{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:B5QDGN2XEPERPU7QVD6FNZIMKU","short_pith_number":"pith:B5QDGN2X","schema_version":"1.0","canonical_sha256":"0f6033375723c917d3f0a8fc56e50c552b150b5c1a77b62bcc0eb6d4baf24a02","source":{"kind":"arxiv","id":"2607.24324","version":1},"attestation_state":"computed","paper":{"title":"Diffusion Bootstrap for High-Dimensional Linear Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"stat.ME","authors_text":"Ce Liang, Wei Ma","submitted_at":"2026-07-27T12:03:48Z","abstract_excerpt":"Classical bootstrap methods can behave poorly in high-dimensional linear models: the pairs bootstrap often yields overly conservative inference, whereas the residual bootstrap can be anti-conservative, reflecting systematic failures in variance calibration. We propose a diffusion-based pairs bootstrap that replaces the empirical joint distribution with a learned generative law. We establish variance consistency under a score approximation assumption, using complementary SDE and PDE arguments. Counterexamples show that terminal $W_4$ convergence alone is insufficient for variance consistency. E"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.24324","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2026-07-27T12:03:48Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"bd4ffd42984b54026d7d18d2ce48678f937e87c6dd416c2645bca5917f826454","abstract_canon_sha256":"52a9e2c1befe8558c9d28b52147bf223cc64b0cecc0d4134743d50d186a8574a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-28T02:23:57.367708Z","signature_b64":"Jj7CtmpP+RMYYebigOVg6m2qMCzoj0JP9JHmfieqasnBfQ/SmoVRqXkkYcVDihMKOZ9kczzjFgV7eHDnye8HCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f6033375723c917d3f0a8fc56e50c552b150b5c1a77b62bcc0eb6d4baf24a02","last_reissued_at":"2026-07-28T02:23:57.366552Z","signature_status":"signed_v1","first_computed_at":"2026-07-28T02:23:57.366552Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Diffusion Bootstrap for High-Dimensional Linear Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"stat.ME","authors_text":"Ce Liang, Wei Ma","submitted_at":"2026-07-27T12:03:48Z","abstract_excerpt":"Classical bootstrap methods can behave poorly in high-dimensional linear models: the pairs bootstrap often yields overly conservative inference, whereas the residual bootstrap can be anti-conservative, reflecting systematic failures in variance calibration. We propose a diffusion-based pairs bootstrap that replaces the empirical joint distribution with a learned generative law. We establish variance consistency under a score approximation assumption, using complementary SDE and PDE arguments. Counterexamples show that terminal $W_4$ convergence alone is insufficient for variance consistency. E"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.24324","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/2607.24324/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.24324","created_at":"2026-07-28T02:23:57.367261+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.24324v1","created_at":"2026-07-28T02:23:57.367261+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.24324","created_at":"2026-07-28T02:23:57.367261+00:00"},{"alias_kind":"pith_short_12","alias_value":"B5QDGN2XEPER","created_at":"2026-07-28T02:23:57.367261+00:00"},{"alias_kind":"pith_short_16","alias_value":"B5QDGN2XEPERPU7Q","created_at":"2026-07-28T02:23:57.367261+00:00"},{"alias_kind":"pith_short_8","alias_value":"B5QDGN2X","created_at":"2026-07-28T02:23:57.367261+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/B5QDGN2XEPERPU7QVD6FNZIMKU","json":"https://pith.science/pith/B5QDGN2XEPERPU7QVD6FNZIMKU.json","graph_json":"https://pith.science/api/pith-number/B5QDGN2XEPERPU7QVD6FNZIMKU/graph.json","events_json":"https://pith.science/api/pith-number/B5QDGN2XEPERPU7QVD6FNZIMKU/events.json","paper":"https://pith.science/paper/B5QDGN2X"},"agent_actions":{"view_html":"https://pith.science/pith/B5QDGN2XEPERPU7QVD6FNZIMKU","download_json":"https://pith.science/pith/B5QDGN2XEPERPU7QVD6FNZIMKU.json","view_paper":"https://pith.science/paper/B5QDGN2X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.24324&json=true","fetch_graph":"https://pith.science/api/pith-number/B5QDGN2XEPERPU7QVD6FNZIMKU/graph.json","fetch_events":"https://pith.science/api/pith-number/B5QDGN2XEPERPU7QVD6FNZIMKU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B5QDGN2XEPERPU7QVD6FNZIMKU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B5QDGN2XEPERPU7QVD6FNZIMKU/action/storage_attestation","attest_author":"https://pith.science/pith/B5QDGN2XEPERPU7QVD6FNZIMKU/action/author_attestation","sign_citation":"https://pith.science/pith/B5QDGN2XEPERPU7QVD6FNZIMKU/action/citation_signature","submit_replication":"https://pith.science/pith/B5QDGN2XEPERPU7QVD6FNZIMKU/action/replication_record"}},"created_at":"2026-07-28T02:23:57.367261+00:00","updated_at":"2026-07-28T02:23:57.367261+00:00"}