{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:CMRGA3ZTJA4UMF2SGBRKDIF5BU","short_pith_number":"pith:CMRGA3ZT","canonical_record":{"source":{"id":"2504.10059","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-04-14T10:02:14Z","cross_cats_sorted":[],"title_canon_sha256":"43e150d2cf95e4484edf7ad74b58b42ea92a191b170c98ffb231d0f6d630974e","abstract_canon_sha256":"49727f3363a5c5ec2ac5368ce5507cc34de1efbd0f250cbd91c190e180610d59"},"schema_version":"1.0"},"canonical_sha256":"1322606f3348394617523062a1a0bd0d06993c9e9e130d01caf30b5dcf0c87b2","source":{"kind":"arxiv","id":"2504.10059","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.10059","created_at":"2026-07-05T10:48:47Z"},{"alias_kind":"arxiv_version","alias_value":"2504.10059v1","created_at":"2026-07-05T10:48:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.10059","created_at":"2026-07-05T10:48:47Z"},{"alias_kind":"pith_short_12","alias_value":"CMRGA3ZTJA4U","created_at":"2026-07-05T10:48:47Z"},{"alias_kind":"pith_short_16","alias_value":"CMRGA3ZTJA4UMF2S","created_at":"2026-07-05T10:48:47Z"},{"alias_kind":"pith_short_8","alias_value":"CMRGA3ZT","created_at":"2026-07-05T10:48:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:CMRGA3ZTJA4UMF2SGBRKDIF5BU","target":"record","payload":{"canonical_record":{"source":{"id":"2504.10059","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-04-14T10:02:14Z","cross_cats_sorted":[],"title_canon_sha256":"43e150d2cf95e4484edf7ad74b58b42ea92a191b170c98ffb231d0f6d630974e","abstract_canon_sha256":"49727f3363a5c5ec2ac5368ce5507cc34de1efbd0f250cbd91c190e180610d59"},"schema_version":"1.0"},"canonical_sha256":"1322606f3348394617523062a1a0bd0d06993c9e9e130d01caf30b5dcf0c87b2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:48:47.127089Z","signature_b64":"oGAd2mG5xUequcK3N+QXMpfS/OcCnSJOdlz3n9umvnP6THtF2NGCVoqMTZVrf5Y23lQ9k5RnCmr8InFtiR+EDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1322606f3348394617523062a1a0bd0d06993c9e9e130d01caf30b5dcf0c87b2","last_reissued_at":"2026-07-05T10:48:47.126474Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:48:47.126474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2504.10059","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:48:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1SwmBPyyq8ffgq59neJGs9L1DW2RdggzOip81JK9WYxNRSRdXZCj3UMCt81P6o0gDYicxNzCe+2BYk4vOaqHCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T20:47:26.926797Z"},"content_sha256":"23820e68f6cbc9dd45cf61f9cba78f25656156376782941228437ff754123298","schema_version":"1.0","event_id":"sha256:23820e68f6cbc9dd45cf61f9cba78f25656156376782941228437ff754123298"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:CMRGA3ZTJA4UMF2SGBRKDIF5BU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Central limit theorem for $\\epsilon$-independent products and higher-order tensors","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Guillaume C\\'ebron, Patrick Oliveira Santos, Pierre Youssef","submitted_at":"2025-04-14T10:02:14Z","abstract_excerpt":"We establish a central limit theorem (CLT) for families of products of $\\epsilon$-independent random variables. We utilize graphon limits to encode the evolution of independence and characterize the limiting distribution. Our framework subsumes a wide class of dependency structures and includes, as a special case, a CLT for higher-order tensor products of free random variables. Our results extend earlier findings and recover as a special case a recent tensor-free CLT, which was obtained through the development of a tensor analogue of free probability. In contrast, our approach is more direct a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.10059","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/2504.10059/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":"2026-07-05T10:48:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CN85lADlNHOcO840dBmun4QrG1PK1JbV0dVPNT30yelxtQzpBPN/piKUTYVOjxt5PjsrOQSAMf4OVarMkkU1Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T20:47:26.927370Z"},"content_sha256":"e0fd7ef22fb89c61d08f6a51c9bde8d2133b02a42fc6993502f6eb7c3b759081","schema_version":"1.0","event_id":"sha256:e0fd7ef22fb89c61d08f6a51c9bde8d2133b02a42fc6993502f6eb7c3b759081"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CMRGA3ZTJA4UMF2SGBRKDIF5BU/bundle.json","state_url":"https://pith.science/pith/CMRGA3ZTJA4UMF2SGBRKDIF5BU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CMRGA3ZTJA4UMF2SGBRKDIF5BU/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":"2026-08-10T20:47:26Z","links":{"resolver":"https://pith.science/pith/CMRGA3ZTJA4UMF2SGBRKDIF5BU","bundle":"https://pith.science/pith/CMRGA3ZTJA4UMF2SGBRKDIF5BU/bundle.json","state":"https://pith.science/pith/CMRGA3ZTJA4UMF2SGBRKDIF5BU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CMRGA3ZTJA4UMF2SGBRKDIF5BU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:CMRGA3ZTJA4UMF2SGBRKDIF5BU","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":"49727f3363a5c5ec2ac5368ce5507cc34de1efbd0f250cbd91c190e180610d59","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-04-14T10:02:14Z","title_canon_sha256":"43e150d2cf95e4484edf7ad74b58b42ea92a191b170c98ffb231d0f6d630974e"},"schema_version":"1.0","source":{"id":"2504.10059","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.10059","created_at":"2026-07-05T10:48:47Z"},{"alias_kind":"arxiv_version","alias_value":"2504.10059v1","created_at":"2026-07-05T10:48:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.10059","created_at":"2026-07-05T10:48:47Z"},{"alias_kind":"pith_short_12","alias_value":"CMRGA3ZTJA4U","created_at":"2026-07-05T10:48:47Z"},{"alias_kind":"pith_short_16","alias_value":"CMRGA3ZTJA4UMF2S","created_at":"2026-07-05T10:48:47Z"},{"alias_kind":"pith_short_8","alias_value":"CMRGA3ZT","created_at":"2026-07-05T10:48:47Z"}],"graph_snapshots":[{"event_id":"sha256:e0fd7ef22fb89c61d08f6a51c9bde8d2133b02a42fc6993502f6eb7c3b759081","target":"graph","created_at":"2026-07-05T10:48:47Z","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/2504.10059/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish a central limit theorem (CLT) for families of products of $\\epsilon$-independent random variables. We utilize graphon limits to encode the evolution of independence and characterize the limiting distribution. Our framework subsumes a wide class of dependency structures and includes, as a special case, a CLT for higher-order tensor products of free random variables. Our results extend earlier findings and recover as a special case a recent tensor-free CLT, which was obtained through the development of a tensor analogue of free probability. In contrast, our approach is more direct a","authors_text":"Guillaume C\\'ebron, Patrick Oliveira Santos, Pierre Youssef","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-04-14T10:02:14Z","title":"Central limit theorem for $\\epsilon$-independent products and higher-order tensors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.10059","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":"sha256:23820e68f6cbc9dd45cf61f9cba78f25656156376782941228437ff754123298","target":"record","created_at":"2026-07-05T10:48:47Z","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":"49727f3363a5c5ec2ac5368ce5507cc34de1efbd0f250cbd91c190e180610d59","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-04-14T10:02:14Z","title_canon_sha256":"43e150d2cf95e4484edf7ad74b58b42ea92a191b170c98ffb231d0f6d630974e"},"schema_version":"1.0","source":{"id":"2504.10059","kind":"arxiv","version":1}},"canonical_sha256":"1322606f3348394617523062a1a0bd0d06993c9e9e130d01caf30b5dcf0c87b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1322606f3348394617523062a1a0bd0d06993c9e9e130d01caf30b5dcf0c87b2","first_computed_at":"2026-07-05T10:48:47.126474Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:48:47.126474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oGAd2mG5xUequcK3N+QXMpfS/OcCnSJOdlz3n9umvnP6THtF2NGCVoqMTZVrf5Y23lQ9k5RnCmr8InFtiR+EDg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:48:47.127089Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.10059","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23820e68f6cbc9dd45cf61f9cba78f25656156376782941228437ff754123298","sha256:e0fd7ef22fb89c61d08f6a51c9bde8d2133b02a42fc6993502f6eb7c3b759081"],"state_sha256":"3d03d4ee0033139b992d3fc6f81d039d7141138765227d87674e120c59ead4ff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hz7qZwCsGqD6dxxphgGe5bNfa1XCkZo2opVsOKEUGCvY6tXG5RoSN3ipN1ZVIbt0w3Frx0FvHm1EvcoFCc/xBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T20:47:26.933289Z","bundle_sha256":"292a6cc20d471f74fcc8c79385dbdfb76ada45a905b094eaaeb20779bb05171b"}}