{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:7WWTR4V52HBJ3UUZZBN3QFWL6K","short_pith_number":"pith:7WWTR4V5","canonical_record":{"source":{"id":"1710.08933","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-10-24T18:07:05Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"e356a62c66be9a9a03993da2bfd3435ae035a65373ec10778d5dcdc5daa281ad","abstract_canon_sha256":"fd861069b4a8b25f5d593e7e0e25e27806165a210043b8449edf53df5b89505b"},"schema_version":"1.0"},"canonical_sha256":"fdad38f2bdd1c29dd299c85bb816cbf283cb05fc54556b12c2002e60fe9a5602","source":{"kind":"arxiv","id":"1710.08933","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.08933","created_at":"2026-05-18T00:28:51Z"},{"alias_kind":"arxiv_version","alias_value":"1710.08933v2","created_at":"2026-05-18T00:28:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.08933","created_at":"2026-05-18T00:28:51Z"},{"alias_kind":"pith_short_12","alias_value":"7WWTR4V52HBJ","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7WWTR4V52HBJ3UUZ","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7WWTR4V5","created_at":"2026-05-18T12:31:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:7WWTR4V52HBJ3UUZZBN3QFWL6K","target":"record","payload":{"canonical_record":{"source":{"id":"1710.08933","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-10-24T18:07:05Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"e356a62c66be9a9a03993da2bfd3435ae035a65373ec10778d5dcdc5daa281ad","abstract_canon_sha256":"fd861069b4a8b25f5d593e7e0e25e27806165a210043b8449edf53df5b89505b"},"schema_version":"1.0"},"canonical_sha256":"fdad38f2bdd1c29dd299c85bb816cbf283cb05fc54556b12c2002e60fe9a5602","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:51.989141Z","signature_b64":"12L4SN+pLbCLsLpe3AqJjJ8OxWqT7bikF08t7/tj9TIqvixM+da1RpaZcUQUWQ7jR1gFuNbMjc2WdLl9shQsBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fdad38f2bdd1c29dd299c85bb816cbf283cb05fc54556b12c2002e60fe9a5602","last_reissued_at":"2026-05-18T00:28:51.988617Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:51.988617Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.08933","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":"2026-05-18T00:28:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eFgW6f1W8uRcYzCZ9ebcs2OxVFNQ6JmEP/C5A2gZmM5/NCxuLdmdf33y+Fdv+HqnKvYgJmKkzk9Zx6J8WOqqDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T18:58:04.497083Z"},"content_sha256":"642f91669110809d89feca377b52f1be240a41e2de39567536db470c20fc048f","schema_version":"1.0","event_id":"sha256:642f91669110809d89feca377b52f1be240a41e2de39567536db470c20fc048f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:7WWTR4V52HBJ3UUZZBN3QFWL6K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Improper posteriors are not improper","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Bo H. Lindqvist, Gunnar Taraldsen, Jarle Tufto","submitted_at":"2017-10-24T18:07:05Z","abstract_excerpt":"In 1933 Kolmogorov constructed a general theory that defines the modern concept of conditional expectation. In 1955 Renyi fomulated a new axiomatic theory for probability motivated by the need to include unbounded measures. We introduce a general concept of conditional expectation in Renyi spaces. In this theory improper priors are allowed, and the resulting posterior can also be improper.\n  In 1965 Lindley published his classic text on Bayesian statistics using the theory of Renyi, but retracted this idea in 1973 due to the appearance of marginalization paradoxes presented by Dawid, Stone, an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.08933","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":"2026-05-18T00:28:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ezR0pvinWpMmPu1jk7wvd/Lc7IM/+JXhqJ036thhcQWYBpgP5riR09zyMoQDEayquTXQNXKkKOZRZGZPCGgnCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T18:58:04.497459Z"},"content_sha256":"c6cbe73fa9a791a1fe9560763f04b427e7c873b5d8fd4544d29469da791a9de5","schema_version":"1.0","event_id":"sha256:c6cbe73fa9a791a1fe9560763f04b427e7c873b5d8fd4544d29469da791a9de5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7WWTR4V52HBJ3UUZZBN3QFWL6K/bundle.json","state_url":"https://pith.science/pith/7WWTR4V52HBJ3UUZZBN3QFWL6K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7WWTR4V52HBJ3UUZZBN3QFWL6K/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":"2026-07-03T18:58:04Z","links":{"resolver":"https://pith.science/pith/7WWTR4V52HBJ3UUZZBN3QFWL6K","bundle":"https://pith.science/pith/7WWTR4V52HBJ3UUZZBN3QFWL6K/bundle.json","state":"https://pith.science/pith/7WWTR4V52HBJ3UUZZBN3QFWL6K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7WWTR4V52HBJ3UUZZBN3QFWL6K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7WWTR4V52HBJ3UUZZBN3QFWL6K","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":"fd861069b4a8b25f5d593e7e0e25e27806165a210043b8449edf53df5b89505b","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-10-24T18:07:05Z","title_canon_sha256":"e356a62c66be9a9a03993da2bfd3435ae035a65373ec10778d5dcdc5daa281ad"},"schema_version":"1.0","source":{"id":"1710.08933","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.08933","created_at":"2026-05-18T00:28:51Z"},{"alias_kind":"arxiv_version","alias_value":"1710.08933v2","created_at":"2026-05-18T00:28:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.08933","created_at":"2026-05-18T00:28:51Z"},{"alias_kind":"pith_short_12","alias_value":"7WWTR4V52HBJ","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7WWTR4V52HBJ3UUZ","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7WWTR4V5","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:c6cbe73fa9a791a1fe9560763f04b427e7c873b5d8fd4544d29469da791a9de5","target":"graph","created_at":"2026-05-18T00:28:51Z","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 1933 Kolmogorov constructed a general theory that defines the modern concept of conditional expectation. In 1955 Renyi fomulated a new axiomatic theory for probability motivated by the need to include unbounded measures. We introduce a general concept of conditional expectation in Renyi spaces. In this theory improper priors are allowed, and the resulting posterior can also be improper.\n  In 1965 Lindley published his classic text on Bayesian statistics using the theory of Renyi, but retracted this idea in 1973 due to the appearance of marginalization paradoxes presented by Dawid, Stone, an","authors_text":"Bo H. Lindqvist, Gunnar Taraldsen, Jarle Tufto","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-10-24T18:07:05Z","title":"Improper posteriors are not improper"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.08933","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":"sha256:642f91669110809d89feca377b52f1be240a41e2de39567536db470c20fc048f","target":"record","created_at":"2026-05-18T00:28:51Z","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":"fd861069b4a8b25f5d593e7e0e25e27806165a210043b8449edf53df5b89505b","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-10-24T18:07:05Z","title_canon_sha256":"e356a62c66be9a9a03993da2bfd3435ae035a65373ec10778d5dcdc5daa281ad"},"schema_version":"1.0","source":{"id":"1710.08933","kind":"arxiv","version":2}},"canonical_sha256":"fdad38f2bdd1c29dd299c85bb816cbf283cb05fc54556b12c2002e60fe9a5602","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fdad38f2bdd1c29dd299c85bb816cbf283cb05fc54556b12c2002e60fe9a5602","first_computed_at":"2026-05-18T00:28:51.988617Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:51.988617Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"12L4SN+pLbCLsLpe3AqJjJ8OxWqT7bikF08t7/tj9TIqvixM+da1RpaZcUQUWQ7jR1gFuNbMjc2WdLl9shQsBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:51.989141Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.08933","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:642f91669110809d89feca377b52f1be240a41e2de39567536db470c20fc048f","sha256:c6cbe73fa9a791a1fe9560763f04b427e7c873b5d8fd4544d29469da791a9de5"],"state_sha256":"914223cbb3f048c0d656f63f81fdbf01128bff666b22b371d71cc369ee652d0d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FkD4n9qc5cc3Eh22EX57mkb5YaF5xFBdJh7pgRwW0OqNEppYxtz007NoDuW04P43r1UgEBnB0vphznBMrsdABg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T18:58:04.499388Z","bundle_sha256":"4cef65f288835af91d4bd16c5e6fe6eb17bbb30a8ed96691504f010dc9732c57"}}