{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:EGR3VIXDKMJZTD3T5N5AJNCTRP","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":"92e0795758f54b3e5dcdb17fd44cfa4527d0c5073f487bd053b542a45f5a3390","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-26T03:34:09Z","title_canon_sha256":"7b711af3b4154b0fe882261f9f88c4ed9434178d08fd15633ef607e47844181d"},"schema_version":"1.0","source":{"id":"1610.08160","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.08160","created_at":"2026-05-18T01:01:14Z"},{"alias_kind":"arxiv_version","alias_value":"1610.08160v1","created_at":"2026-05-18T01:01:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08160","created_at":"2026-05-18T01:01:14Z"},{"alias_kind":"pith_short_12","alias_value":"EGR3VIXDKMJZ","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"EGR3VIXDKMJZTD3T","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"EGR3VIXD","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:ace2014111d2c64aa06b67a61c49996d02f97ea84adb515d94a1c51ed49fa962","target":"graph","created_at":"2026-05-18T01:01:14Z","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":"Given H\\\"older continuous functions $f$ and $\\psi$ on a sub-shift of finite type $\\Sigma_A^{+}$ such that $\\psi$ is not cohomologous to a constant, the classical large deviation principle holds (\\cite{OP}, \\cite{Kif}, \\cite{Y}) with a rate function $I_\\psi\\geq 0$ such that $I_\\psi (p) = 0$ iff $p = \\int \\psi \\, d \\mu$, where $\\mu = \\mu_f$ is the equilibrium state of $f$. In this paper we derive a uniform estimate from below for $I_\\psi$ for $p$ outside an interval containing $\\tilde{\\psi} = \\int \\psi \\, d\\mu$, which depends only on the sub-shift, the function $f$, the norm $|\\psi|_\\infty$, the","authors_text":"Luchezar Stoyanov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-26T03:34:09Z","title":"A uniform estimate for rate functions in large deviations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08160","kind":"arxiv","version":1},"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:eb35d1716bd430b837e9ea796e8af7271a96d4cb32734324e21b7c13bb206a33","target":"record","created_at":"2026-05-18T01:01:14Z","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":"92e0795758f54b3e5dcdb17fd44cfa4527d0c5073f487bd053b542a45f5a3390","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-26T03:34:09Z","title_canon_sha256":"7b711af3b4154b0fe882261f9f88c4ed9434178d08fd15633ef607e47844181d"},"schema_version":"1.0","source":{"id":"1610.08160","kind":"arxiv","version":1}},"canonical_sha256":"21a3baa2e35313998f73eb7a04b4538bf0a96ee23ebf29ffa07e727104f7877b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21a3baa2e35313998f73eb7a04b4538bf0a96ee23ebf29ffa07e727104f7877b","first_computed_at":"2026-05-18T01:01:14.884361Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:14.884361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"atkxwsSo1S2oYZ6xrmpiHnqTAicoQ4ReTq6qxxc8z41A1RcSSM62nzHcZqaZAGD4O5CMfZkHOuYJtMBR/DngDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:14.884933Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.08160","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb35d1716bd430b837e9ea796e8af7271a96d4cb32734324e21b7c13bb206a33","sha256:ace2014111d2c64aa06b67a61c49996d02f97ea84adb515d94a1c51ed49fa962"],"state_sha256":"8e68b58bd7697b8b575208c56b908d27550742c5184b77e4d06c783a45616165"}