{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:RBFOPVRPPL56FLARAZPPERZZEQ","short_pith_number":"pith:RBFOPVRP","canonical_record":{"source":{"id":"2411.13062","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-11-20T06:19:13Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"fa5f4d2fe4126ecd29d545c923a65b9bec25a27a6b17feee5cc7fa0de0cfd16e","abstract_canon_sha256":"1006c8f40b6b8c4976e238635b6b132d62d42efb0df336ef4de4bb6b8f44daf3"},"schema_version":"1.0"},"canonical_sha256":"884ae7d62f7afbe2ac11065ef2473924342b7d40d89fdc784a0f42e96a9dd317","source":{"kind":"arxiv","id":"2411.13062","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:RBFOPVRPPL56FLARAZPPERZZEQ","target":"record","payload":{"canonical_record":{"source":{"id":"2411.13062","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-11-20T06:19:13Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"fa5f4d2fe4126ecd29d545c923a65b9bec25a27a6b17feee5cc7fa0de0cfd16e","abstract_canon_sha256":"1006c8f40b6b8c4976e238635b6b132d62d42efb0df336ef4de4bb6b8f44daf3"},"schema_version":"1.0"},"canonical_sha256":"884ae7d62f7afbe2ac11065ef2473924342b7d40d89fdc784a0f42e96a9dd317","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:41:45.287137Z","signature_b64":"mf5p0BesJv3UpX66BHG08tm7cyEGh2b0+dhsTqI1YFSOXHwB9d2Z1VaXY8j+UA+2wOt2xKRN3LPdkrAWc+aYDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"884ae7d62f7afbe2ac11065ef2473924342b7d40d89fdc784a0f42e96a9dd317","last_reissued_at":"2026-07-05T09:41:45.286713Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:41:45.286713Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.13062","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:41:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jfwnGdjED8cYKWiiBplxaXtPfcxzSPvNwE+1VwxxIvk2TrNeEAnfMbyr/z63TjYud755wy6r1JPhXil+h8moAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T11:03:34.219917Z"},"content_sha256":"d1ce38070ab0b7d5d1905ce2c58034003bdf71bf5886a6bf68fa46e9796b47e4","schema_version":"1.0","event_id":"sha256:d1ce38070ab0b7d5d1905ce2c58034003bdf71bf5886a6bf68fa46e9796b47e4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:RBFOPVRPPL56FLARAZPPERZZEQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Graphon-Theoretic Approach to Central Limit Theorems for $\\epsilon$-Independence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.PR","authors_text":"Guillaume C\\'ebron, Patrick Oliveira Santos, Pierre Youssef","submitted_at":"2024-11-20T06:19:13Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.13062","kind":"arxiv","version":2},"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/2411.13062/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:41:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bB7o95QqoOewgOzc/2MoHr1025Xgf/Nwfwd0DPqBiAy3ueleS28u35rjCNVj6qzHfXYCsVCtEtgknOwUrzSnDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T11:03:34.220526Z"},"content_sha256":"7052eb725ce428fbcb2f00726d49d7214f30bdf2b10a56cd2739003855afed76","schema_version":"1.0","event_id":"sha256:7052eb725ce428fbcb2f00726d49d7214f30bdf2b10a56cd2739003855afed76"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RBFOPVRPPL56FLARAZPPERZZEQ/bundle.json","state_url":"https://pith.science/pith/RBFOPVRPPL56FLARAZPPERZZEQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RBFOPVRPPL56FLARAZPPERZZEQ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-08T11:03:34Z","links":{"resolver":"https://pith.science/pith/RBFOPVRPPL56FLARAZPPERZZEQ","bundle":"https://pith.science/pith/RBFOPVRPPL56FLARAZPPERZZEQ/bundle.json","state":"https://pith.science/pith/RBFOPVRPPL56FLARAZPPERZZEQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RBFOPVRPPL56FLARAZPPERZZEQ/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mQ6kJoiIgLaoycrj7nN8gbl3USqZGaefQ5LO1vImWtJrUo03hmUYnWOx8J2DrEy+4xAMZzRpI5OHnp8FU3EoDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T11:03:34.225378Z","bundle_sha256":"6fbf71bc25bf0b062d6067dc5ca12cddc177071fddec2c7cabafe9f9006f1fe9"}}