{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:L2ZPJDJFESVQWQORQEVVDYQMLC","short_pith_number":"pith:L2ZPJDJF","canonical_record":{"source":{"id":"1704.01354","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-04-05T10:27:19Z","cross_cats_sorted":[],"title_canon_sha256":"40b67642a3ddd1bf9f25b43dd63e67b9b67fea9e313ddc394420b8ba5b37303d","abstract_canon_sha256":"78da61845a6c2fe6e4fec4a515ff4b905bae61df39f57520e530706356c13ddc"},"schema_version":"1.0"},"canonical_sha256":"5eb2f48d2524ab0b41d1812b51e20c5897fca18bfc0ab2024de72558ca8bcc1c","source":{"kind":"arxiv","id":"1704.01354","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.01354","created_at":"2026-05-18T00:46:58Z"},{"alias_kind":"arxiv_version","alias_value":"1704.01354v1","created_at":"2026-05-18T00:46:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.01354","created_at":"2026-05-18T00:46:58Z"},{"alias_kind":"pith_short_12","alias_value":"L2ZPJDJFESVQ","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"L2ZPJDJFESVQWQOR","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"L2ZPJDJF","created_at":"2026-05-18T12:31:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:L2ZPJDJFESVQWQORQEVVDYQMLC","target":"record","payload":{"canonical_record":{"source":{"id":"1704.01354","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-04-05T10:27:19Z","cross_cats_sorted":[],"title_canon_sha256":"40b67642a3ddd1bf9f25b43dd63e67b9b67fea9e313ddc394420b8ba5b37303d","abstract_canon_sha256":"78da61845a6c2fe6e4fec4a515ff4b905bae61df39f57520e530706356c13ddc"},"schema_version":"1.0"},"canonical_sha256":"5eb2f48d2524ab0b41d1812b51e20c5897fca18bfc0ab2024de72558ca8bcc1c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:58.359277Z","signature_b64":"ohqkhZKj+BdcS15COltyk78EB9Onz/0KQ6u4UnU923Er0m/2kIKgQ6vFRvcdx2VS5nxS5YKEpH/p2+67z+L8Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5eb2f48d2524ab0b41d1812b51e20c5897fca18bfc0ab2024de72558ca8bcc1c","last_reissued_at":"2026-05-18T00:46:58.358763Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:58.358763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.01354","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:46:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ymAjbeK1BFWVvvh5tE8KQcswvWys4mhxDFiRd4g7csi/MsT1u6d55oGTMmWmkxUqCunro51enXk8dFJpwMwsCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:13:42.415375Z"},"content_sha256":"117d41e7702ff09923d29a2ca6701ab76858ef137acb2bb5c4cb547a3d7820b9","schema_version":"1.0","event_id":"sha256:117d41e7702ff09923d29a2ca6701ab76858ef137acb2bb5c4cb547a3d7820b9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:L2ZPJDJFESVQWQORQEVVDYQMLC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximating Lyapunov exponents and stationary measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alexandre Baraviera, Pedro Duarte","submitted_at":"2017-04-05T10:27:19Z","abstract_excerpt":"We give a new proof of E. Le Page's theorem on the Holder continuity of the first Lyapunov exponent in the class of irreducible Bernoulli cocycles. This suggests an algorithm to approximate the first Lyapunov exponent, as well as the stationary measure, for such random cocycles."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.01354","kind":"arxiv","version":1},"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":"2026-05-18T00:46:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JumYbJvXZqfXxPlQ9eZ25cMIud1VLgR+qFfaScCfqZFzt2SwQYaz7UhCKNohYop9bat0TVmHOnDSOkk1xkZCAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:13:42.416030Z"},"content_sha256":"0da9489dc59a42856bb891e6d317834c6fabb04eaf5048ac66f697a10849d805","schema_version":"1.0","event_id":"sha256:0da9489dc59a42856bb891e6d317834c6fabb04eaf5048ac66f697a10849d805"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L2ZPJDJFESVQWQORQEVVDYQMLC/bundle.json","state_url":"https://pith.science/pith/L2ZPJDJFESVQWQORQEVVDYQMLC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L2ZPJDJFESVQWQORQEVVDYQMLC/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":"2026-05-31T03:13:42Z","links":{"resolver":"https://pith.science/pith/L2ZPJDJFESVQWQORQEVVDYQMLC","bundle":"https://pith.science/pith/L2ZPJDJFESVQWQORQEVVDYQMLC/bundle.json","state":"https://pith.science/pith/L2ZPJDJFESVQWQORQEVVDYQMLC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L2ZPJDJFESVQWQORQEVVDYQMLC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:L2ZPJDJFESVQWQORQEVVDYQMLC","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":"78da61845a6c2fe6e4fec4a515ff4b905bae61df39f57520e530706356c13ddc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-04-05T10:27:19Z","title_canon_sha256":"40b67642a3ddd1bf9f25b43dd63e67b9b67fea9e313ddc394420b8ba5b37303d"},"schema_version":"1.0","source":{"id":"1704.01354","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.01354","created_at":"2026-05-18T00:46:58Z"},{"alias_kind":"arxiv_version","alias_value":"1704.01354v1","created_at":"2026-05-18T00:46:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.01354","created_at":"2026-05-18T00:46:58Z"},{"alias_kind":"pith_short_12","alias_value":"L2ZPJDJFESVQ","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"L2ZPJDJFESVQWQOR","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"L2ZPJDJF","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:0da9489dc59a42856bb891e6d317834c6fabb04eaf5048ac66f697a10849d805","target":"graph","created_at":"2026-05-18T00:46:58Z","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 give a new proof of E. Le Page's theorem on the Holder continuity of the first Lyapunov exponent in the class of irreducible Bernoulli cocycles. This suggests an algorithm to approximate the first Lyapunov exponent, as well as the stationary measure, for such random cocycles.","authors_text":"Alexandre Baraviera, Pedro Duarte","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-04-05T10:27:19Z","title":"Approximating Lyapunov exponents and stationary measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.01354","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":"sha256:117d41e7702ff09923d29a2ca6701ab76858ef137acb2bb5c4cb547a3d7820b9","target":"record","created_at":"2026-05-18T00:46:58Z","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":"78da61845a6c2fe6e4fec4a515ff4b905bae61df39f57520e530706356c13ddc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-04-05T10:27:19Z","title_canon_sha256":"40b67642a3ddd1bf9f25b43dd63e67b9b67fea9e313ddc394420b8ba5b37303d"},"schema_version":"1.0","source":{"id":"1704.01354","kind":"arxiv","version":1}},"canonical_sha256":"5eb2f48d2524ab0b41d1812b51e20c5897fca18bfc0ab2024de72558ca8bcc1c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5eb2f48d2524ab0b41d1812b51e20c5897fca18bfc0ab2024de72558ca8bcc1c","first_computed_at":"2026-05-18T00:46:58.358763Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:58.358763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ohqkhZKj+BdcS15COltyk78EB9Onz/0KQ6u4UnU923Er0m/2kIKgQ6vFRvcdx2VS5nxS5YKEpH/p2+67z+L8Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:58.359277Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.01354","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:117d41e7702ff09923d29a2ca6701ab76858ef137acb2bb5c4cb547a3d7820b9","sha256:0da9489dc59a42856bb891e6d317834c6fabb04eaf5048ac66f697a10849d805"],"state_sha256":"1f5ecb5294f2b36a98bcb0e6b36e867f38c86e53b7e72e9a05cdaff19643c0ea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z07lAZ7yIlJdgFSHrdgN7g0DWUZbqZt/wXmE36Td6Zmq6TbQTCxT3iZI1aDXZEHJ3PJP/5bUNEgl60rsHgiXCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T03:13:42.419058Z","bundle_sha256":"82ee06094f2b9117c12914f6d4535fea5d30f5a1144f89ce351415471dbf3a6b"}}