{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:IYWLZKA6X27JMZULYGPN63GIIN","short_pith_number":"pith:IYWLZKA6","canonical_record":{"source":{"id":"2605.23664","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2026-05-22T14:13:57Z","cross_cats_sorted":[],"title_canon_sha256":"ac46d2468081646e7c166c40c3798fa5f542bbff415f510c81e1f98b53a1631d","abstract_canon_sha256":"615e2a13f096321b38b2b51253cad157e3ff39bc2b8e320bb236e23fae46889b"},"schema_version":"1.0"},"canonical_sha256":"462cbca81ebebe96668bc19edf6cc843650603d7d9c0a97849f7c064c69ee28a","source":{"kind":"arxiv","id":"2605.23664","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.23664","created_at":"2026-05-25T02:02:24Z"},{"alias_kind":"arxiv_version","alias_value":"2605.23664v1","created_at":"2026-05-25T02:02:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.23664","created_at":"2026-05-25T02:02:24Z"},{"alias_kind":"pith_short_12","alias_value":"IYWLZKA6X27J","created_at":"2026-05-25T02:02:24Z"},{"alias_kind":"pith_short_16","alias_value":"IYWLZKA6X27JMZUL","created_at":"2026-05-25T02:02:24Z"},{"alias_kind":"pith_short_8","alias_value":"IYWLZKA6","created_at":"2026-05-25T02:02:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:IYWLZKA6X27JMZULYGPN63GIIN","target":"record","payload":{"canonical_record":{"source":{"id":"2605.23664","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2026-05-22T14:13:57Z","cross_cats_sorted":[],"title_canon_sha256":"ac46d2468081646e7c166c40c3798fa5f542bbff415f510c81e1f98b53a1631d","abstract_canon_sha256":"615e2a13f096321b38b2b51253cad157e3ff39bc2b8e320bb236e23fae46889b"},"schema_version":"1.0"},"canonical_sha256":"462cbca81ebebe96668bc19edf6cc843650603d7d9c0a97849f7c064c69ee28a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-25T02:02:24.938811Z","signature_b64":"uvjW/rmTDTfWy/y9EV0CQ7uHTSkBVY5/I/+kMryx0Qjz5rqtZwcryZ5PdAY69DY2Mj8Q8fUp8EsiIi+9AFwXDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"462cbca81ebebe96668bc19edf6cc843650603d7d9c0a97849f7c064c69ee28a","last_reissued_at":"2026-05-25T02:02:24.938095Z","signature_status":"signed_v1","first_computed_at":"2026-05-25T02:02:24.938095Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.23664","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":"2026-05-25T02:02:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"irTGO19V8ExjvxKpLZVMMtekHphyzOMDBz/uN+fzby0jsDE2eIo5+KZzNx+/1Q243zEz7K8qsA/tqNb3qmTOCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T16:30:35.739817Z"},"content_sha256":"16a80c99b3c0aac6a60fbcc440999f6eedfd714be60a44130c6d2965133a909b","schema_version":"1.0","event_id":"sha256:16a80c99b3c0aac6a60fbcc440999f6eedfd714be60a44130c6d2965133a909b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:IYWLZKA6X27JMZULYGPN63GIIN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on closed-form solutions for estimating sample size when externally validating a binary prediction model based on $C$-statistic precision","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Denis A. Shah, Erick D. De Wolf, Laurence V. Madden, Pierce A. Paul","submitted_at":"2026-05-22T14:13:57Z","abstract_excerpt":"External validation of clinical prediction models is crucial for assessing whether they are fit for use. The $C$-statistic is a widely used measure of discriminative performance of such models predicting a binary outcome. A method for obtaining the minimum sample size required for the precise estimation of the $C$-statistic during validation, based on the rearrangement of Newcombe's formula for the standard error of the $C$-statistic {SE($C$)}, was recently proposed and implemented in R and Stata software via an iterative computational approach. We present seven novel closed-form solutions, de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.23664","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.23664/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-05-25T02:02:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f9ISvzmcnnRqu9TmlRpdW23o417noU2UhEU38atPMESkd3Mqqbc6iHm1sDLeSskvDO9mVWNgvy31bUwH/4GSDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T16:30:35.740208Z"},"content_sha256":"70fdc8e2f0f1add795cbfd44421e618b5b8edf38d272a2877c068fee02d2843e","schema_version":"1.0","event_id":"sha256:70fdc8e2f0f1add795cbfd44421e618b5b8edf38d272a2877c068fee02d2843e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IYWLZKA6X27JMZULYGPN63GIIN/bundle.json","state_url":"https://pith.science/pith/IYWLZKA6X27JMZULYGPN63GIIN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IYWLZKA6X27JMZULYGPN63GIIN/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":"2026-06-10T16:30:35Z","links":{"resolver":"https://pith.science/pith/IYWLZKA6X27JMZULYGPN63GIIN","bundle":"https://pith.science/pith/IYWLZKA6X27JMZULYGPN63GIIN/bundle.json","state":"https://pith.science/pith/IYWLZKA6X27JMZULYGPN63GIIN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IYWLZKA6X27JMZULYGPN63GIIN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:IYWLZKA6X27JMZULYGPN63GIIN","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":"615e2a13f096321b38b2b51253cad157e3ff39bc2b8e320bb236e23fae46889b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2026-05-22T14:13:57Z","title_canon_sha256":"ac46d2468081646e7c166c40c3798fa5f542bbff415f510c81e1f98b53a1631d"},"schema_version":"1.0","source":{"id":"2605.23664","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.23664","created_at":"2026-05-25T02:02:24Z"},{"alias_kind":"arxiv_version","alias_value":"2605.23664v1","created_at":"2026-05-25T02:02:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.23664","created_at":"2026-05-25T02:02:24Z"},{"alias_kind":"pith_short_12","alias_value":"IYWLZKA6X27J","created_at":"2026-05-25T02:02:24Z"},{"alias_kind":"pith_short_16","alias_value":"IYWLZKA6X27JMZUL","created_at":"2026-05-25T02:02:24Z"},{"alias_kind":"pith_short_8","alias_value":"IYWLZKA6","created_at":"2026-05-25T02:02:24Z"}],"graph_snapshots":[{"event_id":"sha256:70fdc8e2f0f1add795cbfd44421e618b5b8edf38d272a2877c068fee02d2843e","target":"graph","created_at":"2026-05-25T02:02:24Z","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/2605.23664/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"External validation of clinical prediction models is crucial for assessing whether they are fit for use. The $C$-statistic is a widely used measure of discriminative performance of such models predicting a binary outcome. A method for obtaining the minimum sample size required for the precise estimation of the $C$-statistic during validation, based on the rearrangement of Newcombe's formula for the standard error of the $C$-statistic {SE($C$)}, was recently proposed and implemented in R and Stata software via an iterative computational approach. We present seven novel closed-form solutions, de","authors_text":"Denis A. Shah, Erick D. De Wolf, Laurence V. Madden, Pierce A. Paul","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2026-05-22T14:13:57Z","title":"A note on closed-form solutions for estimating sample size when externally validating a binary prediction model based on $C$-statistic precision"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.23664","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":"sha256:16a80c99b3c0aac6a60fbcc440999f6eedfd714be60a44130c6d2965133a909b","target":"record","created_at":"2026-05-25T02:02:24Z","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":"615e2a13f096321b38b2b51253cad157e3ff39bc2b8e320bb236e23fae46889b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2026-05-22T14:13:57Z","title_canon_sha256":"ac46d2468081646e7c166c40c3798fa5f542bbff415f510c81e1f98b53a1631d"},"schema_version":"1.0","source":{"id":"2605.23664","kind":"arxiv","version":1}},"canonical_sha256":"462cbca81ebebe96668bc19edf6cc843650603d7d9c0a97849f7c064c69ee28a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"462cbca81ebebe96668bc19edf6cc843650603d7d9c0a97849f7c064c69ee28a","first_computed_at":"2026-05-25T02:02:24.938095Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-25T02:02:24.938095Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uvjW/rmTDTfWy/y9EV0CQ7uHTSkBVY5/I/+kMryx0Qjz5rqtZwcryZ5PdAY69DY2Mj8Q8fUp8EsiIi+9AFwXDw==","signature_status":"signed_v1","signed_at":"2026-05-25T02:02:24.938811Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.23664","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16a80c99b3c0aac6a60fbcc440999f6eedfd714be60a44130c6d2965133a909b","sha256:70fdc8e2f0f1add795cbfd44421e618b5b8edf38d272a2877c068fee02d2843e"],"state_sha256":"21b8ac039955a86c842f020d59915dc37480f13791849af99bce38315ff4ed21"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TLsBAY1alO0GeEa8DFeENKtZZfNGSz+0EZpsMZGVM1CMExYmx0dbh5jVwfFOoZ1f2c23iXCHw1J7FBpqJBJrCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T16:30:35.742655Z","bundle_sha256":"3727cac658c25671b92f6af34eb8ec62b81ac2e6942f0fdc4fcb3f91f540b6f3"}}