{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:X5ZND7ZNZ4INMQE6TLPZMQNDS2","short_pith_number":"pith:X5ZND7ZN","canonical_record":{"source":{"id":"1603.07314","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-03-23T19:37:58Z","cross_cats_sorted":[],"title_canon_sha256":"7256cd14a3eeb1b044095b393e5accc42aefb9f060f6533ea56375c59701216e","abstract_canon_sha256":"2e996487891e5db1338da7da05d71ce5a00c984d9cfc13f111c6ec4ff06cb79e"},"schema_version":"1.0"},"canonical_sha256":"bf72d1ff2dcf10d6409e9adf9641a3968aa47e6c9215f61151beb10e24d280af","source":{"kind":"arxiv","id":"1603.07314","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.07314","created_at":"2026-05-18T01:12:34Z"},{"alias_kind":"arxiv_version","alias_value":"1603.07314v1","created_at":"2026-05-18T01:12:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07314","created_at":"2026-05-18T01:12:34Z"},{"alias_kind":"pith_short_12","alias_value":"X5ZND7ZNZ4IN","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"X5ZND7ZNZ4INMQE6","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"X5ZND7ZN","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:X5ZND7ZNZ4INMQE6TLPZMQNDS2","target":"record","payload":{"canonical_record":{"source":{"id":"1603.07314","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-03-23T19:37:58Z","cross_cats_sorted":[],"title_canon_sha256":"7256cd14a3eeb1b044095b393e5accc42aefb9f060f6533ea56375c59701216e","abstract_canon_sha256":"2e996487891e5db1338da7da05d71ce5a00c984d9cfc13f111c6ec4ff06cb79e"},"schema_version":"1.0"},"canonical_sha256":"bf72d1ff2dcf10d6409e9adf9641a3968aa47e6c9215f61151beb10e24d280af","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:34.337339Z","signature_b64":"F0s1apAxwz7vt+Eq/vxWBa+81pETa8mUptnmUOfg0krbLqilGmaYHBrwq93tQVTc6hYVpmZ6YpHb1dBcir9YBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf72d1ff2dcf10d6409e9adf9641a3968aa47e6c9215f61151beb10e24d280af","last_reissued_at":"2026-05-18T01:12:34.336893Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:34.336893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.07314","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":"2026-05-18T01:12:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FjwJalJ75Iogc/mkS3CQbx5AJ0j2gIjihuY2WKfjvM/3LTvv3FagzeoxXJadiBGUwf79cWdh0shZhfqvcMcHCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:02:19.010409Z"},"content_sha256":"870ca97b1dbc0c747d873e1d187638e9406c00ce483d7eeec995b448c854774f","schema_version":"1.0","event_id":"sha256:870ca97b1dbc0c747d873e1d187638e9406c00ce483d7eeec995b448c854774f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:X5ZND7ZNZ4INMQE6TLPZMQNDS2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Central limit theorem for a class of globally correlated random variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Adrian A. Budini","submitted_at":"2016-03-23T19:37:58Z","abstract_excerpt":"The standard central limit theorem with a Gaussian attractor for the sum of independent random variables may lose its validity in presence of strong correlations between the added random contributions. Here, we study this problem for similar interchangeable globally correlated random variables. Under these conditions, a hierarchical set of equations is derived for the conditional transition probabilities. This result allows us to define different classes of memory mechanisms that depend on a symmetric way on all involved variables. Depending on the correlation mechanisms and single statistics,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07314","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":""},"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":"2026-05-18T01:12:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KcZpMkLvHzRIm7+WHcixZj3UlpEx5OP3m3zbuoBpVXkmSWw9buZEg5XSMKCmEetsu+Yhe0T/E8cuCAh93wjQCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:02:19.011094Z"},"content_sha256":"e1455aed08301d16dadce8a5306bfd88e8fc4b43dcacef4266d1c6c39dab229f","schema_version":"1.0","event_id":"sha256:e1455aed08301d16dadce8a5306bfd88e8fc4b43dcacef4266d1c6c39dab229f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X5ZND7ZNZ4INMQE6TLPZMQNDS2/bundle.json","state_url":"https://pith.science/pith/X5ZND7ZNZ4INMQE6TLPZMQNDS2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X5ZND7ZNZ4INMQE6TLPZMQNDS2/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":"2026-05-27T11:02:19Z","links":{"resolver":"https://pith.science/pith/X5ZND7ZNZ4INMQE6TLPZMQNDS2","bundle":"https://pith.science/pith/X5ZND7ZNZ4INMQE6TLPZMQNDS2/bundle.json","state":"https://pith.science/pith/X5ZND7ZNZ4INMQE6TLPZMQNDS2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X5ZND7ZNZ4INMQE6TLPZMQNDS2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:X5ZND7ZNZ4INMQE6TLPZMQNDS2","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":"2e996487891e5db1338da7da05d71ce5a00c984d9cfc13f111c6ec4ff06cb79e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-03-23T19:37:58Z","title_canon_sha256":"7256cd14a3eeb1b044095b393e5accc42aefb9f060f6533ea56375c59701216e"},"schema_version":"1.0","source":{"id":"1603.07314","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.07314","created_at":"2026-05-18T01:12:34Z"},{"alias_kind":"arxiv_version","alias_value":"1603.07314v1","created_at":"2026-05-18T01:12:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07314","created_at":"2026-05-18T01:12:34Z"},{"alias_kind":"pith_short_12","alias_value":"X5ZND7ZNZ4IN","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"X5ZND7ZNZ4INMQE6","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"X5ZND7ZN","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:e1455aed08301d16dadce8a5306bfd88e8fc4b43dcacef4266d1c6c39dab229f","target":"graph","created_at":"2026-05-18T01:12:34Z","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"},"paper":{"abstract_excerpt":"The standard central limit theorem with a Gaussian attractor for the sum of independent random variables may lose its validity in presence of strong correlations between the added random contributions. Here, we study this problem for similar interchangeable globally correlated random variables. Under these conditions, a hierarchical set of equations is derived for the conditional transition probabilities. This result allows us to define different classes of memory mechanisms that depend on a symmetric way on all involved variables. Depending on the correlation mechanisms and single statistics,","authors_text":"Adrian A. Budini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-03-23T19:37:58Z","title":"Central limit theorem for a class of globally correlated random variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07314","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":"sha256:870ca97b1dbc0c747d873e1d187638e9406c00ce483d7eeec995b448c854774f","target":"record","created_at":"2026-05-18T01:12:34Z","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":"2e996487891e5db1338da7da05d71ce5a00c984d9cfc13f111c6ec4ff06cb79e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-03-23T19:37:58Z","title_canon_sha256":"7256cd14a3eeb1b044095b393e5accc42aefb9f060f6533ea56375c59701216e"},"schema_version":"1.0","source":{"id":"1603.07314","kind":"arxiv","version":1}},"canonical_sha256":"bf72d1ff2dcf10d6409e9adf9641a3968aa47e6c9215f61151beb10e24d280af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf72d1ff2dcf10d6409e9adf9641a3968aa47e6c9215f61151beb10e24d280af","first_computed_at":"2026-05-18T01:12:34.336893Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:34.336893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F0s1apAxwz7vt+Eq/vxWBa+81pETa8mUptnmUOfg0krbLqilGmaYHBrwq93tQVTc6hYVpmZ6YpHb1dBcir9YBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:34.337339Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.07314","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:870ca97b1dbc0c747d873e1d187638e9406c00ce483d7eeec995b448c854774f","sha256:e1455aed08301d16dadce8a5306bfd88e8fc4b43dcacef4266d1c6c39dab229f"],"state_sha256":"b9affff924ca94029c4fdb885b1bbe6f85662fc8bad3476004ed98df663fa0ff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qMkMfHNfMim+5qUMrbVPRMDZ9qLkAgMJs0bGRESHr8zOXf+596YStVJFR67uu1cs9vU9jl8o1pGMIYYfNPRFAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T11:02:19.014769Z","bundle_sha256":"02bb0cf810c9f790b49b04951de5059722ef55987e854fa6d17151c8788c5905"}}