{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:UMNU7ZBKYGGVZMCZA7IW4DJJVU","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":"7ece7974883ae4512568a5ef71f68c99adcf5c6c5be1d8c5ef15763780f54d55","cross_cats_sorted":["math.MG"],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.GT","submitted_at":"2011-10-29T11:47:24Z","title_canon_sha256":"509c4ff36f7266e56f299cb62846f56e4c9c4dbff2976109d4b1f56c1568e950"},"schema_version":"1.0","source":{"id":"1110.6526","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.6526","created_at":"2026-05-18T03:34:35Z"},{"alias_kind":"arxiv_version","alias_value":"1110.6526v2","created_at":"2026-05-18T03:34:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6526","created_at":"2026-05-18T03:34:35Z"},{"alias_kind":"pith_short_12","alias_value":"UMNU7ZBKYGGV","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UMNU7ZBKYGGVZMCZ","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UMNU7ZBK","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:35c37c9ea0d863296d0d088c557716937f1126704714c9605eefed6c0c14ead0","target":"graph","created_at":"2026-05-18T03:34:35Z","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, for any n, that there is a closed connected orientable surface S so that the hyperbolic space H^n almost-isometrically embeds into the Teichm\\\"uller space of S, with quasi-convex image lying in the thick part. As a consequence, H^n quasi-isometrically embeds in the curve complex of S.","authors_text":"Christopher J. Leininger, Saul Schleimer","cross_cats":["math.MG"],"headline":"","license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.GT","submitted_at":"2011-10-29T11:47:24Z","title":"Hyperbolic spaces in Teichm\\\"uller spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6526","kind":"arxiv","version":2},"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:e4a3c6740a22cd6d5b2cc63aa27175957d2cb6829afa7f46a250625a01706776","target":"record","created_at":"2026-05-18T03:34:35Z","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":"7ece7974883ae4512568a5ef71f68c99adcf5c6c5be1d8c5ef15763780f54d55","cross_cats_sorted":["math.MG"],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.GT","submitted_at":"2011-10-29T11:47:24Z","title_canon_sha256":"509c4ff36f7266e56f299cb62846f56e4c9c4dbff2976109d4b1f56c1568e950"},"schema_version":"1.0","source":{"id":"1110.6526","kind":"arxiv","version":2}},"canonical_sha256":"a31b4fe42ac18d5cb05907d16e0d29ad335d9c88436eb336314fc43a1aecf191","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a31b4fe42ac18d5cb05907d16e0d29ad335d9c88436eb336314fc43a1aecf191","first_computed_at":"2026-05-18T03:34:35.774164Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:35.774164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kpg7FnxVqMdbG4ut2VeIDEqRzD8mD3dtQx1hu0cbjh9sAQUCkDSb4TYbeymk3dnZjifg1C3YIIjE9g1KYf8TDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:35.774761Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.6526","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4a3c6740a22cd6d5b2cc63aa27175957d2cb6829afa7f46a250625a01706776","sha256:35c37c9ea0d863296d0d088c557716937f1126704714c9605eefed6c0c14ead0"],"state_sha256":"49cc9cbacd0046374dc0b6a8ce74312b7a82982cdafbf039712fcd92f346ce67"}