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Naiman, James Allen Fill","submitted_at":"2019-01-17T05:03:26Z","abstract_excerpt":"For iid $d$-dimensional observations $X^{(1)}, X^{(2)}, \\ldots$ with independent Exponential$(1)$ coordinates, consider the boundary (relative to the closed positive orthant), or \"frontier\", $F_n$ of the closed Pareto record-setting (RS) region \\[ \\mbox{RS}_n := \\{0 \\leq x \\in {\\mathbb R}^d: x \\not\\prec X^{(i)}\\ \\mbox{for all $1 \\leq i \\leq n$}\\} \\] at time $n$, where $0 \\leq x$ means that $0 \\leq x_j$ for $1 \\leq j \\leq d$ and $x \\prec y$ means that $x_j < y_j$ for $1 \\leq j \\leq d$. With $x_+ := \\sum_{j = 1}^d x_j$, let \\[ F_n^- := \\min\\{x_+: x \\in F_n\\} \\quad \\mbox{and} \\quad F_n^+ := \\max\\"},"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":"1901.05620","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-01-17T05:03:26Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"0b2d759ede00c9275d0de4f0876596f41a389ec17671ee6067266e6d56715880","abstract_canon_sha256":"8d9ecfb00b5d4ca44e7e8fe6d3657f64721525273b58ebf2e1383a6a475143e7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:33.783035Z","signature_b64":"SMa6RpVT4RNtw2gi5CHO+KxR3VFfU/zHx/TgaN/6qe5YE+5hZYN5XsaYQwuwwPBltWmKkaHFWvZK5CBVc1l3Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c37c3b8a45eae8477ece9a28cfa6a5d4c27a9126ec3878b1cdc46dc71bf5ac0","last_reissued_at":"2026-05-17T23:55:33.782581Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:33.782581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Pareto Record Frontier","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"math.PR","authors_text":"Daniel Q. 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With $x_+ := \\sum_{j = 1}^d x_j$, let \\[ F_n^- := \\min\\{x_+: x \\in F_n\\} \\quad \\mbox{and} \\quad F_n^+ := \\max\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.05620","kind":"arxiv","version":2},"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":"1901.05620","created_at":"2026-05-17T23:55:33.782657+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.05620v2","created_at":"2026-05-17T23:55:33.782657+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.05620","created_at":"2026-05-17T23:55:33.782657+00:00"},{"alias_kind":"pith_short_12","alias_value":"DQ34HOFEL2XI","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_16","alias_value":"DQ34HOFEL2XII57M","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_8","alias_value":"DQ34HOFE","created_at":"2026-05-18T12:33:15.570797+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/DQ34HOFEL2XII57M5GRIZ6TKLV","json":"https://pith.science/pith/DQ34HOFEL2XII57M5GRIZ6TKLV.json","graph_json":"https://pith.science/api/pith-number/DQ34HOFEL2XII57M5GRIZ6TKLV/graph.json","events_json":"https://pith.science/api/pith-number/DQ34HOFEL2XII57M5GRIZ6TKLV/events.json","paper":"https://pith.science/paper/DQ34HOFE"},"agent_actions":{"view_html":"https://pith.science/pith/DQ34HOFEL2XII57M5GRIZ6TKLV","download_json":"https://pith.science/pith/DQ34HOFEL2XII57M5GRIZ6TKLV.json","view_paper":"https://pith.science/paper/DQ34HOFE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.05620&json=true","fetch_graph":"https://pith.science/api/pith-number/DQ34HOFEL2XII57M5GRIZ6TKLV/graph.json","fetch_events":"https://pith.science/api/pith-number/DQ34HOFEL2XII57M5GRIZ6TKLV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DQ34HOFEL2XII57M5GRIZ6TKLV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DQ34HOFEL2XII57M5GRIZ6TKLV/action/storage_attestation","attest_author":"https://pith.science/pith/DQ34HOFEL2XII57M5GRIZ6TKLV/action/author_attestation","sign_citation":"https://pith.science/pith/DQ34HOFEL2XII57M5GRIZ6TKLV/action/citation_signature","submit_replication":"https://pith.science/pith/DQ34HOFEL2XII57M5GRIZ6TKLV/action/replication_record"}},"created_at":"2026-05-17T23:55:33.782657+00:00","updated_at":"2026-05-17T23:55:33.782657+00:00"}