"record","created_at":"2026-05-18T04:09:53Z","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":"01ce99b69cab8edef7c12c2f54fc50a7c17772fc4a7ee893ac25ddca8936aa74","cross_cats_sorted":["q-bio.NC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-01-20T14:36:11Z","title_canon_sha256":"b3a0a40249ff54477285cfab1cc8d0e8e1817f9976bce7c8e29469ac89e776d3"},"schema_version":"1.0","source":{"id":"1101.3915","kind":"arxiv","version":1}},"canonical_sha256":"9ba6b2d7ea6dad5f8ea89b5d4f74f841a79b3553af220caeefd34e5b03714ebe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ba6b2d7ea6dad5f8ea89b5d4f74f841a79b3553af220caeefd34e5b03714ebe","first_computed_at":"2026-05-18T04:09:53.681358Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:53.681358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ga6oaAcIBqZUsbhiDSNqac4Awckh3je2CQcBeEYMXF4Zkk9v//1QYTu59WYzUHXjVpNUWeqwDVb1P9Da0jpXAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:53.681957Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.3915","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f32b8019cb28e3aee387b766a6738a058ed82fca06a258d0c92985547b70e1fe","sha256:5b7bb38ff878f71f38a9e9d4db31c4073f23f6ad9139411261955e9ddd19c6b6"],"state_sha256":"cd6bf814d340f6410e7a52ebf5f80da758127fd66b18de4c4e3960ef4dd2b10c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EMaUeQG/aYjYHUwaD91dAY7b0MVQQWCodw0otImLhD9aN3wMyamu2rVKQrc8YKT2oXZZclL/EAcUQyfLLaY1CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T13:31:24.471792Z","bundle_sha256":"556a9c5e1f5dc589c7756e3e31718f84fe0a9b18f228f56cd65a6848dd69ff5e"}}