{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:RI3OSK4XQASTS77GVSRO2CAI5Q","short_pith_number":"pith:RI3OSK4X","canonical_record":{"source":{"id":"0808.0133","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-08-01T15:00:41Z","cross_cats_sorted":[],"title_canon_sha256":"9b393c310122a07bbde25fc1720891862a35627f6a1588315975766764d1a224","abstract_canon_sha256":"1e3df36f395328ba4da5ef03e22e6e67782d2aeef67506339d6b6434f474c6d0"},"schema_version":"1.0"},"canonical_sha256":"8a36e92b978025397fe6aca2ed0808ec23714debd792193f403a434fcdb33952","source":{"kind":"arxiv","id":"0808.0133","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0808.0133","created_at":"2026-05-18T04:27:58Z"},{"alias_kind":"arxiv_version","alias_value":"0808.0133v1","created_at":"2026-05-18T04:27:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.0133","created_at":"2026-05-18T04:27:58Z"},{"alias_kind":"pith_short_12","alias_value":"RI3OSK4XQAST","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"RI3OSK4XQASTS77G","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"RI3OSK4X","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:RI3OSK4XQASTS77GVSRO2CAI5Q","target":"record","payload":{"canonical_record":{"source":{"id":"0808.0133","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-08-01T15:00:41Z","cross_cats_sorted":[],"title_canon_sha256":"9b393c310122a07bbde25fc1720891862a35627f6a1588315975766764d1a224","abstract_canon_sha256":"1e3df36f395328ba4da5ef03e22e6e67782d2aeef67506339d6b6434f474c6d0"},"schema_version":"1.0"},"canonical_sha256":"8a36e92b978025397fe6aca2ed0808ec23714debd792193f403a434fcdb33952","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:58.366520Z","signature_b64":"HZ3ujFv5dyNQmCsMiijcqvmOwGkhCKf+oM4fBL5MpKbyJmJIUO/4pzS5cJKuXm9AByVZQXgNOdFgRPYPo8+vCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a36e92b978025397fe6aca2ed0808ec23714debd792193f403a434fcdb33952","last_reissued_at":"2026-05-18T04:27:58.366016Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:58.366016Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0808.0133","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":"2026-05-18T04:27:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LmVzDdKU+sInmj0scWCmJI9fRO4a3OSPVyc0FoF74yeZce83adCH4BZPLy5HNDn3Bfsge+I0S+Jy20xcZ8/xBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T14:56:59.476837Z"},"content_sha256":"d3029fe3e2e46e60eaea6f2bcace6a3be90cc079a3c2b2daf40371f431a030b7","schema_version":"1.0","event_id":"sha256:d3029fe3e2e46e60eaea6f2bcace6a3be90cc079a3c2b2daf40371f431a030b7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:RI3OSK4XQASTS77GVSRO2CAI5Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniformly Hyperbolic Finite-Valued SL(2,R)-Cocycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Artur Avila, Jairo Bochi, Jean-Christophe Yoccoz","submitted_at":"2008-08-01T15:00:41Z","abstract_excerpt":"We consider finite families of SL(2,R) matrices whose products display uniform exponential growth. These form open subsets of (SL(2,R))^N, and we study their components, boundary, and complement. We also consider the more general situation where the allowed products of matrices satisfy a Markovian rule."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.0133","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":"2026-05-18T04:27:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8AAZM/C/Dfmx6gNFwbvlu5f8kqr1iJ7FJbyaPhBVpY2r3uBE/wUmq9RJAwdX/yA3pB/2+IeXA+dcdyXYPTSbAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T14:56:59.477179Z"},"content_sha256":"6c6229f1623939811c70222c21fc7af94d8350f27100a6b8066eae8fc32387ed","schema_version":"1.0","event_id":"sha256:6c6229f1623939811c70222c21fc7af94d8350f27100a6b8066eae8fc32387ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RI3OSK4XQASTS77GVSRO2CAI5Q/bundle.json","state_url":"https://pith.science/pith/RI3OSK4XQASTS77GVSRO2CAI5Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RI3OSK4XQASTS77GVSRO2CAI5Q/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":"2026-06-08T14:56:59Z","links":{"resolver":"https://pith.science/pith/RI3OSK4XQASTS77GVSRO2CAI5Q","bundle":"https://pith.science/pith/RI3OSK4XQASTS77GVSRO2CAI5Q/bundle.json","state":"https://pith.science/pith/RI3OSK4XQASTS77GVSRO2CAI5Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RI3OSK4XQASTS77GVSRO2CAI5Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:RI3OSK4XQASTS77GVSRO2CAI5Q","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":"1e3df36f395328ba4da5ef03e22e6e67782d2aeef67506339d6b6434f474c6d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-08-01T15:00:41Z","title_canon_sha256":"9b393c310122a07bbde25fc1720891862a35627f6a1588315975766764d1a224"},"schema_version":"1.0","source":{"id":"0808.0133","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0808.0133","created_at":"2026-05-18T04:27:58Z"},{"alias_kind":"arxiv_version","alias_value":"0808.0133v1","created_at":"2026-05-18T04:27:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.0133","created_at":"2026-05-18T04:27:58Z"},{"alias_kind":"pith_short_12","alias_value":"RI3OSK4XQAST","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"RI3OSK4XQASTS77G","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"RI3OSK4X","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:6c6229f1623939811c70222c21fc7af94d8350f27100a6b8066eae8fc32387ed","target":"graph","created_at":"2026-05-18T04:27:58Z","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 consider finite families of SL(2,R) matrices whose products display uniform exponential growth. These form open subsets of (SL(2,R))^N, and we study their components, boundary, and complement. We also consider the more general situation where the allowed products of matrices satisfy a Markovian rule.","authors_text":"Artur Avila, Jairo Bochi, Jean-Christophe Yoccoz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-08-01T15:00:41Z","title":"Uniformly Hyperbolic Finite-Valued SL(2,R)-Cocycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.0133","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:d3029fe3e2e46e60eaea6f2bcace6a3be90cc079a3c2b2daf40371f431a030b7","target":"record","created_at":"2026-05-18T04:27:58Z","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":"1e3df36f395328ba4da5ef03e22e6e67782d2aeef67506339d6b6434f474c6d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-08-01T15:00:41Z","title_canon_sha256":"9b393c310122a07bbde25fc1720891862a35627f6a1588315975766764d1a224"},"schema_version":"1.0","source":{"id":"0808.0133","kind":"arxiv","version":1}},"canonical_sha256":"8a36e92b978025397fe6aca2ed0808ec23714debd792193f403a434fcdb33952","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a36e92b978025397fe6aca2ed0808ec23714debd792193f403a434fcdb33952","first_computed_at":"2026-05-18T04:27:58.366016Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:58.366016Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HZ3ujFv5dyNQmCsMiijcqvmOwGkhCKf+oM4fBL5MpKbyJmJIUO/4pzS5cJKuXm9AByVZQXgNOdFgRPYPo8+vCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:58.366520Z","signed_message":"canonical_sha256_bytes"},"source_id":"0808.0133","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d3029fe3e2e46e60eaea6f2bcace6a3be90cc079a3c2b2daf40371f431a030b7","sha256:6c6229f1623939811c70222c21fc7af94d8350f27100a6b8066eae8fc32387ed"],"state_sha256":"ef48acc5f6e2f049317b5dd042c5d2d13a60d7a58e60beb6d59403cd49cb8be0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gzd8jqPIMhJh6M3UmTB0Bq8mpC7pyX0GMSDDEhHtEgoMyEJ6WnFIuFGirTf4Oc77fbx+KJBCrWBNa77wsTL/BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T14:56:59.479037Z","bundle_sha256":"b7abf7622867b904f8c68b41352e8be6484a5fd0b8a8936f430f5f25f641c058"}}