{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2004:OBKY44UBQPN65PV6ASLVBWPPTW","short_pith_number":"pith:OBKY44UB","schema_version":"1.0","canonical_sha256":"70558e728183dbeebebe049750d9ef9da2b0b9485163e8d67d65fd8f001a49ac","source":{"kind":"arxiv","id":"math/0410168","version":1},"attestation_state":"computed","paper":{"title":"Measure concentration for Euclidean distance in the case of dependent random variables","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Katalin Marton","submitted_at":"2004-10-06T15:37:52Z","abstract_excerpt":"Let q^n be a continuous density function in n-dimensional Euclidean space.\n We think of q^n as the density function of some random sequence X^n with values in \\BbbR^n. For I\\subset[1,n], let X_I denote the collection of coordinates X_i, i\\in I, and let \\bar X_I denote the collection of coordinates\n X_i, i\\notin I. We denote by Q_I(x_I|\\bar x_I) the joint conditional density function of X_I, given \\bar X_I. We prove measure concentration for q^n in the case when, for an appropriate class of sets I, (i) the conditional densities Q_I(x_I|\\bar x_I), as functions of x_I, uniformly satisfy a logarit"},"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":"math/0410168","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2004-10-06T15:37:52Z","cross_cats_sorted":[],"title_canon_sha256":"0ba2300c52808ec55c41f6cd6c83415c8b8b6bed2d1fdee544257dc05b0b3a42","abstract_canon_sha256":"61bff6a634bf4e74fd4c9173fa864441693dd9c34e2352d2c9a55216050c4561"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:25.782106Z","signature_b64":"O3Lf9bPDJC1XVccyECATP7oerxZvNxTu1Ox0cQ4Yy69joHrE3lsS4uJdI7hQhLnSib4zJBqPMKSUieOTKIGCCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"70558e728183dbeebebe049750d9ef9da2b0b9485163e8d67d65fd8f001a49ac","last_reissued_at":"2026-05-18T01:05:25.781435Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:25.781435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Measure concentration for Euclidean distance in the case of dependent random variables","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Katalin Marton","submitted_at":"2004-10-06T15:37:52Z","abstract_excerpt":"Let q^n be a continuous density function in n-dimensional Euclidean space.\n We think of q^n as the density function of some random sequence X^n with values in \\BbbR^n. For I\\subset[1,n], let X_I denote the collection of coordinates X_i, i\\in I, and let \\bar X_I denote the collection of coordinates\n X_i, i\\notin I. We denote by Q_I(x_I|\\bar x_I) the joint conditional density function of X_I, given \\bar X_I. We prove measure concentration for q^n in the case when, for an appropriate class of sets I, (i) the conditional densities Q_I(x_I|\\bar x_I), as functions of x_I, uniformly satisfy a logarit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0410168","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":""},"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":"math/0410168","created_at":"2026-05-18T01:05:25.781556+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0410168v1","created_at":"2026-05-18T01:05:25.781556+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0410168","created_at":"2026-05-18T01:05:25.781556+00:00"},{"alias_kind":"pith_short_12","alias_value":"OBKY44UBQPN6","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_16","alias_value":"OBKY44UBQPN65PV6","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_8","alias_value":"OBKY44UB","created_at":"2026-05-18T12:25:52.687210+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/OBKY44UBQPN65PV6ASLVBWPPTW","json":"https://pith.science/pith/OBKY44UBQPN65PV6ASLVBWPPTW.json","graph_json":"https://pith.science/api/pith-number/OBKY44UBQPN65PV6ASLVBWPPTW/graph.json","events_json":"https://pith.science/api/pith-number/OBKY44UBQPN65PV6ASLVBWPPTW/events.json","paper":"https://pith.science/paper/OBKY44UB"},"agent_actions":{"view_html":"https://pith.science/pith/OBKY44UBQPN65PV6ASLVBWPPTW","download_json":"https://pith.science/pith/OBKY44UBQPN65PV6ASLVBWPPTW.json","view_paper":"https://pith.science/paper/OBKY44UB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0410168&json=true","fetch_graph":"https://pith.science/api/pith-number/OBKY44UBQPN65PV6ASLVBWPPTW/graph.json","fetch_events":"https://pith.science/api/pith-number/OBKY44UBQPN65PV6ASLVBWPPTW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OBKY44UBQPN65PV6ASLVBWPPTW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OBKY44UBQPN65PV6ASLVBWPPTW/action/storage_attestation","attest_author":"https://pith.science/pith/OBKY44UBQPN65PV6ASLVBWPPTW/action/author_attestation","sign_citation":"https://pith.science/pith/OBKY44UBQPN65PV6ASLVBWPPTW/action/citation_signature","submit_replication":"https://pith.science/pith/OBKY44UBQPN65PV6ASLVBWPPTW/action/replication_record"}},"created_at":"2026-05-18T01:05:25.781556+00:00","updated_at":"2026-05-18T01:05:25.781556+00:00"}