{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:FBE3Y7EYPPQ5FH3HYKHFVPI32R","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":"a7f9621b8b06320c52013a3ba9dece04705f1d438e9aa27771a2f3c81197801b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-10-28T07:29:16Z","title_canon_sha256":"2a1fee1db45a2bd1ed31ed6a4df12e82fec14d559c9140b8a65abed40c128b43"},"schema_version":"1.0","source":{"id":"1110.6269","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.6269","created_at":"2026-05-18T04:02:27Z"},{"alias_kind":"arxiv_version","alias_value":"1110.6269v2","created_at":"2026-05-18T04:02:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6269","created_at":"2026-05-18T04:02:27Z"},{"alias_kind":"pith_short_12","alias_value":"FBE3Y7EYPPQ5","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FBE3Y7EYPPQ5FH3H","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FBE3Y7EY","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:4020446716f4065f29e0d21ac3e1dff7b5ed45d0fdae96c220b64fc3f5024335","target":"graph","created_at":"2026-05-18T04:02:27Z","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 $E$ and $E'$ denote real Banach spaces with dimension at least 2, that $D\\subset E$ and $D'\\subset E'$ are domains, and that $f: D\\to D'$ is a homeomorphism. In this paper, we prove that if there exists some constant $M>1$ (resp. some homeomorphism $\\phi$) such that for all $x\\in D$, $f: B(x,d_D(x))\\to f(B(x,d_D(x)))$ is $M$-QH (resp. $\\phi$-FQC), then $f$ is $M_1$-QH with $M_1=M_1(M)$ (resp. $\\phi_1$-FQC with $\\phi_1=\\phi_1(\\phi)$). We apply our results to establish, in terms of the $j_D$ metric, a sufficient condition for a homeomorphism to be FQC.","authors_text":"Matti Vuorinen, Xiantao Wang, Yaxiang Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-10-28T07:29:16Z","title":"Local properties of quasihyperbolic and freely quasiconformal mappings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6269","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:bc3cf9953a5bc424ab665cc3e6a511745ea2c86aa7a0c01267d822af213dd4bd","target":"record","created_at":"2026-05-18T04:02:27Z","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":"a7f9621b8b06320c52013a3ba9dece04705f1d438e9aa27771a2f3c81197801b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-10-28T07:29:16Z","title_canon_sha256":"2a1fee1db45a2bd1ed31ed6a4df12e82fec14d559c9140b8a65abed40c128b43"},"schema_version":"1.0","source":{"id":"1110.6269","kind":"arxiv","version":2}},"canonical_sha256":"2849bc7c987be1d29f67c28e5abd1bd44cddf973a3e2a3c4f740514d1d7c79d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2849bc7c987be1d29f67c28e5abd1bd44cddf973a3e2a3c4f740514d1d7c79d1","first_computed_at":"2026-05-18T04:02:27.015704Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:27.015704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qfmhOQL5lDkV3ACJcGSwKihwvIUjmhsHlkUZkxUki6+D97nLwtj9PS/De33/0ncvTEi/j9jfa6Q5f+MhXW1NDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:27.016275Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.6269","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc3cf9953a5bc424ab665cc3e6a511745ea2c86aa7a0c01267d822af213dd4bd","sha256:4020446716f4065f29e0d21ac3e1dff7b5ed45d0fdae96c220b64fc3f5024335"],"state_sha256":"a9794e03ae3ac4e2129e99d5c765e578bf0d37708a988f4302d547280237ef35"}