{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:RBFOPVRPPL56FLARAZPPERZZEQ","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":"1006c8f40b6b8c4976e238635b6b132d62d42efb0df336ef4de4bb6b8f44daf3","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-11-20T06:19:13Z","title_canon_sha256":"fa5f4d2fe4126ecd29d545c923a65b9bec25a27a6b17feee5cc7fa0de0cfd16e"},"schema_version":"1.0","source":{"id":"2411.13062","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.13062","created_at":"2026-07-05T09:41:45Z"},{"alias_kind":"arxiv_version","alias_value":"2411.13062v2","created_at":"2026-07-05T09:41:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.13062","created_at":"2026-07-05T09:41:45Z"},{"alias_kind":"pith_short_12","alias_value":"RBFOPVRPPL56","created_at":"2026-07-05T09:41:45Z"},{"alias_kind":"pith_short_16","alias_value":"RBFOPVRPPL56FLAR","created_at":"2026-07-05T09:41:45Z"},{"alias_kind":"pith_short_8","alias_value":"RBFOPVRP","created_at":"2026-07-05T09:41:45Z"}],"graph_snapshots":[{"event_id":"sha256:7052eb725ce428fbcb2f00726d49d7214f30bdf2b10a56cd2739003855afed76","target":"graph","created_at":"2026-07-05T09:41:45Z","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/2411.13062/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 the sum of $\\epsilon$-independent random variables, extending both the classical and free probability setting. Central to our approach is the use of graphon limits to characterize the limiting distribution, which depends on the asymptotic structure of the underlying graphs governing $\\epsilon$-independence. This framework yields a range of exotic limit laws, interpolating between free and classical cases and allowing for mixtures such as free and classical convolutions of the semi-circle and Gaussian distributions. We provide a complete characterization","authors_text":"Guillaume C\\'ebron, Patrick Oliveira Santos, Pierre Youssef","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-11-20T06:19:13Z","title":"Graphon-Theoretic Approach to Central Limit Theorems for $\\epsilon$-Independence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.13062","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:d1ce38070ab0b7d5d1905ce2c58034003bdf71bf5886a6bf68fa46e9796b47e4","target":"record","created_at":"2026-07-05T09:41:45Z","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":"1006c8f40b6b8c4976e238635b6b132d62d42efb0df336ef4de4bb6b8f44daf3","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-11-20T06:19:13Z","title_canon_sha256":"fa5f4d2fe4126ecd29d545c923a65b9bec25a27a6b17feee5cc7fa0de0cfd16e"},"schema_version":"1.0","source":{"id":"2411.13062","kind":"arxiv","version":2}},"canonical_sha256":"884ae7d62f7afbe2ac11065ef2473924342b7d40d89fdc784a0f42e96a9dd317","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"884ae7d62f7afbe2ac11065ef2473924342b7d40d89fdc784a0f42e96a9dd317","first_computed_at":"2026-07-05T09:41:45.286713Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:41:45.286713Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mf5p0BesJv3UpX66BHG08tm7cyEGh2b0+dhsTqI1YFSOXHwB9d2Z1VaXY8j+UA+2wOt2xKRN3LPdkrAWc+aYDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:41:45.287137Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.13062","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d1ce38070ab0b7d5d1905ce2c58034003bdf71bf5886a6bf68fa46e9796b47e4","sha256:7052eb725ce428fbcb2f00726d49d7214f30bdf2b10a56cd2739003855afed76"],"state_sha256":"41f6053320e7c6059e4d67720576e42c679885ffe64c8e8c50620a8e1e33762d"}