{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:HJOHM4UWDVFRY5UYF5ZVAZBSGP","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0b1506315cc917d7ce2f2bdca5cefb251563bc0e1a88a818a56903e642576fbf","cross_cats_sorted":["math-ph","math.CO","math.MP","math.OA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-04-30T15:57:34Z","title_canon_sha256":"725bbfd51c16a1fb7e15af78a817892b7dd330f4adc118b6a10cb17dbf19d629"},"schema_version":"1.0","source":{"id":"2404.19662","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.19662","created_at":"2026-06-03T14:05:15Z"},{"alias_kind":"arxiv_version","alias_value":"2404.19662v1","created_at":"2026-06-03T14:05:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.19662","created_at":"2026-06-03T14:05:15Z"},{"alias_kind":"pith_short_12","alias_value":"HJOHM4UWDVFR","created_at":"2026-06-03T14:05:15Z"},{"alias_kind":"pith_short_16","alias_value":"HJOHM4UWDVFRY5UY","created_at":"2026-06-03T14:05:15Z"},{"alias_kind":"pith_short_8","alias_value":"HJOHM4UW","created_at":"2026-06-03T14:05:15Z"}],"graph_snapshots":[{"event_id":"sha256:cce480252e482b8185ce9c8363d7582f76915e0e95aa1f65aa6cd116953fc471","target":"graph","created_at":"2026-06-03T14:05:15Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2404.19662/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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.","authors_text":"C\\'ecilia Lancien, Patrick Oliveira Santos, Pierre Youssef","cross_cats":["math-ph","math.CO","math.MP","math.OA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-04-30T15:57:34Z","title":"Central Limit Theorem for tensor products of free variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.19662","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:55804ed6926efcdba544be8acac509945483486d4e35ad3410be7e396eb192b3","target":"record","created_at":"2026-06-03T14:05:15Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0b1506315cc917d7ce2f2bdca5cefb251563bc0e1a88a818a56903e642576fbf","cross_cats_sorted":["math-ph","math.CO","math.MP","math.OA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-04-30T15:57:34Z","title_canon_sha256":"725bbfd51c16a1fb7e15af78a817892b7dd330f4adc118b6a10cb17dbf19d629"},"schema_version":"1.0","source":{"id":"2404.19662","kind":"arxiv","version":1}},"canonical_sha256":"3a5c7672961d4b1c76982f7350643233d97417f9b0d2d892ec79f33fde40ab1e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a5c7672961d4b1c76982f7350643233d97417f9b0d2d892ec79f33fde40ab1e","first_computed_at":"2026-06-03T14:05:15.621596Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T14:05:15.621596Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2fMwIzrkL4JOd2J/K8qrb6/ZF900CvuaK70pw7orGpSZ1T1+rXQTG1PiKw7qBgvIV5sN/sDW2v7qDZNwLWNzAg==","signature_status":"signed_v1","signed_at":"2026-06-03T14:05:15.622104Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.19662","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:55804ed6926efcdba544be8acac509945483486d4e35ad3410be7e396eb192b3","sha256:cce480252e482b8185ce9c8363d7582f76915e0e95aa1f65aa6cd116953fc471"],"state_sha256":"0d761e6abcda6da4289d487830d9ee7d7ba89738a703bb7de27b4693ddbfeb39"}