{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VKZZHZ6RZX5LLHMAQUWF5TZO64","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":"e3c35ca461727b73579b36e9fb11c87f44637be84faeb858aecaedb03d68eaf9","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-04-15T13:45:08Z","title_canon_sha256":"04a7ce3ad16482bad02cb6a11dc4d07ad2b6a16a5f18bb4411c7c22bee0b51ac"},"schema_version":"1.0","source":{"id":"1804.05359","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.05359","created_at":"2026-05-18T00:06:28Z"},{"alias_kind":"arxiv_version","alias_value":"1804.05359v2","created_at":"2026-05-18T00:06:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.05359","created_at":"2026-05-18T00:06:28Z"},{"alias_kind":"pith_short_12","alias_value":"VKZZHZ6RZX5L","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VKZZHZ6RZX5LLHMA","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VKZZHZ6R","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:eeeb6e398efe2e3a7fd62d3de10bbfe395f47604e02464b58420cab5946b8714","target":"graph","created_at":"2026-05-18T00:06:28Z","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":"It is well-known that a strict analogue of the Birkhoff Ergodic Theorem in infinite ergodic theory is trivial; it states that for any infinite-measure-preserving ergodic system the Birkhoff average of every integrable function is almost everywhere zero. Nor does a different rescaling of the Birkhoff sum that leads to a non-degenerate pointwise limit exist. In this paper we give a version of Birkhoff's theorem for conservative, ergodic, infinite-measure-preserving dynamical systems where instead of integrable functions we use certain elements of $L^\\infty$, which we generically call global obse","authors_text":"Marco Lenci, Sara Munday","cross_cats":["nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-04-15T13:45:08Z","title":"Pointwise convergence of Birkhoff averages for global observables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.05359","kind":"arxiv","version":2},"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:eac5164f6f1fcfbde6d3a768abba6acbfe4425ea38169ec4f6a72091d3b17ca6","target":"record","created_at":"2026-05-18T00:06:28Z","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":"e3c35ca461727b73579b36e9fb11c87f44637be84faeb858aecaedb03d68eaf9","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-04-15T13:45:08Z","title_canon_sha256":"04a7ce3ad16482bad02cb6a11dc4d07ad2b6a16a5f18bb4411c7c22bee0b51ac"},"schema_version":"1.0","source":{"id":"1804.05359","kind":"arxiv","version":2}},"canonical_sha256":"aab393e7d1cdfab59d80852c5ecf2ef73e2b313d0843cb5df1e5e381d5e0c9d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aab393e7d1cdfab59d80852c5ecf2ef73e2b313d0843cb5df1e5e381d5e0c9d1","first_computed_at":"2026-05-18T00:06:28.801192Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:28.801192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DYX7Cz99MFtYpVBSz5vmltSYyqIoCxTIZDVREeBGurCtp1OdyhEE3PfNWIk6139ubh+1heIN2KYLaAfHwkp1BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:28.801742Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.05359","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eac5164f6f1fcfbde6d3a768abba6acbfe4425ea38169ec4f6a72091d3b17ca6","sha256:eeeb6e398efe2e3a7fd62d3de10bbfe395f47604e02464b58420cab5946b8714"],"state_sha256":"985948a2e25998678f4c4dbfbb10150f2bd04800b36c76cb514675f26bd2552b"}