{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:4WZRYKYETRJUI2OC3PW2VIMZCL","short_pith_number":"pith:4WZRYKYE","canonical_record":{"source":{"id":"1511.00108","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2015-10-31T10:36:41Z","cross_cats_sorted":["stat.ME"],"title_canon_sha256":"f8205a4e611179156b82d006e99ee7de7ea47d75a6d55fe3f3f0fbdab0716706","abstract_canon_sha256":"7db48c21b20a88c9f85aee42f0a20e53427eb6c9ffbcc92073810872916a8c2b"},"schema_version":"1.0"},"canonical_sha256":"e5b31c2b049c534469c2dbedaaa19912e270670c41d556abf164777373854e30","source":{"kind":"arxiv","id":"1511.00108","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.00108","created_at":"2026-05-18T01:28:13Z"},{"alias_kind":"arxiv_version","alias_value":"1511.00108v1","created_at":"2026-05-18T01:28:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.00108","created_at":"2026-05-18T01:28:13Z"},{"alias_kind":"pith_short_12","alias_value":"4WZRYKYETRJU","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4WZRYKYETRJUI2OC","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4WZRYKYE","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:4WZRYKYETRJUI2OC3PW2VIMZCL","target":"record","payload":{"canonical_record":{"source":{"id":"1511.00108","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2015-10-31T10:36:41Z","cross_cats_sorted":["stat.ME"],"title_canon_sha256":"f8205a4e611179156b82d006e99ee7de7ea47d75a6d55fe3f3f0fbdab0716706","abstract_canon_sha256":"7db48c21b20a88c9f85aee42f0a20e53427eb6c9ffbcc92073810872916a8c2b"},"schema_version":"1.0"},"canonical_sha256":"e5b31c2b049c534469c2dbedaaa19912e270670c41d556abf164777373854e30","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:13.289426Z","signature_b64":"6AoMSgkn12wLXJ8nAStrP9BZVCczlWsYecZtQJWORYf8un3xmNFW7tfVSxDANhe+7mjq2C1pwZrZZu4pkbovBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5b31c2b049c534469c2dbedaaa19912e270670c41d556abf164777373854e30","last_reissued_at":"2026-05-18T01:28:13.288834Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:13.288834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.00108","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":"2026-05-18T01:28:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AoES+FFYDfHdtDYMZDltkxK5+j+U6yBew5vTLyMGsIjtgfmvAJToygRTAN7mwDUk4FNOduesu6B3Ga+czXLpBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:38:36.180049Z"},"content_sha256":"2367677ff69be9ea2113ecb2f2ec59c7f775d9b2de212d5a850822e100297b66","schema_version":"1.0","event_id":"sha256:2367677ff69be9ea2113ecb2f2ec59c7f775d9b2de212d5a850822e100297b66"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:4WZRYKYETRJUI2OC3PW2VIMZCL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Recursive computation for evaluating the exact $p$-values of temporal and spatial scan statistics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME"],"primary_cat":"stat.CO","authors_text":"Hisayuki Hara, Kunihiko Takahashi, Satoshi Kuriki","submitted_at":"2015-10-31T10:36:41Z","abstract_excerpt":"Let $V$ be a finite set of indices, and let $B_i$, $i=1,\\ldots,m$, be subsets of $V$ such that $V=\\bigcup_{i=1}^{m}B_i$. Let $X_i$, $i\\in V$, be independent random variables, and let $X_{B_i}=(X_j)_{j\\in B_i}$. In this paper, we propose a recursive computation method to calculate the conditional expectation $E\\bigl[\\prod_{i=1}^m\\chi_i(X_{B_i}) \\,|\\, N\\bigr]$ with $N=\\sum_{i\\in V}X_i$ given, where $\\chi_i$ is an arbitrary function. Our method is based on the recursive summation/integration technique using the Markov property in statistics. To extract the Markov property, we define an undirected"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00108","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":"2026-05-18T01:28:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+kL/jrnMCGMQ5xX9daDQC53OxRRU5ARWgiELyRbVOX6XpJ6hF7jcAIAAT2yjAhDkt/CH1gujnq+clxUnRnv7DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:38:36.180667Z"},"content_sha256":"8e42aebccb4f4a87944952956feb4d18183f5599fdb41b12121dd8c970c91634","schema_version":"1.0","event_id":"sha256:8e42aebccb4f4a87944952956feb4d18183f5599fdb41b12121dd8c970c91634"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4WZRYKYETRJUI2OC3PW2VIMZCL/bundle.json","state_url":"https://pith.science/pith/4WZRYKYETRJUI2OC3PW2VIMZCL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4WZRYKYETRJUI2OC3PW2VIMZCL/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":"2026-05-27T20:38:36Z","links":{"resolver":"https://pith.science/pith/4WZRYKYETRJUI2OC3PW2VIMZCL","bundle":"https://pith.science/pith/4WZRYKYETRJUI2OC3PW2VIMZCL/bundle.json","state":"https://pith.science/pith/4WZRYKYETRJUI2OC3PW2VIMZCL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4WZRYKYETRJUI2OC3PW2VIMZCL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4WZRYKYETRJUI2OC3PW2VIMZCL","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":"7db48c21b20a88c9f85aee42f0a20e53427eb6c9ffbcc92073810872916a8c2b","cross_cats_sorted":["stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2015-10-31T10:36:41Z","title_canon_sha256":"f8205a4e611179156b82d006e99ee7de7ea47d75a6d55fe3f3f0fbdab0716706"},"schema_version":"1.0","source":{"id":"1511.00108","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.00108","created_at":"2026-05-18T01:28:13Z"},{"alias_kind":"arxiv_version","alias_value":"1511.00108v1","created_at":"2026-05-18T01:28:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.00108","created_at":"2026-05-18T01:28:13Z"},{"alias_kind":"pith_short_12","alias_value":"4WZRYKYETRJU","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4WZRYKYETRJUI2OC","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4WZRYKYE","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:8e42aebccb4f4a87944952956feb4d18183f5599fdb41b12121dd8c970c91634","target":"graph","created_at":"2026-05-18T01:28:13Z","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":"Let $V$ be a finite set of indices, and let $B_i$, $i=1,\\ldots,m$, be subsets of $V$ such that $V=\\bigcup_{i=1}^{m}B_i$. Let $X_i$, $i\\in V$, be independent random variables, and let $X_{B_i}=(X_j)_{j\\in B_i}$. In this paper, we propose a recursive computation method to calculate the conditional expectation $E\\bigl[\\prod_{i=1}^m\\chi_i(X_{B_i}) \\,|\\, N\\bigr]$ with $N=\\sum_{i\\in V}X_i$ given, where $\\chi_i$ is an arbitrary function. Our method is based on the recursive summation/integration technique using the Markov property in statistics. To extract the Markov property, we define an undirected","authors_text":"Hisayuki Hara, Kunihiko Takahashi, Satoshi Kuriki","cross_cats":["stat.ME"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2015-10-31T10:36:41Z","title":"Recursive computation for evaluating the exact $p$-values of temporal and spatial scan statistics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00108","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":"sha256:2367677ff69be9ea2113ecb2f2ec59c7f775d9b2de212d5a850822e100297b66","target":"record","created_at":"2026-05-18T01:28:13Z","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":"7db48c21b20a88c9f85aee42f0a20e53427eb6c9ffbcc92073810872916a8c2b","cross_cats_sorted":["stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2015-10-31T10:36:41Z","title_canon_sha256":"f8205a4e611179156b82d006e99ee7de7ea47d75a6d55fe3f3f0fbdab0716706"},"schema_version":"1.0","source":{"id":"1511.00108","kind":"arxiv","version":1}},"canonical_sha256":"e5b31c2b049c534469c2dbedaaa19912e270670c41d556abf164777373854e30","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5b31c2b049c534469c2dbedaaa19912e270670c41d556abf164777373854e30","first_computed_at":"2026-05-18T01:28:13.288834Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:13.288834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6AoMSgkn12wLXJ8nAStrP9BZVCczlWsYecZtQJWORYf8un3xmNFW7tfVSxDANhe+7mjq2C1pwZrZZu4pkbovBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:13.289426Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.00108","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2367677ff69be9ea2113ecb2f2ec59c7f775d9b2de212d5a850822e100297b66","sha256:8e42aebccb4f4a87944952956feb4d18183f5599fdb41b12121dd8c970c91634"],"state_sha256":"debf7348fe94069fa12e2f08e7d1601be221d496bbf71b44da3d50cc8d695077"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mXbwKO7dNc2L1xuuTfeuuIgf7vYI+vkEOOfBD80VSQC2jObH0+ywqzeNjS2raFwO4yEWqTnjbI8/e6rZ//cgDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T20:38:36.183859Z","bundle_sha256":"3a5777e052057d76530eae5a4085b3274e82dba335ad961507e1db0ce7bb82e0"}}