{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:2SHF3YTF4VK4LVTN6PEPVT2WPS","short_pith_number":"pith:2SHF3YTF","schema_version":"1.0","canonical_sha256":"d48e5de265e555c5d66df3c8facf567ca94e9d58bf7840fc38607f196a47b888","source":{"kind":"arxiv","id":"1603.08758","version":3},"attestation_state":"computed","paper":{"title":"Mixtures of classical and free independence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.OA","authors_text":"Janusz Wysoczanski, Roland Speicher","submitted_at":"2016-03-29T13:14:30Z","abstract_excerpt":"We revive the concept of Lambda-freeness of Mlotkowski, which describes a mixture of classical and free independence between algebras of random variables. In particular, we give a description of this in terms of cumulants; this will be instrumental in the subsequent paper [SW] where the quantum symmetries underlying these mixtures of classical and free independences will be considered."},"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":"1603.08758","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-03-29T13:14:30Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"8148348733a2cbb6a734f8af55cdfea06d5d56c5bae1568d0b4f6b54d3b69ad2","abstract_canon_sha256":"c5493615e4c7f2dfb913171855abd34fc91cd65daa6bf67af5d07fc5d9361107"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:38.139878Z","signature_b64":"947qwt4BiYl1LNb9zrjnPvazxJMelZLa7NtJaVBbA0cskTFIwaSVndPKxrgTZFDYCwTV6WRyfxZyWK4aXAb9DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d48e5de265e555c5d66df3c8facf567ca94e9d58bf7840fc38607f196a47b888","last_reissued_at":"2026-05-18T01:15:38.139036Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:38.139036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mixtures of classical and free independence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.OA","authors_text":"Janusz Wysoczanski, Roland Speicher","submitted_at":"2016-03-29T13:14:30Z","abstract_excerpt":"We revive the concept of Lambda-freeness of Mlotkowski, which describes a mixture of classical and free independence between algebras of random variables. In particular, we give a description of this in terms of cumulants; this will be instrumental in the subsequent paper [SW] where the quantum symmetries underlying these mixtures of classical and free independences will be considered."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08758","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":""},"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":"1603.08758","created_at":"2026-05-18T01:15:38.139127+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.08758v3","created_at":"2026-05-18T01:15:38.139127+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08758","created_at":"2026-05-18T01:15:38.139127+00:00"},{"alias_kind":"pith_short_12","alias_value":"2SHF3YTF4VK4","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_16","alias_value":"2SHF3YTF4VK4LVTN","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_8","alias_value":"2SHF3YTF","created_at":"2026-05-18T12:29:55.572404+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/2SHF3YTF4VK4LVTN6PEPVT2WPS","json":"https://pith.science/pith/2SHF3YTF4VK4LVTN6PEPVT2WPS.json","graph_json":"https://pith.science/api/pith-number/2SHF3YTF4VK4LVTN6PEPVT2WPS/graph.json","events_json":"https://pith.science/api/pith-number/2SHF3YTF4VK4LVTN6PEPVT2WPS/events.json","paper":"https://pith.science/paper/2SHF3YTF"},"agent_actions":{"view_html":"https://pith.science/pith/2SHF3YTF4VK4LVTN6PEPVT2WPS","download_json":"https://pith.science/pith/2SHF3YTF4VK4LVTN6PEPVT2WPS.json","view_paper":"https://pith.science/paper/2SHF3YTF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.08758&json=true","fetch_graph":"https://pith.science/api/pith-number/2SHF3YTF4VK4LVTN6PEPVT2WPS/graph.json","fetch_events":"https://pith.science/api/pith-number/2SHF3YTF4VK4LVTN6PEPVT2WPS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2SHF3YTF4VK4LVTN6PEPVT2WPS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2SHF3YTF4VK4LVTN6PEPVT2WPS/action/storage_attestation","attest_author":"https://pith.science/pith/2SHF3YTF4VK4LVTN6PEPVT2WPS/action/author_attestation","sign_citation":"https://pith.science/pith/2SHF3YTF4VK4LVTN6PEPVT2WPS/action/citation_signature","submit_replication":"https://pith.science/pith/2SHF3YTF4VK4LVTN6PEPVT2WPS/action/replication_record"}},"created_at":"2026-05-18T01:15:38.139127+00:00","updated_at":"2026-05-18T01:15:38.139127+00:00"}