{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:HQB2XE2QPJIOW6EHPNLWOHH3UB","short_pith_number":"pith:HQB2XE2Q","canonical_record":{"source":{"id":"1008.1326","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-08-07T11:53:23Z","cross_cats_sorted":[],"title_canon_sha256":"44f02e0801dcf27c03adfea970644705c61ba67025d8f3096249f7871295941e","abstract_canon_sha256":"d41aa1b396aeceeb6f148311ea531ed3f94cbd4b726acb31ba124f327e427f84"},"schema_version":"1.0"},"canonical_sha256":"3c03ab93507a50eb78877b57671cfba063af764d6825dea1f609145e87e106e9","source":{"kind":"arxiv","id":"1008.1326","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.1326","created_at":"2026-05-18T04:42:33Z"},{"alias_kind":"arxiv_version","alias_value":"1008.1326v1","created_at":"2026-05-18T04:42:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.1326","created_at":"2026-05-18T04:42:33Z"},{"alias_kind":"pith_short_12","alias_value":"HQB2XE2QPJIO","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"HQB2XE2QPJIOW6EH","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"HQB2XE2Q","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:HQB2XE2QPJIOW6EHPNLWOHH3UB","target":"record","payload":{"canonical_record":{"source":{"id":"1008.1326","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-08-07T11:53:23Z","cross_cats_sorted":[],"title_canon_sha256":"44f02e0801dcf27c03adfea970644705c61ba67025d8f3096249f7871295941e","abstract_canon_sha256":"d41aa1b396aeceeb6f148311ea531ed3f94cbd4b726acb31ba124f327e427f84"},"schema_version":"1.0"},"canonical_sha256":"3c03ab93507a50eb78877b57671cfba063af764d6825dea1f609145e87e106e9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:33.288656Z","signature_b64":"tdBreSEWJqIMUkx3KRUC3/votUVzq0tqNE7oq/Xc563wRS24EoS+tmZ98qMwhTF2X+v7W3FHuIwIBcQiyY67Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c03ab93507a50eb78877b57671cfba063af764d6825dea1f609145e87e106e9","last_reissued_at":"2026-05-18T04:42:33.288109Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:33.288109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.1326","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":"2026-05-18T04:42:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"brp4aQvJL/4394/BxyGEV9Ob5C38wjnzHJx+CP1aphRyXYeFqF0wN+bNI38KGrY7jsutbBnXjWmv4wIZyulkAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T17:10:39.492859Z"},"content_sha256":"319cbe1a262e7949abe067d48d5fc0d9ed049a871e53087ee7300fe02dd66061","schema_version":"1.0","event_id":"sha256:319cbe1a262e7949abe067d48d5fc0d9ed049a871e53087ee7300fe02dd66061"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:HQB2XE2QPJIOW6EHPNLWOHH3UB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Efficient estimation of one-dimensional diffusion first passage time densities via Monte Carlo simulation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Constantinos Kardaras, Tomoyuki Ichiba","submitted_at":"2010-08-07T11:53:23Z","abstract_excerpt":"We propose a method for estimating first passage time densities of one-dimensional diffusions via Monte Carlo simulation. Our approach involves a representation of the first passage time density as expectation of a functional of the three-dimensional Brownian bridge. As the latter process can be simulated exactly, our method leads to almost unbiased estimators. Furthermore, since the density is estimated directly, a convergence of order $1 / \\sqrt{N}$, where $N$ is the sample size, is achieved, the last being in sharp contrast to the slower non-parametric rates achieved by kernel smoothing of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1326","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":"2026-05-18T04:42:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xyt7M3r5eY7DjYzIz39zmy4azwkSTUAlKEkSND5M1cfLvmVaC7qxUbOKomDnKo1BhXa1m+t9pTHDQLNqKhI3Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T17:10:39.493224Z"},"content_sha256":"84d839d02cece2a946a7d44d4d49c7c92611cfb8aaf03fbb25e75c77aedf7a28","schema_version":"1.0","event_id":"sha256:84d839d02cece2a946a7d44d4d49c7c92611cfb8aaf03fbb25e75c77aedf7a28"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HQB2XE2QPJIOW6EHPNLWOHH3UB/bundle.json","state_url":"https://pith.science/pith/HQB2XE2QPJIOW6EHPNLWOHH3UB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HQB2XE2QPJIOW6EHPNLWOHH3UB/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":"2026-06-02T17:10:39Z","links":{"resolver":"https://pith.science/pith/HQB2XE2QPJIOW6EHPNLWOHH3UB","bundle":"https://pith.science/pith/HQB2XE2QPJIOW6EHPNLWOHH3UB/bundle.json","state":"https://pith.science/pith/HQB2XE2QPJIOW6EHPNLWOHH3UB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HQB2XE2QPJIOW6EHPNLWOHH3UB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:HQB2XE2QPJIOW6EHPNLWOHH3UB","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":"d41aa1b396aeceeb6f148311ea531ed3f94cbd4b726acb31ba124f327e427f84","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-08-07T11:53:23Z","title_canon_sha256":"44f02e0801dcf27c03adfea970644705c61ba67025d8f3096249f7871295941e"},"schema_version":"1.0","source":{"id":"1008.1326","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.1326","created_at":"2026-05-18T04:42:33Z"},{"alias_kind":"arxiv_version","alias_value":"1008.1326v1","created_at":"2026-05-18T04:42:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.1326","created_at":"2026-05-18T04:42:33Z"},{"alias_kind":"pith_short_12","alias_value":"HQB2XE2QPJIO","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"HQB2XE2QPJIOW6EH","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"HQB2XE2Q","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:84d839d02cece2a946a7d44d4d49c7c92611cfb8aaf03fbb25e75c77aedf7a28","target":"graph","created_at":"2026-05-18T04:42:33Z","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 propose a method for estimating first passage time densities of one-dimensional diffusions via Monte Carlo simulation. Our approach involves a representation of the first passage time density as expectation of a functional of the three-dimensional Brownian bridge. As the latter process can be simulated exactly, our method leads to almost unbiased estimators. Furthermore, since the density is estimated directly, a convergence of order $1 / \\sqrt{N}$, where $N$ is the sample size, is achieved, the last being in sharp contrast to the slower non-parametric rates achieved by kernel smoothing of ","authors_text":"Constantinos Kardaras, Tomoyuki Ichiba","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-08-07T11:53:23Z","title":"Efficient estimation of one-dimensional diffusion first passage time densities via Monte Carlo simulation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1326","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":"sha256:319cbe1a262e7949abe067d48d5fc0d9ed049a871e53087ee7300fe02dd66061","target":"record","created_at":"2026-05-18T04:42:33Z","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":"d41aa1b396aeceeb6f148311ea531ed3f94cbd4b726acb31ba124f327e427f84","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-08-07T11:53:23Z","title_canon_sha256":"44f02e0801dcf27c03adfea970644705c61ba67025d8f3096249f7871295941e"},"schema_version":"1.0","source":{"id":"1008.1326","kind":"arxiv","version":1}},"canonical_sha256":"3c03ab93507a50eb78877b57671cfba063af764d6825dea1f609145e87e106e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c03ab93507a50eb78877b57671cfba063af764d6825dea1f609145e87e106e9","first_computed_at":"2026-05-18T04:42:33.288109Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:33.288109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tdBreSEWJqIMUkx3KRUC3/votUVzq0tqNE7oq/Xc563wRS24EoS+tmZ98qMwhTF2X+v7W3FHuIwIBcQiyY67Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:33.288656Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.1326","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:319cbe1a262e7949abe067d48d5fc0d9ed049a871e53087ee7300fe02dd66061","sha256:84d839d02cece2a946a7d44d4d49c7c92611cfb8aaf03fbb25e75c77aedf7a28"],"state_sha256":"a0c25832f73fd75dfc99c2d1a50cb94a10831f1e50a6eb18bbb0ce9d26df7400"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+0Z+QEVa3THsKp2Oa8uSohzPTFJqNtTC6Ny96DUn+MHv+pqUFPfXYr79NhV2u8UkRwtyF3OxpX6FtvgieiBWBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T17:10:39.495560Z","bundle_sha256":"344e394a0829a72e9242d363e8d987a88a581a9222b842c8d708aaa158a91c8e"}}