{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:BZYXRK2VKUV6RSTHAZYBWHJVEX","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":"2b56d2a8ff6f385b78045980a3bb82d85aa9b2f1626e48da448c866ea184bd4d","cross_cats_sorted":["math.GT"],"license":"","primary_cat":"math.DG","submitted_at":"2002-05-29T09:15:39Z","title_canon_sha256":"75d51c7d9f8afbc0e30fbaebc7cc9470c462583b25ad0c5bc9e10c1d3c6d687c"},"schema_version":"1.0","source":{"id":"math/0205305","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0205305","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"arxiv_version","alias_value":"math/0205305v5","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0205305","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"pith_short_12","alias_value":"BZYXRK2VKUV6","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"BZYXRK2VKUV6RSTH","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"BZYXRK2V","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:21f8aa977d188d08e67a29aac189b153b497275677ff0190a5d8da2461ea5ff9","target":"graph","created_at":"2026-05-18T01:38:29Z","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":"Let $(M, \\partial M)$ be a compact 3-manifold with boundary, which admits a convex co-compact hyperbolic metric. We consider the hyperbolic metrics on $M$ such that the boundary is smooth and strictly convex. We show that the induced metrics on the boundary are exactly the metrics with curvature $K>-1$, and that the third fundamental forms of $\\dr M$ are exactly the metrics with curvature $K<1$, for which contractible closed geodesics have length $L>2\\pi$. Each is obtained exactly once.\n  Other related results describe existence and uniqueness properties for other boundary conditions, when the","authors_text":"Jean-Marc Schlenker","cross_cats":["math.GT"],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2002-05-29T09:15:39Z","title":"Hyperbolic manifolds with convex boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0205305","kind":"arxiv","version":5},"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:e38e22343190e62ac0208b6b75a95afa07d124de6dcd87f8889eee73c8dd30a4","target":"record","created_at":"2026-05-18T01:38:29Z","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":"2b56d2a8ff6f385b78045980a3bb82d85aa9b2f1626e48da448c866ea184bd4d","cross_cats_sorted":["math.GT"],"license":"","primary_cat":"math.DG","submitted_at":"2002-05-29T09:15:39Z","title_canon_sha256":"75d51c7d9f8afbc0e30fbaebc7cc9470c462583b25ad0c5bc9e10c1d3c6d687c"},"schema_version":"1.0","source":{"id":"math/0205305","kind":"arxiv","version":5}},"canonical_sha256":"0e7178ab55552be8ca6706701b1d3525e6902df18987a2d9cd64638bb7f7868f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e7178ab55552be8ca6706701b1d3525e6902df18987a2d9cd64638bb7f7868f","first_computed_at":"2026-05-18T01:38:29.567116Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:29.567116Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TZFQYp9iFegMa3jAydrvzzIRjbvLqvYXGWgruVt+ajcWZg2Xa8p5k98zK2hXtB6HJRsoqtjqg+dw3haJD3xdDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:29.567881Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0205305","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e38e22343190e62ac0208b6b75a95afa07d124de6dcd87f8889eee73c8dd30a4","sha256:21f8aa977d188d08e67a29aac189b153b497275677ff0190a5d8da2461ea5ff9"],"state_sha256":"6d254e8ff598e7f93c4a3e2141965548c44fce576172117903e3f595838a040a"}