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Suppose $v,u\\in W^{1,2}(B_1(0):\\mathbb{R}^2)$ are $Q$-quasiregular mappings with $\\int_{B_1(0)} \\det(Du)^{-p} dz\\leq C_p$ for some $p\\in (0,1)$ and $\\int_{B_1(0)} |Du|^2 dz\\leq 1$. There exists constant $M>1$ such that if $$ \\int_{B_1(0)} |S(Du)-S(Dv)|^2 dz=\\epsilon $$ then $$ \\int_{B_{\\frac{1}{2}}(0)} |Dv-R Du| dz\\leq c C_p^{\\frac{1}{p}}\\epsilon^{\\fra"},"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":"1312.0339","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-02T06:35:48Z","cross_cats_sorted":[],"title_canon_sha256":"fe0e9929c9ebee07da7d9498d226f3d7fb102c24fe7c3cb51c030bf6f835deb6","abstract_canon_sha256":"cf31e9101a3868b8e6c24f2007fc5418b70f953aaedc13103e6e5f23d3f076ef"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:46.015981Z","signature_b64":"inXQPyeNFdAu8MbvyM9Mf1Ibdd9nWOrR1KKwkSVWlbMB0KGJ/XeRFrvxeIxN0O3AnVvmka2zk7XICbaG1FZjCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38f2d6e9dda1551006960c272e09a2808dddc8e23aca6a31fe2915ff995395d8","last_reissued_at":"2026-05-18T03:05:46.015278Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:46.015278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rigidity of pairs of quasiregular mappings whose symmetric part of gradient are close","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrew Lorent","submitted_at":"2013-12-02T06:35:48Z","abstract_excerpt":"For $A\\in M^{2\\times 2}$ let $S(A)=\\sqrt{A^T A}$, i.e. the symmetric part of the polar decomposition of $A$. We consider the relation between two quasiregular mappings whose symmetric part of gradient are close. Our main result is the following. Suppose $v,u\\in W^{1,2}(B_1(0):\\mathbb{R}^2)$ are $Q$-quasiregular mappings with $\\int_{B_1(0)} \\det(Du)^{-p} dz\\leq C_p$ for some $p\\in (0,1)$ and $\\int_{B_1(0)} |Du|^2 dz\\leq 1$. There exists constant $M>1$ such that if $$ \\int_{B_1(0)} |S(Du)-S(Dv)|^2 dz=\\epsilon $$ then $$ \\int_{B_{\\frac{1}{2}}(0)} |Dv-R Du| dz\\leq c C_p^{\\frac{1}{p}}\\epsilon^{\\fra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0339","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":"1312.0339","created_at":"2026-05-18T03:05:46.015403+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.0339v1","created_at":"2026-05-18T03:05:46.015403+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.0339","created_at":"2026-05-18T03:05:46.015403+00:00"},{"alias_kind":"pith_short_12","alias_value":"HDZNN2O5UFKR","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"HDZNN2O5UFKRABUW","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"HDZNN2O5","created_at":"2026-05-18T12:27:46.883200+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/HDZNN2O5UFKRABUWBQTS4CNCQC","json":"https://pith.science/pith/HDZNN2O5UFKRABUWBQTS4CNCQC.json","graph_json":"https://pith.science/api/pith-number/HDZNN2O5UFKRABUWBQTS4CNCQC/graph.json","events_json":"https://pith.science/api/pith-number/HDZNN2O5UFKRABUWBQTS4CNCQC/events.json","paper":"https://pith.science/paper/HDZNN2O5"},"agent_actions":{"view_html":"https://pith.science/pith/HDZNN2O5UFKRABUWBQTS4CNCQC","download_json":"https://pith.science/pith/HDZNN2O5UFKRABUWBQTS4CNCQC.json","view_paper":"https://pith.science/paper/HDZNN2O5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.0339&json=true","fetch_graph":"https://pith.science/api/pith-number/HDZNN2O5UFKRABUWBQTS4CNCQC/graph.json","fetch_events":"https://pith.science/api/pith-number/HDZNN2O5UFKRABUWBQTS4CNCQC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HDZNN2O5UFKRABUWBQTS4CNCQC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HDZNN2O5UFKRABUWBQTS4CNCQC/action/storage_attestation","attest_author":"https://pith.science/pith/HDZNN2O5UFKRABUWBQTS4CNCQC/action/author_attestation","sign_citation":"https://pith.science/pith/HDZNN2O5UFKRABUWBQTS4CNCQC/action/citation_signature","submit_replication":"https://pith.science/pith/HDZNN2O5UFKRABUWBQTS4CNCQC/action/replication_record"}},"created_at":"2026-05-18T03:05:46.015403+00:00","updated_at":"2026-05-18T03:05:46.015403+00:00"}