{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:G5Z76DTXK7ASA2SYY2NH4OLYVM","short_pith_number":"pith:G5Z76DTX","canonical_record":{"source":{"id":"1807.11335","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-07-30T13:19:48Z","cross_cats_sorted":[],"title_canon_sha256":"f57d9f06808adcc5920883d53e4436991c427561f976e9e70d1288104dec789f","abstract_canon_sha256":"2cd0f2f4a440e57f1b80f2e78abc37d29b64afead91089da8b1e3d0945808fc0"},"schema_version":"1.0"},"canonical_sha256":"3773ff0e7757c1206a58c69a7e3978ab3e538556d7dc5c8e16d10d614bd0f21b","source":{"kind":"arxiv","id":"1807.11335","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.11335","created_at":"2026-05-18T00:09:32Z"},{"alias_kind":"arxiv_version","alias_value":"1807.11335v1","created_at":"2026-05-18T00:09:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.11335","created_at":"2026-05-18T00:09:32Z"},{"alias_kind":"pith_short_12","alias_value":"G5Z76DTXK7AS","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"G5Z76DTXK7ASA2SY","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"G5Z76DTX","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:G5Z76DTXK7ASA2SYY2NH4OLYVM","target":"record","payload":{"canonical_record":{"source":{"id":"1807.11335","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-07-30T13:19:48Z","cross_cats_sorted":[],"title_canon_sha256":"f57d9f06808adcc5920883d53e4436991c427561f976e9e70d1288104dec789f","abstract_canon_sha256":"2cd0f2f4a440e57f1b80f2e78abc37d29b64afead91089da8b1e3d0945808fc0"},"schema_version":"1.0"},"canonical_sha256":"3773ff0e7757c1206a58c69a7e3978ab3e538556d7dc5c8e16d10d614bd0f21b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:32.200942Z","signature_b64":"gKCINztzfRzEvygW1Po0mvGEVQQUsRivbWDM3eXNpiDtEfl4ni0by/6roK66cuJ6OS4EFQSLe9biL4suGuetBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3773ff0e7757c1206a58c69a7e3978ab3e538556d7dc5c8e16d10d614bd0f21b","last_reissued_at":"2026-05-18T00:09:32.200386Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:32.200386Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.11335","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":"2026-05-18T00:09:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rX3UlkFgC6ejq3JWkGl4izhOZy3XyZLOBGKfTp9M1dJxt3BHvJvs8dLJjMyMEySMjUqvoAM4EGLC/GVFUabvBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T22:43:13.725122Z"},"content_sha256":"1fe1e5fd2e2f8f42c782a79d88ed8a7ed4fb32340b9687a22f81c0666ee37377","schema_version":"1.0","event_id":"sha256:1fe1e5fd2e2f8f42c782a79d88ed8a7ed4fb32340b9687a22f81c0666ee37377"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:G5Z76DTXK7ASA2SYY2NH4OLYVM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characterization of uniform hyperbolicity for fiber-bunched cocycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Renato Velozo","submitted_at":"2018-07-30T13:19:48Z","abstract_excerpt":"We prove a new characterization of uniform hyperbolicity for fiber-bunched cocycles. Specifically, we show that the existence of a uniform gap between the Lyapunov exponents of a fiber-bunched $SL(2,\\mathbb{R})$-cocycle defined over a subshift of finite type or an Anosov diffeomorphism implies uniform hyperbolicity. In addition, we construct an $\\alpha$-H\\\"{o}lder cocycle which has uniform gap between the Lyapunov exponents, however it is not uniformly hyperbolic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11335","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":"2026-05-18T00:09:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VyySNLqjz0wecixM7Rldo5FlV2QBbX2+3gk/+o2QBevk++S95jWuT7o2sH1pNyRVJNLUuSwzJAq9/dJMIR1pCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T22:43:13.725857Z"},"content_sha256":"4a1920587e039f430791a07ea5511f5b7697af2a615c06c3fc105d182f266aab","schema_version":"1.0","event_id":"sha256:4a1920587e039f430791a07ea5511f5b7697af2a615c06c3fc105d182f266aab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G5Z76DTXK7ASA2SYY2NH4OLYVM/bundle.json","state_url":"https://pith.science/pith/G5Z76DTXK7ASA2SYY2NH4OLYVM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G5Z76DTXK7ASA2SYY2NH4OLYVM/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":"2026-06-07T22:43:13Z","links":{"resolver":"https://pith.science/pith/G5Z76DTXK7ASA2SYY2NH4OLYVM","bundle":"https://pith.science/pith/G5Z76DTXK7ASA2SYY2NH4OLYVM/bundle.json","state":"https://pith.science/pith/G5Z76DTXK7ASA2SYY2NH4OLYVM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G5Z76DTXK7ASA2SYY2NH4OLYVM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:G5Z76DTXK7ASA2SYY2NH4OLYVM","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":"2cd0f2f4a440e57f1b80f2e78abc37d29b64afead91089da8b1e3d0945808fc0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-07-30T13:19:48Z","title_canon_sha256":"f57d9f06808adcc5920883d53e4436991c427561f976e9e70d1288104dec789f"},"schema_version":"1.0","source":{"id":"1807.11335","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.11335","created_at":"2026-05-18T00:09:32Z"},{"alias_kind":"arxiv_version","alias_value":"1807.11335v1","created_at":"2026-05-18T00:09:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.11335","created_at":"2026-05-18T00:09:32Z"},{"alias_kind":"pith_short_12","alias_value":"G5Z76DTXK7AS","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"G5Z76DTXK7ASA2SY","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"G5Z76DTX","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:4a1920587e039f430791a07ea5511f5b7697af2a615c06c3fc105d182f266aab","target":"graph","created_at":"2026-05-18T00:09:32Z","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 prove a new characterization of uniform hyperbolicity for fiber-bunched cocycles. Specifically, we show that the existence of a uniform gap between the Lyapunov exponents of a fiber-bunched $SL(2,\\mathbb{R})$-cocycle defined over a subshift of finite type or an Anosov diffeomorphism implies uniform hyperbolicity. In addition, we construct an $\\alpha$-H\\\"{o}lder cocycle which has uniform gap between the Lyapunov exponents, however it is not uniformly hyperbolic.","authors_text":"Renato Velozo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-07-30T13:19:48Z","title":"Characterization of uniform hyperbolicity for fiber-bunched cocycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11335","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":"sha256:1fe1e5fd2e2f8f42c782a79d88ed8a7ed4fb32340b9687a22f81c0666ee37377","target":"record","created_at":"2026-05-18T00:09:32Z","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":"2cd0f2f4a440e57f1b80f2e78abc37d29b64afead91089da8b1e3d0945808fc0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-07-30T13:19:48Z","title_canon_sha256":"f57d9f06808adcc5920883d53e4436991c427561f976e9e70d1288104dec789f"},"schema_version":"1.0","source":{"id":"1807.11335","kind":"arxiv","version":1}},"canonical_sha256":"3773ff0e7757c1206a58c69a7e3978ab3e538556d7dc5c8e16d10d614bd0f21b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3773ff0e7757c1206a58c69a7e3978ab3e538556d7dc5c8e16d10d614bd0f21b","first_computed_at":"2026-05-18T00:09:32.200386Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:32.200386Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gKCINztzfRzEvygW1Po0mvGEVQQUsRivbWDM3eXNpiDtEfl4ni0by/6roK66cuJ6OS4EFQSLe9biL4suGuetBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:32.200942Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.11335","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1fe1e5fd2e2f8f42c782a79d88ed8a7ed4fb32340b9687a22f81c0666ee37377","sha256:4a1920587e039f430791a07ea5511f5b7697af2a615c06c3fc105d182f266aab"],"state_sha256":"9e3f216cf5a8a1aaef89035594240fcd0cc74abfdad1aa60013ca29e4073bfaf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9Rg9LCqcNJsqOOvYkgSlE6ndRliIOHh3svJFCDRrN8B8SsDmS1v0BzsPuKmGlLr1twrTEfPTMc18KUj0evO6AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T22:43:13.729972Z","bundle_sha256":"999cfd906cb1e9e9da7109b4957f2c8ced1e937821ad35fb2630cc8a5426d2c4"}}