{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:W7C7HKWNR7RCMAP46EGM4CD3C6","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":"dd2b2f9bf1f52dc1be70a1799754b6135cf52ab90bbfc17114e89490c2be153a","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-10-25T07:16:37Z","title_canon_sha256":"510f289f159721f29dea7920e8e2147a31a46b14144d705a0f275b7dc47581b8"},"schema_version":"1.0","source":{"id":"1810.10742","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.10742","created_at":"2026-05-17T23:47:48Z"},{"alias_kind":"arxiv_version","alias_value":"1810.10742v3","created_at":"2026-05-17T23:47:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.10742","created_at":"2026-05-17T23:47:48Z"},{"alias_kind":"pith_short_12","alias_value":"W7C7HKWNR7RC","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"W7C7HKWNR7RCMAP4","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"W7C7HKWN","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:67bdc5c1178d78d784fa24ad5374599c479a8b1a3c24d035fef4339142b462c4","target":"graph","created_at":"2026-05-17T23:47:48Z","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 establish quantitative results for the statistical be\\-ha\\-vi\\-our of \\emph{infinite systems}. We consider two kinds of infinite system: i) a conservative dynamical system $(f,X,\\mu)$ preserving a $\\sigma$-finite measure $\\mu$ such that $\\mu(X)=\\infty$; ii) the case where $\\mu$ is a probability measure but we consider the statistical behaviour of an observable $\\phi\\colon X\\to[0,\\infty)$ which is non-integrable: $\\int \\phi \\, d\\mu=\\infty$.\n  In the first part of this work we study the behaviour of Birkhoff sums of systems of the kind ii). For certain weakly chaotic systems, we show that the","authors_text":"Mark Holland, Stefano Galatolo, Tomas Persson, Yiwei Zhang","cross_cats":["math-ph","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-10-25T07:16:37Z","title":"Anomalous time-scaling of extreme events in infinite systems and Birkhoff sums of infinite observables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.10742","kind":"arxiv","version":3},"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":"sha256:48f1390f3f6ba2dc3dd1d100726adf5510ca3488ad9552f8583fdf0b8f32481b","target":"record","created_at":"2026-05-17T23:47:48Z","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":"dd2b2f9bf1f52dc1be70a1799754b6135cf52ab90bbfc17114e89490c2be153a","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-10-25T07:16:37Z","title_canon_sha256":"510f289f159721f29dea7920e8e2147a31a46b14144d705a0f275b7dc47581b8"},"schema_version":"1.0","source":{"id":"1810.10742","kind":"arxiv","version":3}},"canonical_sha256":"b7c5f3aacd8fe22601fcf10cce087b17beb0a41417bb56e9cf50338c6fe6a382","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7c5f3aacd8fe22601fcf10cce087b17beb0a41417bb56e9cf50338c6fe6a382","first_computed_at":"2026-05-17T23:47:48.644746Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:48.644746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AgQ9alhn6tKe8GBLLAdVEPIpjUtZHxWwUev4qs0bXFXXbiZanpchAxJZAU7aQ1Iloytyxp37Xy+ZaA/I1mHtCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:48.645386Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.10742","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48f1390f3f6ba2dc3dd1d100726adf5510ca3488ad9552f8583fdf0b8f32481b","sha256:67bdc5c1178d78d784fa24ad5374599c479a8b1a3c24d035fef4339142b462c4"],"state_sha256":"84d391fce64920ca84ccdd5450c678f3f444bde12383992d4cea556cdcdb5b7c"}