{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KUCMAWDW2MKHQYDOXJRGBS5T3M","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":"a436a8a975de808a2de2b9c5655b0851e6f0d28340596266d1a35f2d2ead4e84","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-07-16T00:17:45Z","title_canon_sha256":"a00971cf3f9dce737d09f1d0c3bba5f25f6a17ac8b9a9aefa1388d807ccf48c6"},"schema_version":"1.0","source":{"id":"1607.04685","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.04685","created_at":"2026-05-18T01:04:10Z"},{"alias_kind":"arxiv_version","alias_value":"1607.04685v1","created_at":"2026-05-18T01:04:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.04685","created_at":"2026-05-18T01:04:10Z"},{"alias_kind":"pith_short_12","alias_value":"KUCMAWDW2MKH","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"KUCMAWDW2MKHQYDO","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"KUCMAWDW","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:0887cc80616f3532d4e9c308a8370231f215a958c2e653955cc312b0b1545314","target":"graph","created_at":"2026-05-18T01:04:10Z","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":"An important class of `physically relevant' measures for dynamical systems with hyperbolic behavior is given by Sinai-Ruelle-Bowen (SRB) measures. We survey various techniques for constructing SRB measures and studying their properties, paying special attention to the geometric `push-forward' approach. After describing this approach in the uniformly hyperbolic setting, we review recent work that extends it to non-uniformly hyperbolic systems.","authors_text":"Stefano Luzzatto, Vaughn Climenhaga, Yakov Pesin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-07-16T00:17:45Z","title":"The geometric approach for constructing Sinai-Ruelle-Bowen measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04685","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":"sha256:849137750ed72119b5262c5b31c65bd7fc8220243cd64c33f75b02dda41496c7","target":"record","created_at":"2026-05-18T01:04:10Z","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":"a436a8a975de808a2de2b9c5655b0851e6f0d28340596266d1a35f2d2ead4e84","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-07-16T00:17:45Z","title_canon_sha256":"a00971cf3f9dce737d09f1d0c3bba5f25f6a17ac8b9a9aefa1388d807ccf48c6"},"schema_version":"1.0","source":{"id":"1607.04685","kind":"arxiv","version":1}},"canonical_sha256":"5504c05876d31478606eba6260cbb3db0888f90fd43c92b44c5678279bc4dc1c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5504c05876d31478606eba6260cbb3db0888f90fd43c92b44c5678279bc4dc1c","first_computed_at":"2026-05-18T01:04:10.477471Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:10.477471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"luukPEU7dzpt2z6ShcAM0xnaY9NP91nTa2E36a10wmyI8b5FsWx+IaadkGo0sisffPNtaT2UXQMNegB31eFwAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:10.478013Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.04685","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:849137750ed72119b5262c5b31c65bd7fc8220243cd64c33f75b02dda41496c7","sha256:0887cc80616f3532d4e9c308a8370231f215a958c2e653955cc312b0b1545314"],"state_sha256":"86f2c815e81c39ee85567bc6c4eb48eb85d6911665358f63b40506499e45ad64"}