{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:2WFLJSBEJYB57H75MY4PQGDKCK","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":"e85b05f73fe1973d0057aced98b282103e308c775a2e4c2ebae292532a4b0c61","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-05-13T17:47:31Z","title_canon_sha256":"3adc1a8eb0fc9ca4f4809e9839e68026a32a3a3131f6e7de940eba5ac4328d4b"},"schema_version":"1.0","source":{"id":"1905.05164","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.05164","created_at":"2026-05-17T23:46:22Z"},{"alias_kind":"arxiv_version","alias_value":"1905.05164v1","created_at":"2026-05-17T23:46:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.05164","created_at":"2026-05-17T23:46:22Z"},{"alias_kind":"pith_short_12","alias_value":"2WFLJSBEJYB5","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"2WFLJSBEJYB57H75","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"2WFLJSBE","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:4ca780059ffee00911b1de30bc0c562ae3165ffa56c7bca0e3d204f573a2378b","target":"graph","created_at":"2026-05-17T23:46:22Z","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":"We show that for every ergodic and aperiodic probability preserving system, there exists a $\\mathbb{Z}$ valued, square integrable function $f$ such that the partial sums process of the time series $\\left\\{f\\circ T^i\\right\\}_{i=0}^\\infty$ satisfies the lattice local limit theorem.","authors_text":"Dalibor Volny, Zemer Kosloff","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-05-13T17:47:31Z","title":"Local limit theorem in deterministic systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.05164","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":"sha256:6db0a20f07450aaeca47ba45e1002a0577f4537d2b05f5497374e37d192b3e5d","target":"record","created_at":"2026-05-17T23:46:22Z","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":"e85b05f73fe1973d0057aced98b282103e308c775a2e4c2ebae292532a4b0c61","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-05-13T17:47:31Z","title_canon_sha256":"3adc1a8eb0fc9ca4f4809e9839e68026a32a3a3131f6e7de940eba5ac4328d4b"},"schema_version":"1.0","source":{"id":"1905.05164","kind":"arxiv","version":1}},"canonical_sha256":"d58ab4c8244e03df9ffd6638f8186a129b2ef38da46294a6ac2a70bdfcb2c9c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d58ab4c8244e03df9ffd6638f8186a129b2ef38da46294a6ac2a70bdfcb2c9c4","first_computed_at":"2026-05-17T23:46:22.358997Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:22.358997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Bd1+B67/9drtsbSBTAhVMZipRnxEtkZgcwnwZEGmLbG+ld2aifyTjjWttInPMiWHoIU1n4UlLvPsRsntMwOjAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:22.359624Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.05164","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6db0a20f07450aaeca47ba45e1002a0577f4537d2b05f5497374e37d192b3e5d","sha256:4ca780059ffee00911b1de30bc0c562ae3165ffa56c7bca0e3d204f573a2378b"],"state_sha256":"08254adfcd3e295c4a9f5f636b8b75c88f5701db0ae6666979864860ccb94ce4"}