{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:6T2XO4LHSDKAOMBYAK3ZBDJCC4","short_pith_number":"pith:6T2XO4LH","canonical_record":{"source":{"id":"2502.12999","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2025-02-18T16:19:28Z","cross_cats_sorted":["cs.LG","math.ST","stat.TH"],"title_canon_sha256":"5d74ae02787b43429c5a6752885f274b4a6c2d685fb4def62ddce1ca9f8d17d4","abstract_canon_sha256":"4e03e3e54209054c44358e6af07af8654cd5155fa789698818fc81b2e4ed5678"},"schema_version":"1.0"},"canonical_sha256":"f4f577716790d407303802b7908d221711eca4246ed091f74e3094be4bed3469","source":{"kind":"arxiv","id":"2502.12999","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.12999","created_at":"2026-07-05T11:54:44Z"},{"alias_kind":"arxiv_version","alias_value":"2502.12999v3","created_at":"2026-07-05T11:54:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.12999","created_at":"2026-07-05T11:54:44Z"},{"alias_kind":"pith_short_12","alias_value":"6T2XO4LHSDKA","created_at":"2026-07-05T11:54:44Z"},{"alias_kind":"pith_short_16","alias_value":"6T2XO4LHSDKAOMBY","created_at":"2026-07-05T11:54:44Z"},{"alias_kind":"pith_short_8","alias_value":"6T2XO4LH","created_at":"2026-07-05T11:54:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:6T2XO4LHSDKAOMBYAK3ZBDJCC4","target":"record","payload":{"canonical_record":{"source":{"id":"2502.12999","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2025-02-18T16:19:28Z","cross_cats_sorted":["cs.LG","math.ST","stat.TH"],"title_canon_sha256":"5d74ae02787b43429c5a6752885f274b4a6c2d685fb4def62ddce1ca9f8d17d4","abstract_canon_sha256":"4e03e3e54209054c44358e6af07af8654cd5155fa789698818fc81b2e4ed5678"},"schema_version":"1.0"},"canonical_sha256":"f4f577716790d407303802b7908d221711eca4246ed091f74e3094be4bed3469","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:54:44.414589Z","signature_b64":"cCGVIwGxxd8i0EJeP+IfbzP3Shil6EN46MoMhdnDBjPMRi/Bbs45q/ye2Zlfkk4pKFPfzw9s5QYDehyYJPlTDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4f577716790d407303802b7908d221711eca4246ed091f74e3094be4bed3469","last_reissued_at":"2026-07-05T11:54:44.414107Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:54:44.414107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.12999","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:54:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8JCX01PvLzkjg58T3lc8ayFJ0W2z3Eqd0gASnnEOsL0aDgfU1oHDMrbvROP30pXRAb8H56nGz3xtY+4jr8sxCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-01T12:27:56.507516Z"},"content_sha256":"a218c68ab280a2fe8fe4b28f332f9dc885725cfa240db090af397a202baa09ff","schema_version":"1.0","event_id":"sha256:a218c68ab280a2fe8fe4b28f332f9dc885725cfa240db090af397a202baa09ff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:6T2XO4LHSDKAOMBYAK3ZBDJCC4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic Optimism of Random-Design Linear and Kernel Regression Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Hengrui Luo, Yunzhang Zhu","submitted_at":"2025-02-18T16:19:28Z","abstract_excerpt":"We derived the closed-form asymptotic optimism of linear regression models under random designs, and generalizes it to kernel ridge regression. Using scaled asymptotic optimism as a generic predictive model complexity measure, we studied the fundamental different behaviors of linear regression model, tangent kernel (NTK) regression model and three-layer fully connected neural networks (NN). Our contribution is two-fold: we provided theoretical ground for using scaled optimism as a model predictive complexity measure; and we show empirically that NN with ReLUs behaves differently from kernel mo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.12999","kind":"arxiv","version":3},"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/2502.12999/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":"2026-07-05T11:54:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nf8MESgjoG3Ot9xnRBp2KjRJlReRWImQVxYqFnnRNTfF7/qNDPUODKJgG7+knCGBOhP20OdpSiVBNXgQ8gcCBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-01T12:27:56.508178Z"},"content_sha256":"de1d560575ae8314d5a31e6025aca206c0de2842ffcb5651d57caeb7983298a1","schema_version":"1.0","event_id":"sha256:de1d560575ae8314d5a31e6025aca206c0de2842ffcb5651d57caeb7983298a1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6T2XO4LHSDKAOMBYAK3ZBDJCC4/bundle.json","state_url":"https://pith.science/pith/6T2XO4LHSDKAOMBYAK3ZBDJCC4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6T2XO4LHSDKAOMBYAK3ZBDJCC4/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":"2026-08-01T12:27:56Z","links":{"resolver":"https://pith.science/pith/6T2XO4LHSDKAOMBYAK3ZBDJCC4","bundle":"https://pith.science/pith/6T2XO4LHSDKAOMBYAK3ZBDJCC4/bundle.json","state":"https://pith.science/pith/6T2XO4LHSDKAOMBYAK3ZBDJCC4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6T2XO4LHSDKAOMBYAK3ZBDJCC4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:6T2XO4LHSDKAOMBYAK3ZBDJCC4","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":"4e03e3e54209054c44358e6af07af8654cd5155fa789698818fc81b2e4ed5678","cross_cats_sorted":["cs.LG","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2025-02-18T16:19:28Z","title_canon_sha256":"5d74ae02787b43429c5a6752885f274b4a6c2d685fb4def62ddce1ca9f8d17d4"},"schema_version":"1.0","source":{"id":"2502.12999","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.12999","created_at":"2026-07-05T11:54:44Z"},{"alias_kind":"arxiv_version","alias_value":"2502.12999v3","created_at":"2026-07-05T11:54:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.12999","created_at":"2026-07-05T11:54:44Z"},{"alias_kind":"pith_short_12","alias_value":"6T2XO4LHSDKA","created_at":"2026-07-05T11:54:44Z"},{"alias_kind":"pith_short_16","alias_value":"6T2XO4LHSDKAOMBY","created_at":"2026-07-05T11:54:44Z"},{"alias_kind":"pith_short_8","alias_value":"6T2XO4LH","created_at":"2026-07-05T11:54:44Z"}],"graph_snapshots":[{"event_id":"sha256:de1d560575ae8314d5a31e6025aca206c0de2842ffcb5651d57caeb7983298a1","target":"graph","created_at":"2026-07-05T11:54:44Z","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/2502.12999/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We derived the closed-form asymptotic optimism of linear regression models under random designs, and generalizes it to kernel ridge regression. Using scaled asymptotic optimism as a generic predictive model complexity measure, we studied the fundamental different behaviors of linear regression model, tangent kernel (NTK) regression model and three-layer fully connected neural networks (NN). Our contribution is two-fold: we provided theoretical ground for using scaled optimism as a model predictive complexity measure; and we show empirically that NN with ReLUs behaves differently from kernel mo","authors_text":"Hengrui Luo, Yunzhang Zhu","cross_cats":["cs.LG","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2025-02-18T16:19:28Z","title":"Asymptotic Optimism of Random-Design Linear and Kernel Regression Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.12999","kind":"arxiv","version":3},"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:a218c68ab280a2fe8fe4b28f332f9dc885725cfa240db090af397a202baa09ff","target":"record","created_at":"2026-07-05T11:54:44Z","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":"4e03e3e54209054c44358e6af07af8654cd5155fa789698818fc81b2e4ed5678","cross_cats_sorted":["cs.LG","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2025-02-18T16:19:28Z","title_canon_sha256":"5d74ae02787b43429c5a6752885f274b4a6c2d685fb4def62ddce1ca9f8d17d4"},"schema_version":"1.0","source":{"id":"2502.12999","kind":"arxiv","version":3}},"canonical_sha256":"f4f577716790d407303802b7908d221711eca4246ed091f74e3094be4bed3469","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4f577716790d407303802b7908d221711eca4246ed091f74e3094be4bed3469","first_computed_at":"2026-07-05T11:54:44.414107Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:54:44.414107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cCGVIwGxxd8i0EJeP+IfbzP3Shil6EN46MoMhdnDBjPMRi/Bbs45q/ye2Zlfkk4pKFPfzw9s5QYDehyYJPlTDg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:54:44.414589Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.12999","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a218c68ab280a2fe8fe4b28f332f9dc885725cfa240db090af397a202baa09ff","sha256:de1d560575ae8314d5a31e6025aca206c0de2842ffcb5651d57caeb7983298a1"],"state_sha256":"8adecd11de4c68cb7b4cc2c924c35af67228393da674437971684898017c9aaa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tOEcrwuaiEYfUeISBvPT3gYl4y1P1JU5jN69tS8n/fOtZ3zqHxN9h3gOy2cK5MQwA9FpMLLpBQDrzmVhqkxwCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-01T12:27:56.511815Z","bundle_sha256":"db00048f7ec5a62989586ebe93f292429de98e07185ca252d6beb9fbaf89ea42"}}