{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:2KSBGPQS4QDN7O5UZ4IEIJZZMM","short_pith_number":"pith:2KSBGPQS","schema_version":"1.0","canonical_sha256":"d2a4133e12e406dfbbb4cf10442739630bf87b6f7083f7404c756cd72b3bb4e7","source":{"kind":"arxiv","id":"1211.2022","version":1},"attestation_state":"computed","paper":{"title":"On bilipschitz extensions in real Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Manzi Huang, Yaxiang Li","submitted_at":"2012-11-09T01:12:25Z","abstract_excerpt":"Suppose that $E$ and $E'$ denote real Banach spaces with dimension at least 2, that $D\\not=E$ and $D'\\not=E'$ are bounded domains with connected boundaries, that $f: D\\to D'$ is an $M$-QH homeomorphism, and that $D'$ is uniform.\n  The main aim of this paper is to prove that $f$ extends to a homeomorphism $\\bar \\bar{D}\\to \\bar{D}'$ and $\\bar{f}|\\partial D$ is bilipschitz if and only if $f$ is bilipschitz in $\\bar{D}$. The answer to some open problem of V\\\"ais\\\"al\\\"a is affirmative under an natural additional condition."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1211.2022","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-11-09T01:12:25Z","cross_cats_sorted":[],"title_canon_sha256":"9cd576a01b1c7fe75eb240beb577efedbec204997cf32f5c325884ac78f8cc75","abstract_canon_sha256":"60dc653cf95e0ed76feca43923884ab52717ab7e3806df8402ae1176a9eb609a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:11.946502Z","signature_b64":"ZRM2CLrSNnjo47/iYWzJM3hzYlxg4MJ3s5nrGd2mSPqMfNKZXIilvHauvHKsTxb20+pOw6pr7TFEWGjvulFADA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d2a4133e12e406dfbbb4cf10442739630bf87b6f7083f7404c756cd72b3bb4e7","last_reissued_at":"2026-05-18T03:41:11.946101Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:11.946101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On bilipschitz extensions in real Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Manzi Huang, Yaxiang Li","submitted_at":"2012-11-09T01:12:25Z","abstract_excerpt":"Suppose that $E$ and $E'$ denote real Banach spaces with dimension at least 2, that $D\\not=E$ and $D'\\not=E'$ are bounded domains with connected boundaries, that $f: D\\to D'$ is an $M$-QH homeomorphism, and that $D'$ is uniform.\n  The main aim of this paper is to prove that $f$ extends to a homeomorphism $\\bar \\bar{D}\\to \\bar{D}'$ and $\\bar{f}|\\partial D$ is bilipschitz if and only if $f$ is bilipschitz in $\\bar{D}$. The answer to some open problem of V\\\"ais\\\"al\\\"a is affirmative under an natural additional condition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2022","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1211.2022","created_at":"2026-05-18T03:41:11.946165+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.2022v1","created_at":"2026-05-18T03:41:11.946165+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.2022","created_at":"2026-05-18T03:41:11.946165+00:00"},{"alias_kind":"pith_short_12","alias_value":"2KSBGPQS4QDN","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_16","alias_value":"2KSBGPQS4QDN7O5U","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_8","alias_value":"2KSBGPQS","created_at":"2026-05-18T12:26:50.516681+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2KSBGPQS4QDN7O5UZ4IEIJZZMM","json":"https://pith.science/pith/2KSBGPQS4QDN7O5UZ4IEIJZZMM.json","graph_json":"https://pith.science/api/pith-number/2KSBGPQS4QDN7O5UZ4IEIJZZMM/graph.json","events_json":"https://pith.science/api/pith-number/2KSBGPQS4QDN7O5UZ4IEIJZZMM/events.json","paper":"https://pith.science/paper/2KSBGPQS"},"agent_actions":{"view_html":"https://pith.science/pith/2KSBGPQS4QDN7O5UZ4IEIJZZMM","download_json":"https://pith.science/pith/2KSBGPQS4QDN7O5UZ4IEIJZZMM.json","view_paper":"https://pith.science/paper/2KSBGPQS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.2022&json=true","fetch_graph":"https://pith.science/api/pith-number/2KSBGPQS4QDN7O5UZ4IEIJZZMM/graph.json","fetch_events":"https://pith.science/api/pith-number/2KSBGPQS4QDN7O5UZ4IEIJZZMM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2KSBGPQS4QDN7O5UZ4IEIJZZMM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2KSBGPQS4QDN7O5UZ4IEIJZZMM/action/storage_attestation","attest_author":"https://pith.science/pith/2KSBGPQS4QDN7O5UZ4IEIJZZMM/action/author_attestation","sign_citation":"https://pith.science/pith/2KSBGPQS4QDN7O5UZ4IEIJZZMM/action/citation_signature","submit_replication":"https://pith.science/pith/2KSBGPQS4QDN7O5UZ4IEIJZZMM/action/replication_record"}},"created_at":"2026-05-18T03:41:11.946165+00:00","updated_at":"2026-05-18T03:41:11.946165+00:00"}