{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:RUEWWU3Q3NGOQSQLAPMXVT7GVA","short_pith_number":"pith:RUEWWU3Q","canonical_record":{"source":{"id":"1004.5515","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-04-30T12:37:15Z","cross_cats_sorted":[],"title_canon_sha256":"319b8e83ded519ffac136920de4db5aacd31915287b93c484b172b1b6cacb41b","abstract_canon_sha256":"be4aeecbcc3c6858a93198f1fe9fe4886cb4ed1e8ae3b152bcbe3fdc2e25bbad"},"schema_version":"1.0"},"canonical_sha256":"8d096b5370db4ce84a0b03d97acfe6a8394af6f027b0118df59bd1aca7d9b26b","source":{"kind":"arxiv","id":"1004.5515","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.5515","created_at":"2026-05-18T04:32:54Z"},{"alias_kind":"arxiv_version","alias_value":"1004.5515v2","created_at":"2026-05-18T04:32:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.5515","created_at":"2026-05-18T04:32:54Z"},{"alias_kind":"pith_short_12","alias_value":"RUEWWU3Q3NGO","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"RUEWWU3Q3NGOQSQL","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"RUEWWU3Q","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:RUEWWU3Q3NGOQSQLAPMXVT7GVA","target":"record","payload":{"canonical_record":{"source":{"id":"1004.5515","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-04-30T12:37:15Z","cross_cats_sorted":[],"title_canon_sha256":"319b8e83ded519ffac136920de4db5aacd31915287b93c484b172b1b6cacb41b","abstract_canon_sha256":"be4aeecbcc3c6858a93198f1fe9fe4886cb4ed1e8ae3b152bcbe3fdc2e25bbad"},"schema_version":"1.0"},"canonical_sha256":"8d096b5370db4ce84a0b03d97acfe6a8394af6f027b0118df59bd1aca7d9b26b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:32:54.541444Z","signature_b64":"s7ynE8aG0MVSnxZRBZ3y64ISvuV1J3vonc6GwtCOKvvIacJQq8y11tdhXIJ4rHPjPG8H93EeX5yjQPciJC3FBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d096b5370db4ce84a0b03d97acfe6a8394af6f027b0118df59bd1aca7d9b26b","last_reissued_at":"2026-05-18T04:32:54.541016Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:32:54.541016Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1004.5515","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:32:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zor+f9efCsvnKzZLS0Uhg7fm3cewdE6cKuRf1/NZgUKFA1ThOZGmhE3DAPoOXqzmIsj0wG00evtf7B4BOnsPAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T19:44:59.183711Z"},"content_sha256":"7b33a54a3dc0f520e01a0653f67a870a1c874c920c2eb911a3eff6d7bb5800e4","schema_version":"1.0","event_id":"sha256:7b33a54a3dc0f520e01a0653f67a870a1c874c920c2eb911a3eff6d7bb5800e4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:RUEWWU3Q3NGOQSQLAPMXVT7GVA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Intertwining of birth-and-death processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jan M. Swart","submitted_at":"2010-04-30T12:37:15Z","abstract_excerpt":"It has been known for a long time that for birth-and-death processes started in zero the first passage time of a given level is distributed as a sum of independent exponentially distributed random variables, the parameters of which are the negatives of the eigenvalues of the stopped process. Recently, Diaconis and Miclo have given a probabilistic proof of this fact by constructing a coupling between a general birth-and-death process and a process whose birth rates are the negatives of the eigenvalues, ordered from high to low, and whose death rates are zero, in such a way that the latter proce"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.5515","kind":"arxiv","version":2},"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":"2026-05-18T04:32:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"clTO67n978QZ1JlErHfV8C0qM0HFZvUUiHMFspdKlt3Dvkn7G8G5sQI+l+1hFRFRYGCryUd1Z+/6LLzzLwGvCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T19:44:59.184055Z"},"content_sha256":"312fde39b3777e493cc70e063fa978e96902fa49d0658571fa8ec0c4ee360648","schema_version":"1.0","event_id":"sha256:312fde39b3777e493cc70e063fa978e96902fa49d0658571fa8ec0c4ee360648"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RUEWWU3Q3NGOQSQLAPMXVT7GVA/bundle.json","state_url":"https://pith.science/pith/RUEWWU3Q3NGOQSQLAPMXVT7GVA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RUEWWU3Q3NGOQSQLAPMXVT7GVA/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":"2026-05-28T19:44:59Z","links":{"resolver":"https://pith.science/pith/RUEWWU3Q3NGOQSQLAPMXVT7GVA","bundle":"https://pith.science/pith/RUEWWU3Q3NGOQSQLAPMXVT7GVA/bundle.json","state":"https://pith.science/pith/RUEWWU3Q3NGOQSQLAPMXVT7GVA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RUEWWU3Q3NGOQSQLAPMXVT7GVA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:RUEWWU3Q3NGOQSQLAPMXVT7GVA","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":"be4aeecbcc3c6858a93198f1fe9fe4886cb4ed1e8ae3b152bcbe3fdc2e25bbad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-04-30T12:37:15Z","title_canon_sha256":"319b8e83ded519ffac136920de4db5aacd31915287b93c484b172b1b6cacb41b"},"schema_version":"1.0","source":{"id":"1004.5515","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.5515","created_at":"2026-05-18T04:32:54Z"},{"alias_kind":"arxiv_version","alias_value":"1004.5515v2","created_at":"2026-05-18T04:32:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.5515","created_at":"2026-05-18T04:32:54Z"},{"alias_kind":"pith_short_12","alias_value":"RUEWWU3Q3NGO","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"RUEWWU3Q3NGOQSQL","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"RUEWWU3Q","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:312fde39b3777e493cc70e063fa978e96902fa49d0658571fa8ec0c4ee360648","target":"graph","created_at":"2026-05-18T04:32:54Z","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":"It has been known for a long time that for birth-and-death processes started in zero the first passage time of a given level is distributed as a sum of independent exponentially distributed random variables, the parameters of which are the negatives of the eigenvalues of the stopped process. Recently, Diaconis and Miclo have given a probabilistic proof of this fact by constructing a coupling between a general birth-and-death process and a process whose birth rates are the negatives of the eigenvalues, ordered from high to low, and whose death rates are zero, in such a way that the latter proce","authors_text":"Jan M. Swart","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-04-30T12:37:15Z","title":"Intertwining of birth-and-death processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.5515","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":"sha256:7b33a54a3dc0f520e01a0653f67a870a1c874c920c2eb911a3eff6d7bb5800e4","target":"record","created_at":"2026-05-18T04:32:54Z","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":"be4aeecbcc3c6858a93198f1fe9fe4886cb4ed1e8ae3b152bcbe3fdc2e25bbad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-04-30T12:37:15Z","title_canon_sha256":"319b8e83ded519ffac136920de4db5aacd31915287b93c484b172b1b6cacb41b"},"schema_version":"1.0","source":{"id":"1004.5515","kind":"arxiv","version":2}},"canonical_sha256":"8d096b5370db4ce84a0b03d97acfe6a8394af6f027b0118df59bd1aca7d9b26b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d096b5370db4ce84a0b03d97acfe6a8394af6f027b0118df59bd1aca7d9b26b","first_computed_at":"2026-05-18T04:32:54.541016Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:54.541016Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s7ynE8aG0MVSnxZRBZ3y64ISvuV1J3vonc6GwtCOKvvIacJQq8y11tdhXIJ4rHPjPG8H93EeX5yjQPciJC3FBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:54.541444Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.5515","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7b33a54a3dc0f520e01a0653f67a870a1c874c920c2eb911a3eff6d7bb5800e4","sha256:312fde39b3777e493cc70e063fa978e96902fa49d0658571fa8ec0c4ee360648"],"state_sha256":"00b2c6e4ec3cf4e7c4de6892e3ee5b7a1ff9427120dc610308e5d2c50f4c958b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aN5QaNzOdG/buUao7q/OnMhGUXLX/oYZrKQ4F/n2lgpEKD8SkJGtJgZH5U3zwmykjgTbWWWERDbmixm68fPkCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T19:44:59.185997Z","bundle_sha256":"2ecce6c507a7ec64918b5976446fae322861382edbb1c741a73f3e7ab0925829"}}