{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OIUW5ZJHM4EXTSDSBW4D743TR2","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":"5f60fe8f88f996d483ba3d42b3a08853bd836e3290a97f14fa2e903f484efc01","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-04T12:18:59Z","title_canon_sha256":"ee41123414248490d4388a04c917b341f29c24fd7da4b01ff21c97d293a09415"},"schema_version":"1.0","source":{"id":"1307.1297","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.1297","created_at":"2026-05-18T03:15:42Z"},{"alias_kind":"arxiv_version","alias_value":"1307.1297v3","created_at":"2026-05-18T03:15:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.1297","created_at":"2026-05-18T03:15:42Z"},{"alias_kind":"pith_short_12","alias_value":"OIUW5ZJHM4EX","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OIUW5ZJHM4EXTSDS","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OIUW5ZJH","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:3ec8a5c93e12124528b3718593de18deb5314f9aec879b95d60b33e545595a46","target":"graph","created_at":"2026-05-18T03:15:42Z","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":"Consider a topologically exact $C^3$ interval map without non-flat critical points. Following the works we did in \\cite{LiRiv12two}, we give two equivalent characterizations of hyperbolic H\\\"{o}lder continuous potential in terms of the Lyapunov exponents and the measure-theoretic entropies of equilibrium states for those potentials.","authors_text":"Huaibin Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-04T12:18:59Z","title":"Equivalent characterizations of hyperbolic H\\\"older potential for interval maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1297","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:aebf3e3b285ac95a2e7748c381ab3bf786e735c2684d2246e866f863713f32d0","target":"record","created_at":"2026-05-18T03:15:42Z","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":"5f60fe8f88f996d483ba3d42b3a08853bd836e3290a97f14fa2e903f484efc01","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-04T12:18:59Z","title_canon_sha256":"ee41123414248490d4388a04c917b341f29c24fd7da4b01ff21c97d293a09415"},"schema_version":"1.0","source":{"id":"1307.1297","kind":"arxiv","version":3}},"canonical_sha256":"72296ee527670979c8720db83ff3738ebba6cf5774791446cc8d61e5c7dce443","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"72296ee527670979c8720db83ff3738ebba6cf5774791446cc8d61e5c7dce443","first_computed_at":"2026-05-18T03:15:42.960584Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:42.960584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jSoZiq5RS380m3P+h61VXL8yF4vrdagMY4jNadp3wvF+hpwZHmLK58r/z2BlAM6cwtCLTBWaGpusoxa7mVgMBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:42.961269Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.1297","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aebf3e3b285ac95a2e7748c381ab3bf786e735c2684d2246e866f863713f32d0","sha256:3ec8a5c93e12124528b3718593de18deb5314f9aec879b95d60b33e545595a46"],"state_sha256":"bc2e2a949b7a59b88a7ccde87157400fe4c94b7845c83ff9195fe43c8ba764e6"}