{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:3UYBXZA3XLT4K64PDWOPL6ML6F","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":"7d93544816a0b28e7b66d0c8f9fdb305429b43c9353d1afdb6f77fe692eb96cc","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2025-07-22T16:25:07Z","title_canon_sha256":"08c71f7aae8fe965efd43cf01b942dd842cd9a234e2311e84ea0d069937a9ab2"},"schema_version":"1.0","source":{"id":"2507.16740","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.16740","created_at":"2026-07-05T11:41:30Z"},{"alias_kind":"arxiv_version","alias_value":"2507.16740v1","created_at":"2026-07-05T11:41:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.16740","created_at":"2026-07-05T11:41:30Z"},{"alias_kind":"pith_short_12","alias_value":"3UYBXZA3XLT4","created_at":"2026-07-05T11:41:30Z"},{"alias_kind":"pith_short_16","alias_value":"3UYBXZA3XLT4K64P","created_at":"2026-07-05T11:41:30Z"},{"alias_kind":"pith_short_8","alias_value":"3UYBXZA3","created_at":"2026-07-05T11:41:30Z"}],"graph_snapshots":[{"event_id":"sha256:59b731dae8174dfc6e0456e81dded78a8e89846afe827805bcda7b65778e7875","target":"graph","created_at":"2026-07-05T11:41:30Z","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/2507.16740/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\{T^z\\}$ be an ergodic action of the group $Z^n$ by automorphisms of the probability space $(X,m)$, $\\sum_{i}^\\infty a_i<\\infty$, $a_i>0$. For any sequence $M_k\\to +\\infty$ there exist $N_k>M_k$ and a function $ f\\in L_1(X,m)$ such that $$m\\left(\\ x:\\ \\left|\\, A(x,N_k,f) - \\int f \\, dm\\, \\right|\\ >\\ a_k \\ \\right)\\ \\to\\ 1,$$ where $$A(x,N,f) =\\frac 1 {N^n} \\sum_{z\\in Q_N} f(T^{z}x),$$ $$Q_N=\\{(z_1,\\dots,z_n)\\}\\, :\\, 1\\leq z_1,\\dots,z_n\\leq N\\}.$$","authors_text":"Valery V. Ryzhikov","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2025-07-22T16:25:07Z","title":"Slow convergence of Birkhoff ergodic averages"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.16740","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:dbc7e7bc2dc809a5c31252700fb0c8d0520168103cb9e5b7a6b352dc0dd0045e","target":"record","created_at":"2026-07-05T11:41:30Z","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":"7d93544816a0b28e7b66d0c8f9fdb305429b43c9353d1afdb6f77fe692eb96cc","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2025-07-22T16:25:07Z","title_canon_sha256":"08c71f7aae8fe965efd43cf01b942dd842cd9a234e2311e84ea0d069937a9ab2"},"schema_version":"1.0","source":{"id":"2507.16740","kind":"arxiv","version":1}},"canonical_sha256":"dd301be41bbae7c57b8f1d9cf5f98bf1739da3e936c2d3e55bdd716370069765","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd301be41bbae7c57b8f1d9cf5f98bf1739da3e936c2d3e55bdd716370069765","first_computed_at":"2026-07-05T11:41:30.213089Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:41:30.213089Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AKJw8qdBAOee0689vOXybe3evgp4d7a+TR+2hSDsWkT+9qTpA1OA0Ns0tJVEPT38ops0nGUHn5NMpH+sNJvCBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:41:30.214210Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.16740","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dbc7e7bc2dc809a5c31252700fb0c8d0520168103cb9e5b7a6b352dc0dd0045e","sha256:59b731dae8174dfc6e0456e81dded78a8e89846afe827805bcda7b65778e7875"],"state_sha256":"60cb1fb565ae8c2e909e5f7917c554605918d3d594b33560d999f34f85f3f590"}