{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:ZOUXIMHS5AYBQZ4AB6ZCFVA3CA","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":"e78ede910e17afbfdb3589b5c411a7552117823e4f14d6ed542d7dc3184f5417","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-09-13T16:42:19Z","title_canon_sha256":"3e4d5d4d5b00468cb3bf13a19608b4dbd088e7e2eecd8cb027d6e7abebfed278"},"schema_version":"1.0","source":{"id":"0909.2426","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.2426","created_at":"2026-05-18T04:32:34Z"},{"alias_kind":"arxiv_version","alias_value":"0909.2426v2","created_at":"2026-05-18T04:32:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.2426","created_at":"2026-05-18T04:32:34Z"},{"alias_kind":"pith_short_12","alias_value":"ZOUXIMHS5AYB","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"ZOUXIMHS5AYBQZ4A","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"ZOUXIMHS","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:0eb3e201a2cdd365488679f8bbd01e14c97321f17a125dcc9aabce1b34f8e2b3","target":"graph","created_at":"2026-05-18T04:32:34Z","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":"An almost Fuchsian 3-manifold is a quasi-Fuchsian manifold which contains an incompressible closed minimal surface with principal curvatures in the range of $(-1,1)$. Such a 3-manifold $M$ admits a foliation of parallel surfaces, whose locus in Teichm\\\"{u}ller space is represented as a path $\\gamma$, we show that $\\gamma$ joins the conformal structures of the two components of the conformal boundary of $M$. Moreover, we obtain an upper bound for the Teichm\\\"{u}ller distance between any two points on $\\gamma$, in particular, the Teichm\\\"{u}ller distance between the two components of the conform","authors_text":"Biao Wang, Ren Guo, Zheng Huang","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-09-13T16:42:19Z","title":"Quasi-Fuchsian 3-Manifolds and Metrics on Teichm\\\"{u}ller Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.2426","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":"sha256:8083cb4a5cdd68c3567b906549ea9fc3cf727a0abb0511b9afcc4c0e36a0b96b","target":"record","created_at":"2026-05-18T04:32:34Z","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":"e78ede910e17afbfdb3589b5c411a7552117823e4f14d6ed542d7dc3184f5417","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-09-13T16:42:19Z","title_canon_sha256":"3e4d5d4d5b00468cb3bf13a19608b4dbd088e7e2eecd8cb027d6e7abebfed278"},"schema_version":"1.0","source":{"id":"0909.2426","kind":"arxiv","version":2}},"canonical_sha256":"cba97430f2e8301867800fb222d41b103296eaecc770d4d21cba199c1f3c817e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cba97430f2e8301867800fb222d41b103296eaecc770d4d21cba199c1f3c817e","first_computed_at":"2026-05-18T04:32:34.120237Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:34.120237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OHFJulE07PbxS+b70Jxmtr1cTicNR4D2QNsK+F96ZRm7VlfXmzP2poBNiJQEHFXXoOwmCcHJCJ4hubb2LUxpBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:34.120720Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.2426","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8083cb4a5cdd68c3567b906549ea9fc3cf727a0abb0511b9afcc4c0e36a0b96b","sha256:0eb3e201a2cdd365488679f8bbd01e14c97321f17a125dcc9aabce1b34f8e2b3"],"state_sha256":"94c5e984e6d21664dd771177a38b851844488d2e7ab66d0aca8c462ab3c5d9a4"}