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More precisely, we consider variationally biharmonic maps $u\\in W^{2,2}(\\Omega,N)$, which are defined as critical points of the bi-energy that satisfy a certain stationarity condition up to the boundary. For weakly convergent sequences of variationally biharmonic maps, we demonstrate that the only obstruction that can prevent the strong compa"},"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":"1907.01908","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-07-03T12:55:21Z","cross_cats_sorted":[],"title_canon_sha256":"f6154d60b6e1acb67db68dbc7ba865e79e6ed75f66e422db94b680e09823e537","abstract_canon_sha256":"dd7648652cd4126540d3a3f13ab7bd786b09e0ef8499c09ab1fa74b6450693f2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:34.589941Z","signature_b64":"Te+8WaLxvKKyBo1XJje/KDV/iZ+HyzqK2keaHRmWU0FVtMFnEi/mfmbNeQRGP0XtFVZctVgWI5Ev31VMgI2vDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"684b180fd05845aab00db3bd626306a598e67b7985150232d0f54a80fda6b8aa","last_reissued_at":"2026-05-17T23:41:34.589250Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:34.589250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Blow-up analysis and boundary regularity for variationally biharmonic maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Christoph Scheven, Serdar Altuntas","submitted_at":"2019-07-03T12:55:21Z","abstract_excerpt":"We consider critical points $u:\\Omega\\to N$ of the bi-energy\n  \\[\n  \\int_\\Omega |\\Delta u|^2\\,d x,\n  \\]\n  where $\\Omega\\subset\\mathbb{R}^m$ is a bounded smooth domain of dimension $m\\ge 5$ and $N\\subset\\mathbb{R}^L$ a compact submanifold without boundary. More precisely, we consider variationally biharmonic maps $u\\in W^{2,2}(\\Omega,N)$, which are defined as critical points of the bi-energy that satisfy a certain stationarity condition up to the boundary. For weakly convergent sequences of variationally biharmonic maps, we demonstrate that the only obstruction that can prevent the strong compa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.01908","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":"1907.01908","created_at":"2026-05-17T23:41:34.589397+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.01908v1","created_at":"2026-05-17T23:41:34.589397+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.01908","created_at":"2026-05-17T23:41:34.589397+00:00"},{"alias_kind":"pith_short_12","alias_value":"NBFRQD6QLBC2","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_16","alias_value":"NBFRQD6QLBC2VMAN","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_8","alias_value":"NBFRQD6Q","created_at":"2026-05-18T12:33:24.271573+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/NBFRQD6QLBC2VMANWO6WEYYGUW","json":"https://pith.science/pith/NBFRQD6QLBC2VMANWO6WEYYGUW.json","graph_json":"https://pith.science/api/pith-number/NBFRQD6QLBC2VMANWO6WEYYGUW/graph.json","events_json":"https://pith.science/api/pith-number/NBFRQD6QLBC2VMANWO6WEYYGUW/events.json","paper":"https://pith.science/paper/NBFRQD6Q"},"agent_actions":{"view_html":"https://pith.science/pith/NBFRQD6QLBC2VMANWO6WEYYGUW","download_json":"https://pith.science/pith/NBFRQD6QLBC2VMANWO6WEYYGUW.json","view_paper":"https://pith.science/paper/NBFRQD6Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.01908&json=true","fetch_graph":"https://pith.science/api/pith-number/NBFRQD6QLBC2VMANWO6WEYYGUW/graph.json","fetch_events":"https://pith.science/api/pith-number/NBFRQD6QLBC2VMANWO6WEYYGUW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NBFRQD6QLBC2VMANWO6WEYYGUW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NBFRQD6QLBC2VMANWO6WEYYGUW/action/storage_attestation","attest_author":"https://pith.science/pith/NBFRQD6QLBC2VMANWO6WEYYGUW/action/author_attestation","sign_citation":"https://pith.science/pith/NBFRQD6QLBC2VMANWO6WEYYGUW/action/citation_signature","submit_replication":"https://pith.science/pith/NBFRQD6QLBC2VMANWO6WEYYGUW/action/replication_record"}},"created_at":"2026-05-17T23:41:34.589397+00:00","updated_at":"2026-05-17T23:41:34.589397+00:00"}