{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:QN3EEAAPRXQPYVK4WYOOMVEEQ7","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":"679ff5c2d3e5a05759d4d5aada4086c1ac97cd27010af3ef4120b3969ec2c5b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-08-22T09:17:57Z","title_canon_sha256":"446075fc844400ec3280034945c21949c609183abee228a0b1fe66bc3dd0655b"},"schema_version":"1.0","source":{"id":"1908.08270","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.08270","created_at":"2026-07-05T05:19:31Z"},{"alias_kind":"arxiv_version","alias_value":"1908.08270v3","created_at":"2026-07-05T05:19:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.08270","created_at":"2026-07-05T05:19:31Z"},{"alias_kind":"pith_short_12","alias_value":"QN3EEAAPRXQP","created_at":"2026-07-05T05:19:31Z"},{"alias_kind":"pith_short_16","alias_value":"QN3EEAAPRXQPYVK4","created_at":"2026-07-05T05:19:31Z"},{"alias_kind":"pith_short_8","alias_value":"QN3EEAAP","created_at":"2026-07-05T05:19:31Z"}],"graph_snapshots":[{"event_id":"sha256:c2de501846f46e72ffd86ca9add4be98a5a30b6d22b35b6950800c1971bd1b91","target":"graph","created_at":"2026-07-05T05:19:31Z","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/1908.08270/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a class of dynamical systems, which we call weakly coarse expanding, which is a generalization to the postcritically infinite case of expanding Thurston maps as discussed by Bonk-Meyer and is closely related to coarse expanding conformal systems as defined by Haissinsky-Pilgrim. We prove existence and uniqueness of equilibrium states for a wide class of potentials, as well as statistical laws such as a central limit theorem, law of iterated logarithm, exponential decay of correlations and a large deviation principle. Further, if the system is defined on the 2-sphere, we prove all s","authors_text":"Anna Zdunik, Feliks Przytycki, Giulio Tiozzo, Mariusz Urbanski, Tushar Das","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-08-22T09:17:57Z","title":"Thermodynamic formalism for coarse expanding dynamical systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.08270","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":"sha256:9e097c6453e0526fd7ebeb9775b867ed7aa5e1a5f1528873fc66e1cb1ccd2dd5","target":"record","created_at":"2026-07-05T05:19:31Z","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":"679ff5c2d3e5a05759d4d5aada4086c1ac97cd27010af3ef4120b3969ec2c5b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-08-22T09:17:57Z","title_canon_sha256":"446075fc844400ec3280034945c21949c609183abee228a0b1fe66bc3dd0655b"},"schema_version":"1.0","source":{"id":"1908.08270","kind":"arxiv","version":3}},"canonical_sha256":"837642000f8de0fc555cb61ce6548487dba6266c65fcc98ef1cc8f3296b6be90","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"837642000f8de0fc555cb61ce6548487dba6266c65fcc98ef1cc8f3296b6be90","first_computed_at":"2026-07-05T05:19:31.929310Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:19:31.929310Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pHp1kvAS/2sOylUmO3bQuGAXjwrbMkQbyjyvoxCG0bvpv9JbHcsvPwuKRlAPAqNWv81QWhfAKFD7+D2i1pnlAA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:19:31.929830Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.08270","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e097c6453e0526fd7ebeb9775b867ed7aa5e1a5f1528873fc66e1cb1ccd2dd5","sha256:c2de501846f46e72ffd86ca9add4be98a5a30b6d22b35b6950800c1971bd1b91"],"state_sha256":"c318c0e39a4d677edc223648b4262416bfb4038963ef564855745717f415a7a0"}