{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:5IH54EP7A3TCWFVEQKBX6EV4H3","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":"10372bc5214ee5002bb14f22201586ad4956b0564caa28825d10a26cff972c31","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-10-06T16:29:24Z","title_canon_sha256":"0c5c2fb6893bc8eb0e6163585d9f6ebbc5be824e2cc935c0f4b38c6eb9f7c6df"},"schema_version":"1.0","source":{"id":"0910.1050","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.1050","created_at":"2026-05-18T02:52:42Z"},{"alias_kind":"arxiv_version","alias_value":"0910.1050v4","created_at":"2026-05-18T02:52:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.1050","created_at":"2026-05-18T02:52:42Z"},{"alias_kind":"pith_short_12","alias_value":"5IH54EP7A3TC","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"5IH54EP7A3TCWFVE","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"5IH54EP7","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:89e14d725fadfa5b5d4e010f594e7370df8435956dfa5758bf5770ef3c09f8a3","target":"graph","created_at":"2026-05-18T02:52:42Z","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":"A Riemann surface $M$ is said to be $K$-quasiconformally homogeneous if for every two points $p,q \\in M$, there exists a $K$-quasiconformal homeomorphism $f \\colon M \\rightarrow M$ such that $f(p) = q$. In this paper, we show there exists a universal constant $K_0 > 1$ such that if $M$ is a $K$-quasiconformally homogeneous hyperbolic genus zero surface other than the disk $\\mathbb{D}$, then $K \\geq K_0$. This answers a question by Gehring and Palka.","authors_text":"Ferry Kwakkel, Vlad Markovic","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-10-06T16:29:24Z","title":"Quasiconformal Homogeneity of Genus Zero Surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.1050","kind":"arxiv","version":4},"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:e73367b86756e98d025ad18fa182f9231195c6b14eb4b3f07d52e8083221ec01","target":"record","created_at":"2026-05-18T02:52:42Z","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":"10372bc5214ee5002bb14f22201586ad4956b0564caa28825d10a26cff972c31","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-10-06T16:29:24Z","title_canon_sha256":"0c5c2fb6893bc8eb0e6163585d9f6ebbc5be824e2cc935c0f4b38c6eb9f7c6df"},"schema_version":"1.0","source":{"id":"0910.1050","kind":"arxiv","version":4}},"canonical_sha256":"ea0fde11ff06e62b16a482837f12bc3efeae1ec9048fa5c47f7cbb0e0e5037c9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea0fde11ff06e62b16a482837f12bc3efeae1ec9048fa5c47f7cbb0e0e5037c9","first_computed_at":"2026-05-18T02:52:42.532422Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:42.532422Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XZnDMcUGAHj7NqcIR3BknOJQ+w4CIMCU3TuAA176Gwy/9L4hDVfxjArrP8Ok7GLKNgzQ1NtkjQyxZclUAByXCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:42.532849Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.1050","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e73367b86756e98d025ad18fa182f9231195c6b14eb4b3f07d52e8083221ec01","sha256:89e14d725fadfa5b5d4e010f594e7370df8435956dfa5758bf5770ef3c09f8a3"],"state_sha256":"b4cb4ef2fd31b9399e251bc3fcca624740f8d717d840d968ab479e44d4e7fc5d"}