{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:K2BHYD26JKAPBIVUQ26S73P7A4","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":"2c19e97a292c16e2794cdf71dcdc246eb940659dea2d9dc82bb571dc695ace3d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-07-19T13:33:28Z","title_canon_sha256":"3ac010d9ec91e181ea31c1789bf4e72ab0f6dbd9a6509e203295a04ec821b0a9"},"schema_version":"1.0","source":{"id":"1107.3711","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.3711","created_at":"2026-05-18T04:17:16Z"},{"alias_kind":"arxiv_version","alias_value":"1107.3711v1","created_at":"2026-05-18T04:17:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.3711","created_at":"2026-05-18T04:17:16Z"},{"alias_kind":"pith_short_12","alias_value":"K2BHYD26JKAP","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"K2BHYD26JKAPBIVU","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"K2BHYD26","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:c6317d6f7fa567265fd7426d6b47a093aa60c31d6f715286685636a41865603a","target":"graph","created_at":"2026-05-18T04:17:16Z","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":"Suppose f is a $C^{1+\\alpha}$ surface diffeomorphism, and m is an equilibrium measure of a Holder continuous potential. We show that if m has positive metric entropy, then f is measure theoretically isomorphic to the product of a Bernoulli scheme and a finite rotation.","authors_text":"Omri Sarig","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-07-19T13:33:28Z","title":"Bernoulli equilibrium states for surface diffeomorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.3711","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:d130c4b854db9e4b01d499c1cc4eb817aea0190a24e9db5f2455aa0859d95ce6","target":"record","created_at":"2026-05-18T04:17:16Z","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":"2c19e97a292c16e2794cdf71dcdc246eb940659dea2d9dc82bb571dc695ace3d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-07-19T13:33:28Z","title_canon_sha256":"3ac010d9ec91e181ea31c1789bf4e72ab0f6dbd9a6509e203295a04ec821b0a9"},"schema_version":"1.0","source":{"id":"1107.3711","kind":"arxiv","version":1}},"canonical_sha256":"56827c0f5e4a80f0a2b486bd2fedff07217c3743d061a1b00e773a6ca7e1d4bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"56827c0f5e4a80f0a2b486bd2fedff07217c3743d061a1b00e773a6ca7e1d4bf","first_computed_at":"2026-05-18T04:17:16.160283Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:17:16.160283Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qVIgq+tUnbYJndTJoEJxVN1TS/xo3zGeLnZ6syJ3BXK1FWLavqnjuc1wYc7kvxZ5i1v7gpUwJLj0IVxt9o9DCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:17:16.161251Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.3711","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d130c4b854db9e4b01d499c1cc4eb817aea0190a24e9db5f2455aa0859d95ce6","sha256:c6317d6f7fa567265fd7426d6b47a093aa60c31d6f715286685636a41865603a"],"state_sha256":"9d4d11d824fcd411f51f69b68a98e62930593213a531d198a304870fd49f9504"}