{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:HJOHM4UWDVFRY5UYF5ZVAZBSGP","short_pith_number":"pith:HJOHM4UW","schema_version":"1.0","canonical_sha256":"3a5c7672961d4b1c76982f7350643233d97417f9b0d2d892ec79f33fde40ab1e","source":{"kind":"arxiv","id":"2404.19662","version":1},"attestation_state":"computed","paper":{"title":"Central Limit Theorem for tensor products of free variables","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP","math.OA"],"primary_cat":"math.PR","authors_text":"C\\'ecilia Lancien, Patrick Oliveira Santos, Pierre Youssef","submitted_at":"2024-04-30T15:57:34Z","abstract_excerpt":"We establish a central limit theorem for tensor product random variables $c_k:=a_k \\otimes a_k$, where $(a_k)_{k \\in \\mathbb{N}}$ is a free family of variables. We show that if the variables $a_k$ are centered, the limiting law is the semi-circle. Otherwise, the limiting law depends on the mean and variance of the variables $a_k$ and corresponds to a free interpolation between the semi-circle law and the classical convolution of two semi-circle laws."},"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":"2404.19662","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-04-30T15:57:34Z","cross_cats_sorted":["math-ph","math.CO","math.MP","math.OA"],"title_canon_sha256":"725bbfd51c16a1fb7e15af78a817892b7dd330f4adc118b6a10cb17dbf19d629","abstract_canon_sha256":"0b1506315cc917d7ce2f2bdca5cefb251563bc0e1a88a818a56903e642576fbf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T14:05:15.622104Z","signature_b64":"2fMwIzrkL4JOd2J/K8qrb6/ZF900CvuaK70pw7orGpSZ1T1+rXQTG1PiKw7qBgvIV5sN/sDW2v7qDZNwLWNzAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a5c7672961d4b1c76982f7350643233d97417f9b0d2d892ec79f33fde40ab1e","last_reissued_at":"2026-06-03T14:05:15.621596Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T14:05:15.621596Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Central Limit Theorem for tensor products of free variables","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP","math.OA"],"primary_cat":"math.PR","authors_text":"C\\'ecilia Lancien, Patrick Oliveira Santos, Pierre Youssef","submitted_at":"2024-04-30T15:57:34Z","abstract_excerpt":"We establish a central limit theorem for tensor product random variables $c_k:=a_k \\otimes a_k$, where $(a_k)_{k \\in \\mathbb{N}}$ is a free family of variables. We show that if the variables $a_k$ are centered, the limiting law is the semi-circle. Otherwise, the limiting law depends on the mean and variance of the variables $a_k$ and corresponds to a free interpolation between the semi-circle law and the classical convolution of two semi-circle laws."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.19662","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/2404.19662/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":"2404.19662","created_at":"2026-06-03T14:05:15.621657+00:00"},{"alias_kind":"arxiv_version","alias_value":"2404.19662v1","created_at":"2026-06-03T14:05:15.621657+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.19662","created_at":"2026-06-03T14:05:15.621657+00:00"},{"alias_kind":"pith_short_12","alias_value":"HJOHM4UWDVFR","created_at":"2026-06-03T14:05:15.621657+00:00"},{"alias_kind":"pith_short_16","alias_value":"HJOHM4UWDVFRY5UY","created_at":"2026-06-03T14:05:15.621657+00:00"},{"alias_kind":"pith_short_8","alias_value":"HJOHM4UW","created_at":"2026-06-03T14:05:15.621657+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/HJOHM4UWDVFRY5UYF5ZVAZBSGP","json":"https://pith.science/pith/HJOHM4UWDVFRY5UYF5ZVAZBSGP.json","graph_json":"https://pith.science/api/pith-number/HJOHM4UWDVFRY5UYF5ZVAZBSGP/graph.json","events_json":"https://pith.science/api/pith-number/HJOHM4UWDVFRY5UYF5ZVAZBSGP/events.json","paper":"https://pith.science/paper/HJOHM4UW"},"agent_actions":{"view_html":"https://pith.science/pith/HJOHM4UWDVFRY5UYF5ZVAZBSGP","download_json":"https://pith.science/pith/HJOHM4UWDVFRY5UYF5ZVAZBSGP.json","view_paper":"https://pith.science/paper/HJOHM4UW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2404.19662&json=true","fetch_graph":"https://pith.science/api/pith-number/HJOHM4UWDVFRY5UYF5ZVAZBSGP/graph.json","fetch_events":"https://pith.science/api/pith-number/HJOHM4UWDVFRY5UYF5ZVAZBSGP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HJOHM4UWDVFRY5UYF5ZVAZBSGP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HJOHM4UWDVFRY5UYF5ZVAZBSGP/action/storage_attestation","attest_author":"https://pith.science/pith/HJOHM4UWDVFRY5UYF5ZVAZBSGP/action/author_attestation","sign_citation":"https://pith.science/pith/HJOHM4UWDVFRY5UYF5ZVAZBSGP/action/citation_signature","submit_replication":"https://pith.science/pith/HJOHM4UWDVFRY5UYF5ZVAZBSGP/action/replication_record"}},"created_at":"2026-06-03T14:05:15.621657+00:00","updated_at":"2026-06-03T14:05:15.621657+00:00"}