{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:EVMVTOBC3TRKGWQGTRQB5664K6","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":"842aec90e0582466d8133797444995109cc545efdf22bec7c45f1234f702a4c2","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-28T20:38:07Z","title_canon_sha256":"925cb72fbe27ab5d5441f8fba658171a3f8ad90bd8da81ce9d60bd918802c078"},"schema_version":"1.0","source":{"id":"1603.08556","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.08556","created_at":"2026-05-18T00:42:13Z"},{"alias_kind":"arxiv_version","alias_value":"1603.08556v2","created_at":"2026-05-18T00:42:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08556","created_at":"2026-05-18T00:42:13Z"},{"alias_kind":"pith_short_12","alias_value":"EVMVTOBC3TRK","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"EVMVTOBC3TRKGWQG","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"EVMVTOBC","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:081d7ab1ae7397098a9b4015bbb1446e4fe84805202d0f2a87c9eaaa1e2b723d","target":"graph","created_at":"2026-05-18T00:42:13Z","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 effect thermodynamical formalism for the non-uniformly hyperbolic $C^\\infty$ map of the two dimensional torus known as the Katok map. It is a slowdown of a linear Anosov map near the origin and it is a local (but not small) perturbation. We prove the existence of equilibrium measures for any continuous potential function and obtain uniqueness of equilibrium measures associated to the geometric $t$-potential $\\varphi_t=-t\\log |df|_{E^u(x)}|$ for any $t\\in(t_0,\\infty)$, $t\\neq 1$ where $E^u(x)$ denotes the unstable direction. We show that $t_0$ tends to $-\\infty$ as the size of the perturbati","authors_text":"Ke Zhang, Samuel Senti, Yakov Pesin","cross_cats":["math-ph","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-28T20:38:07Z","title":"Thermodynamics of the Katok Map"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08556","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":"sha256:5c26675aea89265a4fa9062bc747f41b6192a172357c75d0b7812f9eea77d18f","target":"record","created_at":"2026-05-18T00:42:13Z","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":"842aec90e0582466d8133797444995109cc545efdf22bec7c45f1234f702a4c2","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-28T20:38:07Z","title_canon_sha256":"925cb72fbe27ab5d5441f8fba658171a3f8ad90bd8da81ce9d60bd918802c078"},"schema_version":"1.0","source":{"id":"1603.08556","kind":"arxiv","version":2}},"canonical_sha256":"255959b822dce2a35a069c601efbdc579fe4b46eda2e185e3da28627a88327cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"255959b822dce2a35a069c601efbdc579fe4b46eda2e185e3da28627a88327cb","first_computed_at":"2026-05-18T00:42:13.196115Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:13.196115Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"12P48GML2r2JE7b6LBFyCj9YsL/Ne1GtWXeIOjzg/g0s7Z8/R50Bsv4EZdA4XvlN/R9Tgc245si+aQQarzMJAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:13.196769Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.08556","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c26675aea89265a4fa9062bc747f41b6192a172357c75d0b7812f9eea77d18f","sha256:081d7ab1ae7397098a9b4015bbb1446e4fe84805202d0f2a87c9eaaa1e2b723d"],"state_sha256":"69e7a7fa67c051dbe7d9f29eb760c96c9c6ab3c2fa0b49e28ba7d9c4ad785c97"}