{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:YR7OO4X6SLG4WEBYGXNWPOCXVO","short_pith_number":"pith:YR7OO4X6","canonical_record":{"source":{"id":"1612.01882","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-12-06T15:56:17Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"faaabf366c8867b71cd5eabb1e66d45d04dfbf34e0d92165b24d05ae5f24b95b","abstract_canon_sha256":"ceb34c2ac9ec26dea97d9e2cb48ea7f4f6f5da6be3e5396166c146145ea01da1"},"schema_version":"1.0"},"canonical_sha256":"c47ee772fe92cdcb103835db67b857abb8f044534c9da4fc2491b252d3fc051b","source":{"kind":"arxiv","id":"1612.01882","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.01882","created_at":"2026-05-18T00:55:47Z"},{"alias_kind":"arxiv_version","alias_value":"1612.01882v1","created_at":"2026-05-18T00:55:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.01882","created_at":"2026-05-18T00:55:47Z"},{"alias_kind":"pith_short_12","alias_value":"YR7OO4X6SLG4","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YR7OO4X6SLG4WEBY","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YR7OO4X6","created_at":"2026-05-18T12:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:YR7OO4X6SLG4WEBYGXNWPOCXVO","target":"record","payload":{"canonical_record":{"source":{"id":"1612.01882","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-12-06T15:56:17Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"faaabf366c8867b71cd5eabb1e66d45d04dfbf34e0d92165b24d05ae5f24b95b","abstract_canon_sha256":"ceb34c2ac9ec26dea97d9e2cb48ea7f4f6f5da6be3e5396166c146145ea01da1"},"schema_version":"1.0"},"canonical_sha256":"c47ee772fe92cdcb103835db67b857abb8f044534c9da4fc2491b252d3fc051b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:47.456751Z","signature_b64":"gjI+D1Hidsyxx0j+W/vtzkFQHcnDVcTYI0w23weut4iU8Q9EDtQkXFC7Ce/zf/QRDb67b+kHf9sBvwLtxuHBBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c47ee772fe92cdcb103835db67b857abb8f044534c9da4fc2491b252d3fc051b","last_reissued_at":"2026-05-18T00:55:47.456297Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:47.456297Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.01882","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":"2026-05-18T00:55:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x1Er7eVfMD7m15RjJ4YrStQnOhORX/n8v/mbxvvPT8OqPzNOCc4cEnLtKmLO7abOP+96iRc8SeL+E4SKt6ViDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T19:25:40.207557Z"},"content_sha256":"3e3b900c0962d02364ab4cc388eaf6790d88245fdeb172cb468270f5f6949959","schema_version":"1.0","event_id":"sha256:3e3b900c0962d02364ab4cc388eaf6790d88245fdeb172cb468270f5f6949959"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:YR7OO4X6SLG4WEBYGXNWPOCXVO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fiducial, confidence and objective Bayesian posterior distributions for a multidimensional parameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Eugenio Melilli, Piero Veronese","submitted_at":"2016-12-06T15:56:17Z","abstract_excerpt":"We propose a way to construct fiducial distributions for a multidimensional parameter using a step-by-step conditional procedure related to the inferential importance of the components of the parameter. For discrete models, in which the non-uniqueness of the fiducial distribution is well known, we propose to use the geometric mean of the \"extreme cases\" and show its good behavior with respect to the more traditional arithmetic mean. Connections with the generalized fiducial inference approach developed by Hannig and with confidence distributions are also analyzed. The suggested procedure stron"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01882","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":"2026-05-18T00:55:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u30hp/qWudlKIMYGHXrsbC5XnH4sbX6QoNR1exdjr9U2ywVBQ774UxKJnAX7oV6mJlDj/Vci7CJbwNuyBMtHCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T19:25:40.207908Z"},"content_sha256":"c5716675053b5ce717d018575290c687d97ec4679c0e1ca9393db4f561e8f560","schema_version":"1.0","event_id":"sha256:c5716675053b5ce717d018575290c687d97ec4679c0e1ca9393db4f561e8f560"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YR7OO4X6SLG4WEBYGXNWPOCXVO/bundle.json","state_url":"https://pith.science/pith/YR7OO4X6SLG4WEBYGXNWPOCXVO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YR7OO4X6SLG4WEBYGXNWPOCXVO/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":"2026-06-24T19:25:40Z","links":{"resolver":"https://pith.science/pith/YR7OO4X6SLG4WEBYGXNWPOCXVO","bundle":"https://pith.science/pith/YR7OO4X6SLG4WEBYGXNWPOCXVO/bundle.json","state":"https://pith.science/pith/YR7OO4X6SLG4WEBYGXNWPOCXVO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YR7OO4X6SLG4WEBYGXNWPOCXVO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:YR7OO4X6SLG4WEBYGXNWPOCXVO","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":"ceb34c2ac9ec26dea97d9e2cb48ea7f4f6f5da6be3e5396166c146145ea01da1","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-12-06T15:56:17Z","title_canon_sha256":"faaabf366c8867b71cd5eabb1e66d45d04dfbf34e0d92165b24d05ae5f24b95b"},"schema_version":"1.0","source":{"id":"1612.01882","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.01882","created_at":"2026-05-18T00:55:47Z"},{"alias_kind":"arxiv_version","alias_value":"1612.01882v1","created_at":"2026-05-18T00:55:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.01882","created_at":"2026-05-18T00:55:47Z"},{"alias_kind":"pith_short_12","alias_value":"YR7OO4X6SLG4","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YR7OO4X6SLG4WEBY","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YR7OO4X6","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:c5716675053b5ce717d018575290c687d97ec4679c0e1ca9393db4f561e8f560","target":"graph","created_at":"2026-05-18T00:55:47Z","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":"We propose a way to construct fiducial distributions for a multidimensional parameter using a step-by-step conditional procedure related to the inferential importance of the components of the parameter. For discrete models, in which the non-uniqueness of the fiducial distribution is well known, we propose to use the geometric mean of the \"extreme cases\" and show its good behavior with respect to the more traditional arithmetic mean. Connections with the generalized fiducial inference approach developed by Hannig and with confidence distributions are also analyzed. The suggested procedure stron","authors_text":"Eugenio Melilli, Piero Veronese","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-12-06T15:56:17Z","title":"Fiducial, confidence and objective Bayesian posterior distributions for a multidimensional parameter"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01882","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":"sha256:3e3b900c0962d02364ab4cc388eaf6790d88245fdeb172cb468270f5f6949959","target":"record","created_at":"2026-05-18T00:55:47Z","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":"ceb34c2ac9ec26dea97d9e2cb48ea7f4f6f5da6be3e5396166c146145ea01da1","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-12-06T15:56:17Z","title_canon_sha256":"faaabf366c8867b71cd5eabb1e66d45d04dfbf34e0d92165b24d05ae5f24b95b"},"schema_version":"1.0","source":{"id":"1612.01882","kind":"arxiv","version":1}},"canonical_sha256":"c47ee772fe92cdcb103835db67b857abb8f044534c9da4fc2491b252d3fc051b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c47ee772fe92cdcb103835db67b857abb8f044534c9da4fc2491b252d3fc051b","first_computed_at":"2026-05-18T00:55:47.456297Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:47.456297Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gjI+D1Hidsyxx0j+W/vtzkFQHcnDVcTYI0w23weut4iU8Q9EDtQkXFC7Ce/zf/QRDb67b+kHf9sBvwLtxuHBBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:47.456751Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.01882","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3e3b900c0962d02364ab4cc388eaf6790d88245fdeb172cb468270f5f6949959","sha256:c5716675053b5ce717d018575290c687d97ec4679c0e1ca9393db4f561e8f560"],"state_sha256":"97e150e965ecdc1c3eba31551bfac90be4a79f884aed0807561459e1f1568694"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ll0a3t7PB2MBExOAvUIz1EgzIwmbbCgt5B5Fpzx28oOPoG2lha6Ir/tUzxA/YlUcmG3A4eC5CYIPzniP9MCCAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T19:25:40.209860Z","bundle_sha256":"37b46314a1b8cbf59bd033c28a9bdd73d40ee8fab9d34bc55bfb807716c6a86b"}}