{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:5UNR4I6AGZ6BSQ3ADW2XGVAXRE","short_pith_number":"pith:5UNR4I6A","schema_version":"1.0","canonical_sha256":"ed1b1e23c0367c1943601db5735417893e768cac31f4a70abc5157c5672d2266","source":{"kind":"arxiv","id":"2507.07206","version":2},"attestation_state":"computed","paper":{"title":"Global invertibility of Sobolev mappings with prescribed homeomorphic boundary values","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Sabrina Traver (Syracuse University)","submitted_at":"2025-07-09T18:29:55Z","abstract_excerpt":"Let $X, Y \\subset \\mathbb{R}^n$ be Lipschitz domains, and suppose there is a homeomorphism $\\varphi \\colon \\overline{X} \\to \\overline{Y}$. We consider the class of Sobolev mappings $f \\in W^{1,n} (X, \\mathbb{R}^n)$ with a strictly positive Jacobian determinant almost everywhere, whose Sobolev trace coincides with $\\varphi$ on $\\partial X$. We prove that every mapping in this class extends continuously to $\\overline{X}$ and is a monotone (continuous) surjection from $\\overline{X}$ onto $\\overline{Y}$ in the sense of C.B. Morrey. As monotone mappings, they may squeeze but not fold the reference "},"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":"2507.07206","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2025-07-09T18:29:55Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"1fdc0efaa120e73ce90ca4d6166978b103af9c2dd549fc3e69f9c7e2fe192369","abstract_canon_sha256":"aa80404044ecc3ea711cca2bdabb92e8b64de41ed1987f6caec12e7847b06b0a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-25T02:01:05.478277Z","signature_b64":"nRpDoi/YjA131d0MVVuy6EfBl9vbD93euVFIU6BTyFoIu1wAbQa1FSzXLnckpUKRTX6c15r4Z95ajYdswY1sBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed1b1e23c0367c1943601db5735417893e768cac31f4a70abc5157c5672d2266","last_reissued_at":"2026-05-25T02:01:05.477673Z","signature_status":"signed_v1","first_computed_at":"2026-05-25T02:01:05.477673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global invertibility of Sobolev mappings with prescribed homeomorphic boundary values","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Sabrina Traver (Syracuse University)","submitted_at":"2025-07-09T18:29:55Z","abstract_excerpt":"Let $X, Y \\subset \\mathbb{R}^n$ be Lipschitz domains, and suppose there is a homeomorphism $\\varphi \\colon \\overline{X} \\to \\overline{Y}$. We consider the class of Sobolev mappings $f \\in W^{1,n} (X, \\mathbb{R}^n)$ with a strictly positive Jacobian determinant almost everywhere, whose Sobolev trace coincides with $\\varphi$ on $\\partial X$. We prove that every mapping in this class extends continuously to $\\overline{X}$ and is a monotone (continuous) surjection from $\\overline{X}$ onto $\\overline{Y}$ in the sense of C.B. Morrey. As monotone mappings, they may squeeze but not fold the reference "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.07206","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.07206/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2507.07206","created_at":"2026-05-25T02:01:05.477761+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.07206v2","created_at":"2026-05-25T02:01:05.477761+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.07206","created_at":"2026-05-25T02:01:05.477761+00:00"},{"alias_kind":"pith_short_12","alias_value":"5UNR4I6AGZ6B","created_at":"2026-05-25T02:01:05.477761+00:00"},{"alias_kind":"pith_short_16","alias_value":"5UNR4I6AGZ6BSQ3A","created_at":"2026-05-25T02:01:05.477761+00:00"},{"alias_kind":"pith_short_8","alias_value":"5UNR4I6A","created_at":"2026-05-25T02:01:05.477761+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/5UNR4I6AGZ6BSQ3ADW2XGVAXRE","json":"https://pith.science/pith/5UNR4I6AGZ6BSQ3ADW2XGVAXRE.json","graph_json":"https://pith.science/api/pith-number/5UNR4I6AGZ6BSQ3ADW2XGVAXRE/graph.json","events_json":"https://pith.science/api/pith-number/5UNR4I6AGZ6BSQ3ADW2XGVAXRE/events.json","paper":"https://pith.science/paper/5UNR4I6A"},"agent_actions":{"view_html":"https://pith.science/pith/5UNR4I6AGZ6BSQ3ADW2XGVAXRE","download_json":"https://pith.science/pith/5UNR4I6AGZ6BSQ3ADW2XGVAXRE.json","view_paper":"https://pith.science/paper/5UNR4I6A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.07206&json=true","fetch_graph":"https://pith.science/api/pith-number/5UNR4I6AGZ6BSQ3ADW2XGVAXRE/graph.json","fetch_events":"https://pith.science/api/pith-number/5UNR4I6AGZ6BSQ3ADW2XGVAXRE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5UNR4I6AGZ6BSQ3ADW2XGVAXRE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5UNR4I6AGZ6BSQ3ADW2XGVAXRE/action/storage_attestation","attest_author":"https://pith.science/pith/5UNR4I6AGZ6BSQ3ADW2XGVAXRE/action/author_attestation","sign_citation":"https://pith.science/pith/5UNR4I6AGZ6BSQ3ADW2XGVAXRE/action/citation_signature","submit_replication":"https://pith.science/pith/5UNR4I6AGZ6BSQ3ADW2XGVAXRE/action/replication_record"}},"created_at":"2026-05-25T02:01:05.477761+00:00","updated_at":"2026-05-25T02:01:05.477761+00:00"}