{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:WT5OHWDTTU2GIJUTSIQYYBVCGG","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":"159aef2064cce5d91dcf85a1c073f0bd1ca9f0303ccc42d4439a19f15bacfed3","cross_cats_sorted":["astro-ph.IM","hep-ex","stat.ME"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2025-05-10T05:50:32Z","title_canon_sha256":"503d7e0e4788b4210dd46995998f5223952d14ec45d177bbaf034f103164dd2b"},"schema_version":"1.0","source":{"id":"2505.06521","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.06521","created_at":"2026-07-05T11:56:56Z"},{"alias_kind":"arxiv_version","alias_value":"2505.06521v2","created_at":"2026-07-05T11:56:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.06521","created_at":"2026-07-05T11:56:56Z"},{"alias_kind":"pith_short_12","alias_value":"WT5OHWDTTU2G","created_at":"2026-07-05T11:56:56Z"},{"alias_kind":"pith_short_16","alias_value":"WT5OHWDTTU2GIJUT","created_at":"2026-07-05T11:56:56Z"},{"alias_kind":"pith_short_8","alias_value":"WT5OHWDT","created_at":"2026-07-05T11:56:56Z"}],"graph_snapshots":[{"event_id":"sha256:85f26280c004a29081457f0b60139c58b0e76cac8a55fa9de0ef43faab19eb8d","target":"graph","created_at":"2026-07-05T11:56:56Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2505.06521/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"When combining apparently inconsistent experimental results, one often implements errors on errors. The Particle Data Group's phenomenological prescription offers a practical solution but lacks a firm theoretical foundation. To address this, D'Agostini and Cowan have proposed Bayesian and frequentist approaches, respectively, both introducing gamma-distributed auxiliary variables to model uncertainty in quoted errors. In this Letter, we show that these two formulations admit a parameter-by-parameter correspondence, and are structurally equivalent. This identification clarifies how Bayesian pri","authors_text":"Kin-ya Oda, Satoshi Mishima","cross_cats":["astro-ph.IM","hep-ex","stat.ME"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2025-05-10T05:50:32Z","title":"Implementing Errors on Errors: Bayesian vs Frequentist"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.06521","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:c58fbc2674fbd61a1d3786a7f8914597942e8aed8479100bdf6874728b81bfbe","target":"record","created_at":"2026-07-05T11:56:56Z","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":"159aef2064cce5d91dcf85a1c073f0bd1ca9f0303ccc42d4439a19f15bacfed3","cross_cats_sorted":["astro-ph.IM","hep-ex","stat.ME"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2025-05-10T05:50:32Z","title_canon_sha256":"503d7e0e4788b4210dd46995998f5223952d14ec45d177bbaf034f103164dd2b"},"schema_version":"1.0","source":{"id":"2505.06521","kind":"arxiv","version":2}},"canonical_sha256":"b4fae3d8739d3464269392218c06a231b141783f61783bf27300ba1419c456b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b4fae3d8739d3464269392218c06a231b141783f61783bf27300ba1419c456b5","first_computed_at":"2026-07-05T11:56:56.868160Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:56:56.868160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F0r5wi0Gz82aF2ToCDxm7Y7UQt+uxo/G/H/6Acy44YskVFrYf8pA1Vb2yK4nd59rCSMxO9Ivkgy3pArRh9XiCg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:56:56.868772Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.06521","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c58fbc2674fbd61a1d3786a7f8914597942e8aed8479100bdf6874728b81bfbe","sha256:85f26280c004a29081457f0b60139c58b0e76cac8a55fa9de0ef43faab19eb8d"],"state_sha256":"87d76cbd5937bfef4fd98ad8b1dfdaa31a1c8a5a7d046125daaab2dc1630be95"}