{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:B6722UWH66Y3ADZQZK2K4EIC45","short_pith_number":"pith:B6722UWH","canonical_record":{"source":{"id":"2608.02539","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"econ.EM","submitted_at":"2026-08-03T17:28:17Z","cross_cats_sorted":["cs.LG","math.ST","stat.TH"],"title_canon_sha256":"cfe2667ebf33513e674d054c0d9857de2a4fb60a3f33fc9250ca587624b434fd","abstract_canon_sha256":"649343da9c7f4558debb4e5134185ae8c7f1aee804c5c28dca9ee983054db81d"},"schema_version":"1.0"},"canonical_sha256":"0fbfad52c7f7b1b00f30cab4ae1102e75ad7b2954883bbd6de0ff440d21d7d37","source":{"kind":"arxiv","id":"2608.02539","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.02539","created_at":"2026-08-04T02:44:04Z"},{"alias_kind":"arxiv_version","alias_value":"2608.02539v1","created_at":"2026-08-04T02:44:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.02539","created_at":"2026-08-04T02:44:04Z"},{"alias_kind":"pith_short_12","alias_value":"B6722UWH66Y3","created_at":"2026-08-04T02:44:04Z"},{"alias_kind":"pith_short_16","alias_value":"B6722UWH66Y3ADZQ","created_at":"2026-08-04T02:44:04Z"},{"alias_kind":"pith_short_8","alias_value":"B6722UWH","created_at":"2026-08-04T02:44:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:B6722UWH66Y3ADZQZK2K4EIC45","target":"record","payload":{"canonical_record":{"source":{"id":"2608.02539","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"econ.EM","submitted_at":"2026-08-03T17:28:17Z","cross_cats_sorted":["cs.LG","math.ST","stat.TH"],"title_canon_sha256":"cfe2667ebf33513e674d054c0d9857de2a4fb60a3f33fc9250ca587624b434fd","abstract_canon_sha256":"649343da9c7f4558debb4e5134185ae8c7f1aee804c5c28dca9ee983054db81d"},"schema_version":"1.0"},"canonical_sha256":"0fbfad52c7f7b1b00f30cab4ae1102e75ad7b2954883bbd6de0ff440d21d7d37","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-04T02:44:04.083892Z","signature_b64":"z1tpb/jT13fWz4VT0kEJ4tvkbqrRbpVoi9Yn8vIDDH7KVgVxyuoe+WR2ks2QIiK2J5Manbu/b7kWF+jiZpDhDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0fbfad52c7f7b1b00f30cab4ae1102e75ad7b2954883bbd6de0ff440d21d7d37","last_reissued_at":"2026-08-04T02:44:04.081723Z","signature_status":"signed_v1","first_computed_at":"2026-08-04T02:44:04.081723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.02539","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":"2026-08-04T02:44:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pb6I+hMRmx9tca8+GVV2qhYkNxLuXYtYJ5GtJvq3CJogRbz3I2KnZZwMHEmP0mppmrH9IgHSSIvxSx3v694+Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T01:57:08.324321Z"},"content_sha256":"07fe6d6905091ebadffc85cb4861f2b6a50b72835304cfb935787ab7d76981da","schema_version":"1.0","event_id":"sha256:07fe6d6905091ebadffc85cb4861f2b6a50b72835304cfb935787ab7d76981da"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:B6722UWH66Y3ADZQZK2K4EIC45","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Simple Approximation to the Distribution of the Ridge Regression Estimator","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.LG","math.ST","stat.TH"],"primary_cat":"econ.EM","authors_text":"Amilcar Velez, Haomin Yu, Jos\\'e Luis Montiel Olea, Ryan Strong, Zhuoheng Xu","submitted_at":"2026-08-03T17:28:17Z","abstract_excerpt":"We present a simple Gaussian approximation to the finite-sample distribution of the classical ridge regression estimator. Our approximation captures the fact that, in finite samples, the ridge regression estimator trades off bias and variance to reduce estimation and prediction error. Our approximation is based on nonstandard asymptotics where $i)$ we let the estimator's regularization parameter grow proportionally to the sample size; and $ii)$ we treat the population regression coefficients as \\emph{local} to the reference vector that defines the estimator's direction of shrinkage. In contras"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.02539","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/2608.02539/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":"2026-08-04T02:44:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UikJx26/V4yYMZC7NxGHffh9QsRZ4fwr05pFhpy29blzNLd0hamJF0J4ZgiQSKhCBnW79+3ujEN395bQrPi2AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T01:57:08.324857Z"},"content_sha256":"e33616d44581768f62ac16024fb09aa8a30d5dddb6f3d706da5323131f810574","schema_version":"1.0","event_id":"sha256:e33616d44581768f62ac16024fb09aa8a30d5dddb6f3d706da5323131f810574"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B6722UWH66Y3ADZQZK2K4EIC45/bundle.json","state_url":"https://pith.science/pith/B6722UWH66Y3ADZQZK2K4EIC45/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B6722UWH66Y3ADZQZK2K4EIC45/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":"2026-08-09T01:57:08Z","links":{"resolver":"https://pith.science/pith/B6722UWH66Y3ADZQZK2K4EIC45","bundle":"https://pith.science/pith/B6722UWH66Y3ADZQZK2K4EIC45/bundle.json","state":"https://pith.science/pith/B6722UWH66Y3ADZQZK2K4EIC45/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B6722UWH66Y3ADZQZK2K4EIC45/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:B6722UWH66Y3ADZQZK2K4EIC45","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":"649343da9c7f4558debb4e5134185ae8c7f1aee804c5c28dca9ee983054db81d","cross_cats_sorted":["cs.LG","math.ST","stat.TH"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"econ.EM","submitted_at":"2026-08-03T17:28:17Z","title_canon_sha256":"cfe2667ebf33513e674d054c0d9857de2a4fb60a3f33fc9250ca587624b434fd"},"schema_version":"1.0","source":{"id":"2608.02539","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.02539","created_at":"2026-08-04T02:44:04Z"},{"alias_kind":"arxiv_version","alias_value":"2608.02539v1","created_at":"2026-08-04T02:44:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.02539","created_at":"2026-08-04T02:44:04Z"},{"alias_kind":"pith_short_12","alias_value":"B6722UWH66Y3","created_at":"2026-08-04T02:44:04Z"},{"alias_kind":"pith_short_16","alias_value":"B6722UWH66Y3ADZQ","created_at":"2026-08-04T02:44:04Z"},{"alias_kind":"pith_short_8","alias_value":"B6722UWH","created_at":"2026-08-04T02:44:04Z"}],"graph_snapshots":[{"event_id":"sha256:e33616d44581768f62ac16024fb09aa8a30d5dddb6f3d706da5323131f810574","target":"graph","created_at":"2026-08-04T02:44:04Z","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/2608.02539/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a simple Gaussian approximation to the finite-sample distribution of the classical ridge regression estimator. Our approximation captures the fact that, in finite samples, the ridge regression estimator trades off bias and variance to reduce estimation and prediction error. Our approximation is based on nonstandard asymptotics where $i)$ we let the estimator's regularization parameter grow proportionally to the sample size; and $ii)$ we treat the population regression coefficients as \\emph{local} to the reference vector that defines the estimator's direction of shrinkage. In contras","authors_text":"Amilcar Velez, Haomin Yu, Jos\\'e Luis Montiel Olea, Ryan Strong, Zhuoheng Xu","cross_cats":["cs.LG","math.ST","stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"econ.EM","submitted_at":"2026-08-03T17:28:17Z","title":"A Simple Approximation to the Distribution of the Ridge Regression Estimator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.02539","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":"sha256:07fe6d6905091ebadffc85cb4861f2b6a50b72835304cfb935787ab7d76981da","target":"record","created_at":"2026-08-04T02:44:04Z","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":"649343da9c7f4558debb4e5134185ae8c7f1aee804c5c28dca9ee983054db81d","cross_cats_sorted":["cs.LG","math.ST","stat.TH"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"econ.EM","submitted_at":"2026-08-03T17:28:17Z","title_canon_sha256":"cfe2667ebf33513e674d054c0d9857de2a4fb60a3f33fc9250ca587624b434fd"},"schema_version":"1.0","source":{"id":"2608.02539","kind":"arxiv","version":1}},"canonical_sha256":"0fbfad52c7f7b1b00f30cab4ae1102e75ad7b2954883bbd6de0ff440d21d7d37","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0fbfad52c7f7b1b00f30cab4ae1102e75ad7b2954883bbd6de0ff440d21d7d37","first_computed_at":"2026-08-04T02:44:04.081723Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-04T02:44:04.081723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z1tpb/jT13fWz4VT0kEJ4tvkbqrRbpVoi9Yn8vIDDH7KVgVxyuoe+WR2ks2QIiK2J5Manbu/b7kWF+jiZpDhDg==","signature_status":"signed_v1","signed_at":"2026-08-04T02:44:04.083892Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.02539","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:07fe6d6905091ebadffc85cb4861f2b6a50b72835304cfb935787ab7d76981da","sha256:e33616d44581768f62ac16024fb09aa8a30d5dddb6f3d706da5323131f810574"],"state_sha256":"f57eecf9b99a1fb292c3b314cd4f983f5b50cf88937f785999b28ea0d2ea7007"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0xA6Jlm/8Xax8IhdOw9uQ0rKfPEqWreUnM8ioXkVsE1QGwv4z1+duxWRtVM4INPE+0YrpJfiASzv3WOc0k5xAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T01:57:08.330161Z","bundle_sha256":"9936d50fcc9d58b0089e0ca65f9031ded39e05eb9ae906634e4feceedcfd28a1"}}