{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:3FO4EJ2WWSYGEGLDGNPCSALYUI","short_pith_number":"pith:3FO4EJ2W","schema_version":"1.0","canonical_sha256":"d95dc22756b4b0621963335e290178a2322aba34ff2db8283655985db5001b74","source":{"kind":"arxiv","id":"1811.10007","version":1},"attestation_state":"computed","paper":{"title":"Bi-Free Extreme Values","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.OA","authors_text":"Hao-Wei Huang, Jiun-Chau Wang","submitted_at":"2018-11-25T13:27:47Z","abstract_excerpt":"In this paper, we continue Voiculescu's recent work on the analogous extreme value theory in the context of bi-free probability theory. We derive various equivalent conditions for a bivariate distribution function to be bi-freely max-infinitely divisible. A bi-freely max-infinitely divisible distribution function can be expressed in terms of its marginals and a special form of copulas. Such a distribution function is shown to be also max-infinitely divisible in the classical sense. In addition, we characterize the set of bi-free extreme value distribution functions. A distribution function of "},"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":"1811.10007","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-11-25T13:27:47Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"d0bd833f9daeaa6b407d8d37074e7ae7bc72b5cb4ff53c47a79788c35acdb0ab","abstract_canon_sha256":"cda38a69c28307cd934dc794ede993963fb8b44393e23712a3f291537cf0d0b6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:58.885779Z","signature_b64":"q11LEKdKQQaoOk1Eoi8B4cMG/IMNHOodMkSr4QBI9EeKjKwJggvd5hkfGNQfBnew39RwsBPNHpHDXq9DHtVXDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d95dc22756b4b0621963335e290178a2322aba34ff2db8283655985db5001b74","last_reissued_at":"2026-05-17T23:59:58.885229Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:58.885229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bi-Free Extreme Values","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.OA","authors_text":"Hao-Wei Huang, Jiun-Chau Wang","submitted_at":"2018-11-25T13:27:47Z","abstract_excerpt":"In this paper, we continue Voiculescu's recent work on the analogous extreme value theory in the context of bi-free probability theory. We derive various equivalent conditions for a bivariate distribution function to be bi-freely max-infinitely divisible. A bi-freely max-infinitely divisible distribution function can be expressed in terms of its marginals and a special form of copulas. Such a distribution function is shown to be also max-infinitely divisible in the classical sense. In addition, we characterize the set of bi-free extreme value distribution functions. A distribution function of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.10007","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":"1811.10007","created_at":"2026-05-17T23:59:58.885327+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.10007v1","created_at":"2026-05-17T23:59:58.885327+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.10007","created_at":"2026-05-17T23:59:58.885327+00:00"},{"alias_kind":"pith_short_12","alias_value":"3FO4EJ2WWSYG","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_16","alias_value":"3FO4EJ2WWSYGEGLD","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_8","alias_value":"3FO4EJ2W","created_at":"2026-05-18T12:32:02.567920+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/3FO4EJ2WWSYGEGLDGNPCSALYUI","json":"https://pith.science/pith/3FO4EJ2WWSYGEGLDGNPCSALYUI.json","graph_json":"https://pith.science/api/pith-number/3FO4EJ2WWSYGEGLDGNPCSALYUI/graph.json","events_json":"https://pith.science/api/pith-number/3FO4EJ2WWSYGEGLDGNPCSALYUI/events.json","paper":"https://pith.science/paper/3FO4EJ2W"},"agent_actions":{"view_html":"https://pith.science/pith/3FO4EJ2WWSYGEGLDGNPCSALYUI","download_json":"https://pith.science/pith/3FO4EJ2WWSYGEGLDGNPCSALYUI.json","view_paper":"https://pith.science/paper/3FO4EJ2W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.10007&json=true","fetch_graph":"https://pith.science/api/pith-number/3FO4EJ2WWSYGEGLDGNPCSALYUI/graph.json","fetch_events":"https://pith.science/api/pith-number/3FO4EJ2WWSYGEGLDGNPCSALYUI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3FO4EJ2WWSYGEGLDGNPCSALYUI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3FO4EJ2WWSYGEGLDGNPCSALYUI/action/storage_attestation","attest_author":"https://pith.science/pith/3FO4EJ2WWSYGEGLDGNPCSALYUI/action/author_attestation","sign_citation":"https://pith.science/pith/3FO4EJ2WWSYGEGLDGNPCSALYUI/action/citation_signature","submit_replication":"https://pith.science/pith/3FO4EJ2WWSYGEGLDGNPCSALYUI/action/replication_record"}},"created_at":"2026-05-17T23:59:58.885327+00:00","updated_at":"2026-05-17T23:59:58.885327+00:00"}