{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:WB2UH3H5KNT3CW3AA2RNPUB2NM","short_pith_number":"pith:WB2UH3H5","canonical_record":{"source":{"id":"1103.5243","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-03-27T18:45:02Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"f5ed5f47b4662d3bf35260640e3893da148229e65afa50f3c13d6d734e40beb5","abstract_canon_sha256":"19e74b8ae1663ca17057b8ac6852bb88666ec4870cf5906cb1c1a20b55199720"},"schema_version":"1.0"},"canonical_sha256":"b07543ecfd5367b15b6006a2d7d03a6b192b4e195c7e73b7cff1222595e0696b","source":{"kind":"arxiv","id":"1103.5243","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.5243","created_at":"2026-05-18T04:25:02Z"},{"alias_kind":"arxiv_version","alias_value":"1103.5243v3","created_at":"2026-05-18T04:25:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.5243","created_at":"2026-05-18T04:25:02Z"},{"alias_kind":"pith_short_12","alias_value":"WB2UH3H5KNT3","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WB2UH3H5KNT3CW3A","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WB2UH3H5","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:WB2UH3H5KNT3CW3AA2RNPUB2NM","target":"record","payload":{"canonical_record":{"source":{"id":"1103.5243","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-03-27T18:45:02Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"f5ed5f47b4662d3bf35260640e3893da148229e65afa50f3c13d6d734e40beb5","abstract_canon_sha256":"19e74b8ae1663ca17057b8ac6852bb88666ec4870cf5906cb1c1a20b55199720"},"schema_version":"1.0"},"canonical_sha256":"b07543ecfd5367b15b6006a2d7d03a6b192b4e195c7e73b7cff1222595e0696b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:25:02.815979Z","signature_b64":"0lbE09ngSIHVTz3ZmCCsw6KVQcirALZDU+G8krh+seZL/IxJ16lS5YcSwXNcLEWswU+0RNahn9ZphNE+3i7WDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b07543ecfd5367b15b6006a2d7d03a6b192b4e195c7e73b7cff1222595e0696b","last_reissued_at":"2026-05-18T04:25:02.815309Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:25:02.815309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.5243","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:25:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t82GB2icjj1JUg6ilQLM0MXVJyWmJQLvz+py0/1QQ7E6VosNb3EINC+rlJs+pfRPK5rs+zlwN7hKdaLM6g6ZAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:41:53.211350Z"},"content_sha256":"b07f888739c4c2dd4d18c0d0f2a5300ceeb6796087dd555aa91368bb7bf3baf9","schema_version":"1.0","event_id":"sha256:b07f888739c4c2dd4d18c0d0f2a5300ceeb6796087dd555aa91368bb7bf3baf9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:WB2UH3H5KNT3CW3AA2RNPUB2NM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Raikov-Type Theorem for Radial Poisson Distributions: A Proof of Kingman's Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Thu Van Nguyen","submitted_at":"2011-03-27T18:45:02Z","abstract_excerpt":"In the present paper we prove the following conjecture in Kingman, J.F.C., Random walks with spherical symmetry, Acta Math.,109, (1963), 11-53. concerning a famous Raikov's theorem of decomposition of Poisson random variables:\n  \"If a radial sum of two independent random variables X and Y is radial Poisson, then each of them must be radial Poisson.\""},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.5243","kind":"arxiv","version":3},"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":"2026-05-18T04:25:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FrhGEVJL2HOgZNvD9Qaec+bI6W/R3xfnCyHPdr+PRNH0wQ3G3Q/WqIAIO8OwYIl+GqcEBrCcmaURhqDMgepFBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:41:53.211693Z"},"content_sha256":"e6021c527a66bfff2753edd133ad22396eacd7f88146c45313a01fb24934a4c6","schema_version":"1.0","event_id":"sha256:e6021c527a66bfff2753edd133ad22396eacd7f88146c45313a01fb24934a4c6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WB2UH3H5KNT3CW3AA2RNPUB2NM/bundle.json","state_url":"https://pith.science/pith/WB2UH3H5KNT3CW3AA2RNPUB2NM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WB2UH3H5KNT3CW3AA2RNPUB2NM/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":"2026-06-24T18:41:53Z","links":{"resolver":"https://pith.science/pith/WB2UH3H5KNT3CW3AA2RNPUB2NM","bundle":"https://pith.science/pith/WB2UH3H5KNT3CW3AA2RNPUB2NM/bundle.json","state":"https://pith.science/pith/WB2UH3H5KNT3CW3AA2RNPUB2NM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WB2UH3H5KNT3CW3AA2RNPUB2NM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:WB2UH3H5KNT3CW3AA2RNPUB2NM","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":"19e74b8ae1663ca17057b8ac6852bb88666ec4870cf5906cb1c1a20b55199720","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-03-27T18:45:02Z","title_canon_sha256":"f5ed5f47b4662d3bf35260640e3893da148229e65afa50f3c13d6d734e40beb5"},"schema_version":"1.0","source":{"id":"1103.5243","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.5243","created_at":"2026-05-18T04:25:02Z"},{"alias_kind":"arxiv_version","alias_value":"1103.5243v3","created_at":"2026-05-18T04:25:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.5243","created_at":"2026-05-18T04:25:02Z"},{"alias_kind":"pith_short_12","alias_value":"WB2UH3H5KNT3","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WB2UH3H5KNT3CW3A","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WB2UH3H5","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:e6021c527a66bfff2753edd133ad22396eacd7f88146c45313a01fb24934a4c6","target":"graph","created_at":"2026-05-18T04:25:02Z","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":"In the present paper we prove the following conjecture in Kingman, J.F.C., Random walks with spherical symmetry, Acta Math.,109, (1963), 11-53. concerning a famous Raikov's theorem of decomposition of Poisson random variables:\n  \"If a radial sum of two independent random variables X and Y is radial Poisson, then each of them must be radial Poisson.\"","authors_text":"Thu Van Nguyen","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-03-27T18:45:02Z","title":"A Raikov-Type Theorem for Radial Poisson Distributions: A Proof of Kingman's Conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.5243","kind":"arxiv","version":3},"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:b07f888739c4c2dd4d18c0d0f2a5300ceeb6796087dd555aa91368bb7bf3baf9","target":"record","created_at":"2026-05-18T04:25:02Z","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":"19e74b8ae1663ca17057b8ac6852bb88666ec4870cf5906cb1c1a20b55199720","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-03-27T18:45:02Z","title_canon_sha256":"f5ed5f47b4662d3bf35260640e3893da148229e65afa50f3c13d6d734e40beb5"},"schema_version":"1.0","source":{"id":"1103.5243","kind":"arxiv","version":3}},"canonical_sha256":"b07543ecfd5367b15b6006a2d7d03a6b192b4e195c7e73b7cff1222595e0696b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b07543ecfd5367b15b6006a2d7d03a6b192b4e195c7e73b7cff1222595e0696b","first_computed_at":"2026-05-18T04:25:02.815309Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:25:02.815309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0lbE09ngSIHVTz3ZmCCsw6KVQcirALZDU+G8krh+seZL/IxJ16lS5YcSwXNcLEWswU+0RNahn9ZphNE+3i7WDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:25:02.815979Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.5243","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b07f888739c4c2dd4d18c0d0f2a5300ceeb6796087dd555aa91368bb7bf3baf9","sha256:e6021c527a66bfff2753edd133ad22396eacd7f88146c45313a01fb24934a4c6"],"state_sha256":"762596d693a837071f10190e670d8b84e818b9ccd7d296ea5e75f1639ce848ba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D5GAYAY7mzP1ScDfXLwFNI9gEtTReZxGJaC0itqjdyU6inn/v93/QJGHRGxLo7mVZazeEANKVvfc5gKMyirSCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T18:41:53.213540Z","bundle_sha256":"de9555e45fb054394899d302e9a54356aeb79d904c9747f788ba20e7751e01c4"}}