{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:DUSH22Y3PFYMOXQ6AOM3PUUN2U","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":"ecae58cce514064a82a0e70bc144c83257bf2df27da0eadfe14a8291cd379270","cross_cats_sorted":["math.CO","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-07-02T14:05:41Z","title_canon_sha256":"ea11926563e5972fdcd1cfa20de7e3730ee849c48d2be3d4a227cd4755a38387"},"schema_version":"1.0","source":{"id":"2407.02276","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.02276","created_at":"2026-07-05T11:45:13Z"},{"alias_kind":"arxiv_version","alias_value":"2407.02276v2","created_at":"2026-07-05T11:45:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.02276","created_at":"2026-07-05T11:45:13Z"},{"alias_kind":"pith_short_12","alias_value":"DUSH22Y3PFYM","created_at":"2026-07-05T11:45:13Z"},{"alias_kind":"pith_short_16","alias_value":"DUSH22Y3PFYMOXQ6","created_at":"2026-07-05T11:45:13Z"},{"alias_kind":"pith_short_8","alias_value":"DUSH22Y3","created_at":"2026-07-05T11:45:13Z"}],"graph_snapshots":[{"event_id":"sha256:5523236038fdd405c094560c7edcb99c570c1733d51a78872f0b822c0d9af502","target":"graph","created_at":"2026-07-05T11:45:13Z","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/2407.02276/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study mixtures of free, monotone, and Boolean independence described by a directed graph $G = (V,E)$ in the context of $\\mathcal{T}$-free convolutions of Jekel and Liu. We prove general limit theorems for the associated additive convolution operations $\\boxplus_G$. For a sequence of digraphs $G_n = (V_n,E_n)$, we give sufficient conditions for the limit $\\widehat{\\mu} = \\lim_{n \\to \\infty} \\boxplus_{G_n}(\\mu_n)$ to exist whenever the Boolean convolution powers $\\mu_n^{\\uplus |V_n|}$ converge to some $\\mu$. This in particular includes central limit and Poisson limit theorems, as well as limi","authors_text":"David Jekel, Janusz Wysocza\\'nski, Lahcen Oussi","cross_cats":["math.CO","math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-07-02T14:05:41Z","title":"General limit theorems for mixtures of free, monotone, and boolean independence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.02276","kind":"arxiv","version":2},"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:d50fd6c6633904a014b53d4976b5e95166f4eff4415a56bbc5475d4c0a37196c","target":"record","created_at":"2026-07-05T11:45:13Z","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":"ecae58cce514064a82a0e70bc144c83257bf2df27da0eadfe14a8291cd379270","cross_cats_sorted":["math.CO","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-07-02T14:05:41Z","title_canon_sha256":"ea11926563e5972fdcd1cfa20de7e3730ee849c48d2be3d4a227cd4755a38387"},"schema_version":"1.0","source":{"id":"2407.02276","kind":"arxiv","version":2}},"canonical_sha256":"1d247d6b1b7970c75e1e0399b7d28dd507a4755ca6fc035eb8310ff6935d1a82","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d247d6b1b7970c75e1e0399b7d28dd507a4755ca6fc035eb8310ff6935d1a82","first_computed_at":"2026-07-05T11:45:13.227783Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:45:13.227783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N/Wbgzo294opgIHh0kREaCb7SbkG9TuyTyyoO/Hu9IfsdEjyH/poEsFaZO5iJM4E2KO5jYk4rwuEX0shkz7dBg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:45:13.228261Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.02276","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d50fd6c6633904a014b53d4976b5e95166f4eff4415a56bbc5475d4c0a37196c","sha256:5523236038fdd405c094560c7edcb99c570c1733d51a78872f0b822c0d9af502"],"state_sha256":"9f362a796ea414614579c1e4492bd745669c2cc35d6d6a26d99460394d2527a3"}