{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:YZOWVNQCRCPFOPCHINWTKYRWYH","short_pith_number":"pith:YZOWVNQC","canonical_record":{"source":{"id":"1708.04129","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2017-07-31T12:16:04Z","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP","math.PR"],"title_canon_sha256":"a73eaa1f9360a3b2948c998a74c11fba0545a1b09129d318787f18dd9028e936","abstract_canon_sha256":"bd3b942d065900a9caed554f2c5ddd413b308df14b820c8ce5db5390a2ae2485"},"schema_version":"1.0"},"canonical_sha256":"c65d6ab602889e573c47436d356236c1f2b8c177684270cc90e9baef8bae0577","source":{"kind":"arxiv","id":"1708.04129","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.04129","created_at":"2026-07-05T01:01:31Z"},{"alias_kind":"arxiv_version","alias_value":"1708.04129v1","created_at":"2026-07-05T01:01:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.04129","created_at":"2026-07-05T01:01:31Z"},{"alias_kind":"pith_short_12","alias_value":"YZOWVNQCRCPF","created_at":"2026-07-05T01:01:31Z"},{"alias_kind":"pith_short_16","alias_value":"YZOWVNQCRCPFOPCH","created_at":"2026-07-05T01:01:31Z"},{"alias_kind":"pith_short_8","alias_value":"YZOWVNQC","created_at":"2026-07-05T01:01:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:YZOWVNQCRCPFOPCHINWTKYRWYH","target":"record","payload":{"canonical_record":{"source":{"id":"1708.04129","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2017-07-31T12:16:04Z","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP","math.PR"],"title_canon_sha256":"a73eaa1f9360a3b2948c998a74c11fba0545a1b09129d318787f18dd9028e936","abstract_canon_sha256":"bd3b942d065900a9caed554f2c5ddd413b308df14b820c8ce5db5390a2ae2485"},"schema_version":"1.0"},"canonical_sha256":"c65d6ab602889e573c47436d356236c1f2b8c177684270cc90e9baef8bae0577","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:01:31.784507Z","signature_b64":"yWF838/OxlqGIgoI6hD7n18xHjvgZSlC5ubcZLvQ+RdWzJHFkUZeYqY/og1vqnfzAbcwEbe3kUHo2Hx+atfNCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c65d6ab602889e573c47436d356236c1f2b8c177684270cc90e9baef8bae0577","last_reissued_at":"2026-07-05T01:01:31.784076Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:01:31.784076Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.04129","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":"2026-07-05T01:01:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zIv2B86ZLiCbERzBX6wZym1xdOvEoQvkBAxWpP24Ef92usSt1+aB6Og7Yv8xHhzXNaHuLhffxdTpTRPF+eIdCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-01T01:10:46.838935Z"},"content_sha256":"0125b58136544ab0cb1b99d91cf1d2d775fdbacd18a864e2ee7ff7b7097a9893","schema_version":"1.0","event_id":"sha256:0125b58136544ab0cb1b99d91cf1d2d775fdbacd18a864e2ee7ff7b7097a9893"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:YZOWVNQCRCPFOPCHINWTKYRWYH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classical limit theorems and high entropy MIXMAX random number generator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP","math.PR"],"primary_cat":"hep-lat","authors_text":"George Savvidy, Hayk Poghosyan, Konstantin Savvidy","submitted_at":"2017-07-31T12:16:04Z","abstract_excerpt":"We investigate the interrelation between the distribution of stochastic fluctuations of independent random variables in probability theory and the distribution of time averages in deterministic Anosov C-systems. On the one hand, in probability theory, our interest dwells on three basic topics: the laws of large numbers, the central limit theorem and the law of the iterated logarithm for sequences of real-valued random variables. On the other hand we have chaotic, uniformly hyperbolic Anosov C-systems defined on tori which have mixing of all orders and nonzero Kolmogorov entropy. These extraord"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04129","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/1708.04129/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":"2026-07-05T01:01:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/FjIJYxJAhBDa12XQK+qLKqyuHvGNEUYJ4jNRW+L9zNYmCEXJigq3peoGbAebknJdFP4QSDOyGyKOYB9Wl/4BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-01T01:10:46.839558Z"},"content_sha256":"06b1f6211641a00e139f168efedac132f3da5f7c35079a924a39a22cd66289f5","schema_version":"1.0","event_id":"sha256:06b1f6211641a00e139f168efedac132f3da5f7c35079a924a39a22cd66289f5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YZOWVNQCRCPFOPCHINWTKYRWYH/bundle.json","state_url":"https://pith.science/pith/YZOWVNQCRCPFOPCHINWTKYRWYH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YZOWVNQCRCPFOPCHINWTKYRWYH/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":"2026-08-01T01:10:46Z","links":{"resolver":"https://pith.science/pith/YZOWVNQCRCPFOPCHINWTKYRWYH","bundle":"https://pith.science/pith/YZOWVNQCRCPFOPCHINWTKYRWYH/bundle.json","state":"https://pith.science/pith/YZOWVNQCRCPFOPCHINWTKYRWYH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YZOWVNQCRCPFOPCHINWTKYRWYH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YZOWVNQCRCPFOPCHINWTKYRWYH","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":"bd3b942d065900a9caed554f2c5ddd413b308df14b820c8ce5db5390a2ae2485","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2017-07-31T12:16:04Z","title_canon_sha256":"a73eaa1f9360a3b2948c998a74c11fba0545a1b09129d318787f18dd9028e936"},"schema_version":"1.0","source":{"id":"1708.04129","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.04129","created_at":"2026-07-05T01:01:31Z"},{"alias_kind":"arxiv_version","alias_value":"1708.04129v1","created_at":"2026-07-05T01:01:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.04129","created_at":"2026-07-05T01:01:31Z"},{"alias_kind":"pith_short_12","alias_value":"YZOWVNQCRCPF","created_at":"2026-07-05T01:01:31Z"},{"alias_kind":"pith_short_16","alias_value":"YZOWVNQCRCPFOPCH","created_at":"2026-07-05T01:01:31Z"},{"alias_kind":"pith_short_8","alias_value":"YZOWVNQC","created_at":"2026-07-05T01:01:31Z"}],"graph_snapshots":[{"event_id":"sha256:06b1f6211641a00e139f168efedac132f3da5f7c35079a924a39a22cd66289f5","target":"graph","created_at":"2026-07-05T01:01:31Z","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/1708.04129/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the interrelation between the distribution of stochastic fluctuations of independent random variables in probability theory and the distribution of time averages in deterministic Anosov C-systems. On the one hand, in probability theory, our interest dwells on three basic topics: the laws of large numbers, the central limit theorem and the law of the iterated logarithm for sequences of real-valued random variables. On the other hand we have chaotic, uniformly hyperbolic Anosov C-systems defined on tori which have mixing of all orders and nonzero Kolmogorov entropy. These extraord","authors_text":"George Savvidy, Hayk Poghosyan, Konstantin Savvidy","cross_cats":["cond-mat.stat-mech","math-ph","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2017-07-31T12:16:04Z","title":"Classical limit theorems and high entropy MIXMAX random number generator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04129","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":"sha256:0125b58136544ab0cb1b99d91cf1d2d775fdbacd18a864e2ee7ff7b7097a9893","target":"record","created_at":"2026-07-05T01:01:31Z","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":"bd3b942d065900a9caed554f2c5ddd413b308df14b820c8ce5db5390a2ae2485","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2017-07-31T12:16:04Z","title_canon_sha256":"a73eaa1f9360a3b2948c998a74c11fba0545a1b09129d318787f18dd9028e936"},"schema_version":"1.0","source":{"id":"1708.04129","kind":"arxiv","version":1}},"canonical_sha256":"c65d6ab602889e573c47436d356236c1f2b8c177684270cc90e9baef8bae0577","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c65d6ab602889e573c47436d356236c1f2b8c177684270cc90e9baef8bae0577","first_computed_at":"2026-07-05T01:01:31.784076Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:01:31.784076Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yWF838/OxlqGIgoI6hD7n18xHjvgZSlC5ubcZLvQ+RdWzJHFkUZeYqY/og1vqnfzAbcwEbe3kUHo2Hx+atfNCg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:01:31.784507Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.04129","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0125b58136544ab0cb1b99d91cf1d2d775fdbacd18a864e2ee7ff7b7097a9893","sha256:06b1f6211641a00e139f168efedac132f3da5f7c35079a924a39a22cd66289f5"],"state_sha256":"8953205c295566329caaacbe827454b2aa4d4c38611af96064d5a113d19bdb91"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fO9KddJiAFCpI2Zi32rRCDVdfdEylMjpqXyXHZulvMmr2V1bcwegyrPGE+QuZll/VMhWkPfzixS1wSzbt2V3Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-01T01:10:46.845895Z","bundle_sha256":"ce8c93fef1d0a5d0e612ba626ad7d3056ab4ccef8c4f296a3a5348ff408d5bf6"}}