{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HYHV7D22QQJWYL2XIPP3JGFEOQ","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":"a0d3713618b7721cf4e581c62dd403376cafbf74ee6a1d34a0167ef75579695e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-11T07:49:02Z","title_canon_sha256":"079133b8661876d8e2972b0cf4d9543fb6ddbc96168e45998dc54ee12c41ef06"},"schema_version":"1.0","source":{"id":"1206.2120","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.2120","created_at":"2026-05-18T03:17:44Z"},{"alias_kind":"arxiv_version","alias_value":"1206.2120v2","created_at":"2026-05-18T03:17:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.2120","created_at":"2026-05-18T03:17:44Z"},{"alias_kind":"pith_short_12","alias_value":"HYHV7D22QQJW","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HYHV7D22QQJWYL2X","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HYHV7D22","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:94a8d21c9529fb03c671bd99a835a6177d1bb1945281262550a8ed6d358798cd","target":"graph","created_at":"2026-05-18T03:17:44Z","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"},"paper":{"abstract_excerpt":"We are concerned with the first hitting times of the Bessel processes. We give explicit expressions for the densities by means of the zeros of the Bessel functions and show their asymptotic behavior.","authors_text":"Hiroyuki Matsumoto, Yuji Hamana","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-11T07:49:02Z","title":"The probability densities of the first hitting times of Bessel processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.2120","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":"sha256:8fe386c4d0d12392d37b5add516d71a77d9ae0fd892f7fab246648c9db5033f9","target":"record","created_at":"2026-05-18T03:17:44Z","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":"a0d3713618b7721cf4e581c62dd403376cafbf74ee6a1d34a0167ef75579695e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-11T07:49:02Z","title_canon_sha256":"079133b8661876d8e2972b0cf4d9543fb6ddbc96168e45998dc54ee12c41ef06"},"schema_version":"1.0","source":{"id":"1206.2120","kind":"arxiv","version":2}},"canonical_sha256":"3e0f5f8f5a84136c2f5743dfb498a47400e6e55f8bcee8812e7c5ad7daa2b3cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e0f5f8f5a84136c2f5743dfb498a47400e6e55f8bcee8812e7c5ad7daa2b3cc","first_computed_at":"2026-05-18T03:17:44.717821Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:44.717821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Dyj+Vlo/f3ch7X0eA7VqRWp9jbMdBHl5Qd9Nn2PDWRfKSEfkUEJ8/SaXwvQ02XIcjT8eaY6W690Z0aAZY1HfBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:44.718593Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.2120","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8fe386c4d0d12392d37b5add516d71a77d9ae0fd892f7fab246648c9db5033f9","sha256:94a8d21c9529fb03c671bd99a835a6177d1bb1945281262550a8ed6d358798cd"],"state_sha256":"79899385c20c873ee64ab064407f4e66dc91f2eccdf23471a055d0140952546b"}