{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:VYULNTD2LMNU4Y5PYYAAY3EVFP","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":"b1e78c2d2f123ee7832df6acaac5247c8c54d3e6cf0d19a3704b433d4dad24a3","cross_cats_sorted":["q-fin.RM"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.AP","submitted_at":"2026-06-16T23:51:50Z","title_canon_sha256":"541416304c3c02ed50164784220269e27250b1f11a9c89a5efb6a20a1d9728da"},"schema_version":"1.0","source":{"id":"2606.18545","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.18545","created_at":"2026-06-19T16:11:40Z"},{"alias_kind":"arxiv_version","alias_value":"2606.18545v1","created_at":"2026-06-19T16:11:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.18545","created_at":"2026-06-19T16:11:40Z"},{"alias_kind":"pith_short_12","alias_value":"VYULNTD2LMNU","created_at":"2026-06-19T16:11:40Z"},{"alias_kind":"pith_short_16","alias_value":"VYULNTD2LMNU4Y5P","created_at":"2026-06-19T16:11:40Z"},{"alias_kind":"pith_short_8","alias_value":"VYULNTD2","created_at":"2026-06-19T16:11:40Z"}],"graph_snapshots":[{"event_id":"sha256:06e98cbbfdd39d21d7841fc3452d490f8d8fad0b594e27c4ecbdaa6c9f1345d6","target":"graph","created_at":"2026-06-19T16:11:40Z","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/2606.18545/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The probabilistic reading of the cumulative accuracy profile (CAP) has a long industry lineage. Falkenstein, Boral and Carty (2000) state, in discrete form, that the default rate at a score percentile equals the portfolio average rate times the local slope of the power curve; van der Burgt (2008, 2019) formalizes this as the continuous identity $p(D\\mid x) = p_D\\, dy/dx$ and imports the continuous form as a working fact; Tasche (2009) analyzes the resulting calibration method; Voloshyn and Voloshyn (2023) substitute Bayes' theorem, $f(x\\mid D)=p(D\\mid x) f(x)/p_D$, into the area integral and w","authors_text":"Denis Burakov","cross_cats":["q-fin.RM"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.AP","submitted_at":"2026-06-16T23:51:50Z","title":"The Gini-Bayes Connection: The CAP Slope as Bayes' Theorem, with Applications to Weight of Evidence, Somers' $D$, and Calibration"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.18545","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:ec413dfa48ac984e9009cd428ab64d7cebead7d189e53e00cb1abe4efe00a2b4","target":"record","created_at":"2026-06-19T16:11:40Z","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":"b1e78c2d2f123ee7832df6acaac5247c8c54d3e6cf0d19a3704b433d4dad24a3","cross_cats_sorted":["q-fin.RM"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.AP","submitted_at":"2026-06-16T23:51:50Z","title_canon_sha256":"541416304c3c02ed50164784220269e27250b1f11a9c89a5efb6a20a1d9728da"},"schema_version":"1.0","source":{"id":"2606.18545","kind":"arxiv","version":1}},"canonical_sha256":"ae28b6cc7a5b1b4e63afc6000c6c952be02f280d3d2fedc903b7bf26db430e21","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae28b6cc7a5b1b4e63afc6000c6c952be02f280d3d2fedc903b7bf26db430e21","first_computed_at":"2026-06-19T16:11:40.542642Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:11:40.542642Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wwz38kqwn8IZ54XYrtZwhWts/IX5jWUyrogQh5oQUwkaHiHnqCkgUEnFT/J25Xy5sSEbJMbgKEzo0saXApenCw==","signature_status":"signed_v1","signed_at":"2026-06-19T16:11:40.543044Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.18545","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec413dfa48ac984e9009cd428ab64d7cebead7d189e53e00cb1abe4efe00a2b4","sha256:06e98cbbfdd39d21d7841fc3452d490f8d8fad0b594e27c4ecbdaa6c9f1345d6"],"state_sha256":"423889d889716bdba5fe3c6f6f3c0cd750802b8966ea4038b78edd568ebd38bc"}