{"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"}