{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:WEEYN5F3P35W4NORRWGCPKRKG3","short_pith_number":"pith:WEEYN5F3","canonical_record":{"source":{"id":"1108.4334","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-08-22T14:51:56Z","cross_cats_sorted":[],"title_canon_sha256":"d101554910242fcb6e9e7591b6528675d7439411127b10344daca55f322eb6f6","abstract_canon_sha256":"fca3b5708bf1b4c4f9aba7f861a32315aae687fa051a1e303a18ab1b2f9a3147"},"schema_version":"1.0"},"canonical_sha256":"b10986f4bb7efb6e35d18d8c27aa2a36dd2dd32334aa14749096029b30bee49d","source":{"kind":"arxiv","id":"1108.4334","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.4334","created_at":"2026-05-18T04:07:19Z"},{"alias_kind":"arxiv_version","alias_value":"1108.4334v2","created_at":"2026-05-18T04:07:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.4334","created_at":"2026-05-18T04:07:19Z"},{"alias_kind":"pith_short_12","alias_value":"WEEYN5F3P35W","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WEEYN5F3P35W4NOR","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WEEYN5F3","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:WEEYN5F3P35W4NORRWGCPKRKG3","target":"record","payload":{"canonical_record":{"source":{"id":"1108.4334","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-08-22T14:51:56Z","cross_cats_sorted":[],"title_canon_sha256":"d101554910242fcb6e9e7591b6528675d7439411127b10344daca55f322eb6f6","abstract_canon_sha256":"fca3b5708bf1b4c4f9aba7f861a32315aae687fa051a1e303a18ab1b2f9a3147"},"schema_version":"1.0"},"canonical_sha256":"b10986f4bb7efb6e35d18d8c27aa2a36dd2dd32334aa14749096029b30bee49d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:19.412892Z","signature_b64":"2/1Ati25Q/QWVs4/AKzlilYDhQ1t2QSUb7qiiSWTjjwC4t7ByfZogOL+KaXZmERMXXLDiDFebEhOq8/YBN7bDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b10986f4bb7efb6e35d18d8c27aa2a36dd2dd32334aa14749096029b30bee49d","last_reissued_at":"2026-05-18T04:07:19.412367Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:19.412367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.4334","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:07:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PpmX48UivNua6atb7L4TNGNJ+lsWnv0SN2jvON7g+ToLqvvNPkEka0zU5jYYvDtQaQY1fm7xgQCb8uMnfiiKCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T07:24:13.068650Z"},"content_sha256":"016a67764e4fdd93ca272f756007f94a45f3436199689338290cb31bd42fede1","schema_version":"1.0","event_id":"sha256:016a67764e4fdd93ca272f756007f94a45f3436199689338290cb31bd42fede1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:WEEYN5F3P35W4NORRWGCPKRKG3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniform hyperbolic approximations of measures with non zero Lyapunov exponents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Fernando J S\\'anchez-Salas, Stefano Luzzatto","submitted_at":"2011-08-22T14:51:56Z","abstract_excerpt":"We show that for any C^1+alpha diffeomorphism of a compact Riemannian manifold, every non-atomic, ergodic, invariant probability measure with non-zero Lyapunov exponents is approximated by uniformly hyperbolic sets in the sense that there exists a sequence Omega_n of compact, topologically transitive, locally maximal, uniformly hyperbolic sets, such that for any sequence mu_n of f-invariant ergodic probability measures with supp (mu_n) in Omega_n we have mu_n -> mu in the weak-* topology."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.4334","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:07:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VrRw7Z5Q0q1ec/pvodySiFs5JGhnSOlffq0GS4Wbq6OSjWyJt1cKxyq4lXNDUOqO9/94wD8g3P5doeo25SHQBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T07:24:13.069006Z"},"content_sha256":"0411c5cffab3c4fc248266acd21093d86dbbedff3745d2d4e1985d444dc72e9e","schema_version":"1.0","event_id":"sha256:0411c5cffab3c4fc248266acd21093d86dbbedff3745d2d4e1985d444dc72e9e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WEEYN5F3P35W4NORRWGCPKRKG3/bundle.json","state_url":"https://pith.science/pith/WEEYN5F3P35W4NORRWGCPKRKG3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WEEYN5F3P35W4NORRWGCPKRKG3/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-07T07:24:13Z","links":{"resolver":"https://pith.science/pith/WEEYN5F3P35W4NORRWGCPKRKG3","bundle":"https://pith.science/pith/WEEYN5F3P35W4NORRWGCPKRKG3/bundle.json","state":"https://pith.science/pith/WEEYN5F3P35W4NORRWGCPKRKG3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WEEYN5F3P35W4NORRWGCPKRKG3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:WEEYN5F3P35W4NORRWGCPKRKG3","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":"fca3b5708bf1b4c4f9aba7f861a32315aae687fa051a1e303a18ab1b2f9a3147","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-08-22T14:51:56Z","title_canon_sha256":"d101554910242fcb6e9e7591b6528675d7439411127b10344daca55f322eb6f6"},"schema_version":"1.0","source":{"id":"1108.4334","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.4334","created_at":"2026-05-18T04:07:19Z"},{"alias_kind":"arxiv_version","alias_value":"1108.4334v2","created_at":"2026-05-18T04:07:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.4334","created_at":"2026-05-18T04:07:19Z"},{"alias_kind":"pith_short_12","alias_value":"WEEYN5F3P35W","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WEEYN5F3P35W4NOR","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WEEYN5F3","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:0411c5cffab3c4fc248266acd21093d86dbbedff3745d2d4e1985d444dc72e9e","target":"graph","created_at":"2026-05-18T04:07:19Z","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 show that for any C^1+alpha diffeomorphism of a compact Riemannian manifold, every non-atomic, ergodic, invariant probability measure with non-zero Lyapunov exponents is approximated by uniformly hyperbolic sets in the sense that there exists a sequence Omega_n of compact, topologically transitive, locally maximal, uniformly hyperbolic sets, such that for any sequence mu_n of f-invariant ergodic probability measures with supp (mu_n) in Omega_n we have mu_n -> mu in the weak-* topology.","authors_text":"Fernando J S\\'anchez-Salas, Stefano Luzzatto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-08-22T14:51:56Z","title":"Uniform hyperbolic approximations of measures with non zero Lyapunov exponents"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.4334","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":"sha256:016a67764e4fdd93ca272f756007f94a45f3436199689338290cb31bd42fede1","target":"record","created_at":"2026-05-18T04:07:19Z","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":"fca3b5708bf1b4c4f9aba7f861a32315aae687fa051a1e303a18ab1b2f9a3147","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-08-22T14:51:56Z","title_canon_sha256":"d101554910242fcb6e9e7591b6528675d7439411127b10344daca55f322eb6f6"},"schema_version":"1.0","source":{"id":"1108.4334","kind":"arxiv","version":2}},"canonical_sha256":"b10986f4bb7efb6e35d18d8c27aa2a36dd2dd32334aa14749096029b30bee49d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b10986f4bb7efb6e35d18d8c27aa2a36dd2dd32334aa14749096029b30bee49d","first_computed_at":"2026-05-18T04:07:19.412367Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:19.412367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2/1Ati25Q/QWVs4/AKzlilYDhQ1t2QSUb7qiiSWTjjwC4t7ByfZogOL+KaXZmERMXXLDiDFebEhOq8/YBN7bDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:19.412892Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.4334","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:016a67764e4fdd93ca272f756007f94a45f3436199689338290cb31bd42fede1","sha256:0411c5cffab3c4fc248266acd21093d86dbbedff3745d2d4e1985d444dc72e9e"],"state_sha256":"20dfb618e937054b8781b8666e35cc7df4b20b40df881cf22767b748b3bc8561"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MQLAouiTCeFixg3TnNAWVxgt+5DRknaAXBchkGxCAeP0Ln/PdGh+z5CYWN/HiFPbzAX7h2Gg9zrdogt++927Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T07:24:13.071765Z","bundle_sha256":"6ed0392f35268803318cbbf00e23e3c46eba7daf2883c00bebad999b9a2c7da8"}}