{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6GCXPOA2AACPVDUPFVZRQYAB34","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":"e00072188b28ff1d0f938f8dfcb1f4ec8678b839a4dd066594248fe658a242b7","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CV","submitted_at":"2015-01-29T08:32:10Z","title_canon_sha256":"069c0072fefa7b046da5c76cc338729ba90743d1caecd54503157a7e654db2f2"},"schema_version":"1.0","source":{"id":"1501.07375","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.07375","created_at":"2026-05-18T02:27:31Z"},{"alias_kind":"arxiv_version","alias_value":"1501.07375v2","created_at":"2026-05-18T02:27:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.07375","created_at":"2026-05-18T02:27:31Z"},{"alias_kind":"pith_short_12","alias_value":"6GCXPOA2AACP","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6GCXPOA2AACPVDUP","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6GCXPOA2","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:b457da18c790a98a78353b744d8e7c5cd4f656d0ac13692637b40e4d558a290a","target":"graph","created_at":"2026-05-18T02:27:31Z","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":"Suppose that $X$ and $Y$ are quasiconvex and complete metric spaces, that $G\\subset X$ and $G'\\subset Y$ are domains, and that $f: G\\to G'$ is a homeomorphism. Our main result is the following subinvariance property of the class of uniform domains: Suppose both $f$ and $f^{-1}$ are weakly quasisymmetric mappings and $G'$ is a quasiconvex domain. Then the image $f(D)$ of every uniform subdomain $D$ in $G$ under $f$ is uniform. The subinvariance of uniform domains with respect to freely quasiconformal mappings or quasihyperbolic mappings is also studied with the additional condition that both $G","authors_text":"Manzi Huang, Qingshan Zhou, Xiantao Wang, Yaxiang Li","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CV","submitted_at":"2015-01-29T08:32:10Z","title":"On the subinvariance of uniform domains in metric spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07375","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":"sha256:5d3bca684c41627838f307700f7d39159f1049af202f6d33ecb436a91661550d","target":"record","created_at":"2026-05-18T02:27:31Z","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":"e00072188b28ff1d0f938f8dfcb1f4ec8678b839a4dd066594248fe658a242b7","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CV","submitted_at":"2015-01-29T08:32:10Z","title_canon_sha256":"069c0072fefa7b046da5c76cc338729ba90743d1caecd54503157a7e654db2f2"},"schema_version":"1.0","source":{"id":"1501.07375","kind":"arxiv","version":2}},"canonical_sha256":"f18577b81a0004fa8e8f2d73186001df11ee41be8147ca2adeb24a035e25d801","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f18577b81a0004fa8e8f2d73186001df11ee41be8147ca2adeb24a035e25d801","first_computed_at":"2026-05-18T02:27:31.520087Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:31.520087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W2pN1pITExd3J3YeRzHWeQ6z0IT1phB7VQkFtYAx03bFgIkv9su0/nQHDbZgCVidsVYfFDS9RMA5PDSgIu2CAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:31.520832Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.07375","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d3bca684c41627838f307700f7d39159f1049af202f6d33ecb436a91661550d","sha256:b457da18c790a98a78353b744d8e7c5cd4f656d0ac13692637b40e4d558a290a"],"state_sha256":"3c7c414b9e9bddcc0b501426f98cb86f9cbfcafad7623a1bbc8c9e08ab1c5ac6"}