{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:FPZJSMWBAVV5IZIHZ3HK73D2YU","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":"0ce99e4b25b4b71f1819a358de71479720d4f63c11e2268f6fc4ea21bf660aa6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-06-26T20:06:45Z","title_canon_sha256":"0d07525cee475d9f0a1fa19ba71ba0997cbf48ca9711d4bbf16b8ae0a7cb11ba"},"schema_version":"1.0","source":{"id":"0806.4385","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0806.4385","created_at":"2026-05-18T04:42:36Z"},{"alias_kind":"arxiv_version","alias_value":"0806.4385v3","created_at":"2026-05-18T04:42:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0806.4385","created_at":"2026-05-18T04:42:36Z"},{"alias_kind":"pith_short_12","alias_value":"FPZJSMWBAVV5","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"FPZJSMWBAVV5IZIH","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"FPZJSMWB","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:b5595bd9f840e130966d54ae31a1d44c1b6873c44ebaa03c08c72e452902d71d","target":"graph","created_at":"2026-05-18T04:42:36Z","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 consider the thermodynamic formalism of a complex rational map $f$ of degree at least two, viewed as a dynamical system acting on the Riemann sphere. More precisely, for a real parameter $t$ we study the (non-)existence of equilibrium states of $f$ for the potential $-t \\ln |f'|$, and the analytic dependence on $t$ of the corresponding pressure function. We give a fairly complete description of the thermodynamic formalism of a rational map that is \"expanding away from critical points\" and that has arbitrarily small \"nice sets\" with some additional properties. Our results apply in particular","authors_text":"Feliks Przytycki, Juan Rivera-Letelier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-06-26T20:06:45Z","title":"Nice inducing schemes and the thermodynamics of rational maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.4385","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:a7f41e02dca070ad3542fbb2f35c00f5b1250adae5e77efd98e1ad19a77d451e","target":"record","created_at":"2026-05-18T04:42:36Z","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":"0ce99e4b25b4b71f1819a358de71479720d4f63c11e2268f6fc4ea21bf660aa6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-06-26T20:06:45Z","title_canon_sha256":"0d07525cee475d9f0a1fa19ba71ba0997cbf48ca9711d4bbf16b8ae0a7cb11ba"},"schema_version":"1.0","source":{"id":"0806.4385","kind":"arxiv","version":3}},"canonical_sha256":"2bf29932c1056bd46507ceceafec7ac53c827e937264321c2dfc9a63e6f4c2fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2bf29932c1056bd46507ceceafec7ac53c827e937264321c2dfc9a63e6f4c2fe","first_computed_at":"2026-05-18T04:42:36.241219Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:36.241219Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nekahHg+aPhRQfbUFSFNL/JJy5uFQs9yeUy/4MxdFFGLhZ2O5fssWifdR+Gmj1u51a/hEUd4i/XMOZ4U41DKCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:36.241835Z","signed_message":"canonical_sha256_bytes"},"source_id":"0806.4385","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a7f41e02dca070ad3542fbb2f35c00f5b1250adae5e77efd98e1ad19a77d451e","sha256:b5595bd9f840e130966d54ae31a1d44c1b6873c44ebaa03c08c72e452902d71d"],"state_sha256":"2aa9a8ccd544400d72b4dc59172a5e558edaf404e79776da5576a2ae7ab1ad77"}