{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HULWOWQX65ZA6D4LDKWWG7POH5","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":"4ff77e75a4ab424d58f9c5e99618438f24930c83e7410d0216a9934105a4cc6f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-07T07:42:23Z","title_canon_sha256":"d8de77a69c9f5f095fea371d3ddcc732f5cee568cb3c168d3817af302b09fb5e"},"schema_version":"1.0","source":{"id":"1401.1296","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.1296","created_at":"2026-05-18T01:20:47Z"},{"alias_kind":"arxiv_version","alias_value":"1401.1296v1","created_at":"2026-05-18T01:20:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.1296","created_at":"2026-05-18T01:20:47Z"},{"alias_kind":"pith_short_12","alias_value":"HULWOWQX65ZA","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HULWOWQX65ZA6D4L","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HULWOWQX","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:308fc6d2a101a2f5cb8c01428a99ce564de41424eb0ab39a7d57765f1e2871aa","target":"graph","created_at":"2026-05-18T01:20:47Z","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":"The asymptotic behavior of the tail probabilities for the first hitting times of the Bessel process with arbitrary index is shown without using the explicit expressions for the distribution function obtained in the authors' previous works.","authors_text":"Hiroyuki Matsumoto, Yuji Hamana","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-07T07:42:23Z","title":"Asymptotics of the probability distributions of the first hitting times of Bessel processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1296","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":"sha256:1e3b682267ecb8d29f297e7f8cb3efecfa8f66d6ff7d4be94400c601c843ced2","target":"record","created_at":"2026-05-18T01:20:47Z","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":"4ff77e75a4ab424d58f9c5e99618438f24930c83e7410d0216a9934105a4cc6f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-07T07:42:23Z","title_canon_sha256":"d8de77a69c9f5f095fea371d3ddcc732f5cee568cb3c168d3817af302b09fb5e"},"schema_version":"1.0","source":{"id":"1401.1296","kind":"arxiv","version":1}},"canonical_sha256":"3d17675a17f7720f0f8b1aad637dee3f539c4fbf0ef32e73b5c8e3c160f714bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d17675a17f7720f0f8b1aad637dee3f539c4fbf0ef32e73b5c8e3c160f714bc","first_computed_at":"2026-05-18T01:20:47.599252Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:47.599252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2hInFVYfcPwdhBqAPjF/XEOCUMesfPGsMJN2kXckdSghFj9uf2FghWW5BMKzjPfB8RmcTfkSkJzzltN8agzfAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:47.599722Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.1296","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e3b682267ecb8d29f297e7f8cb3efecfa8f66d6ff7d4be94400c601c843ced2","sha256:308fc6d2a101a2f5cb8c01428a99ce564de41424eb0ab39a7d57765f1e2871aa"],"state_sha256":"3b9da476025b136d8fde7be94bc84c1d0c8db7f7ec7b10436926c0f3535ef832"}