{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:KVC3WJRY22O4ISLWULE46GDDCK","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":"03bff1f68abe28fc45385864f280c4eb4b744ea5ea5bb326e22b7eabe04b79f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-05-27T16:01:15Z","title_canon_sha256":"f41e9e53d848fc56493eb8a31360c774359bb1a9aa3955f9b251a77cddeaade2"},"schema_version":"1.0","source":{"id":"2605.28668","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.28668","created_at":"2026-05-28T02:04:59Z"},{"alias_kind":"arxiv_version","alias_value":"2605.28668v1","created_at":"2026-05-28T02:04:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.28668","created_at":"2026-05-28T02:04:59Z"},{"alias_kind":"pith_short_12","alias_value":"KVC3WJRY22O4","created_at":"2026-05-28T02:04:59Z"},{"alias_kind":"pith_short_16","alias_value":"KVC3WJRY22O4ISLW","created_at":"2026-05-28T02:04:59Z"},{"alias_kind":"pith_short_8","alias_value":"KVC3WJRY","created_at":"2026-05-28T02:04:59Z"}],"graph_snapshots":[{"event_id":"sha256:b06231e1a9038cc59258038e516c48c78ffdc6a2da64d471b49b823a42754495","target":"graph","created_at":"2026-05-28T02:04:59Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2605.28668/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $n\\geq 3$ and let $\\Omega \\subset \\mathbb{R}^n$ be a $\\mathcal{C}^1$ bounded domain which is diffeomorphic to a ball. We investigate here the problem of finding critical points of the $n$-energy in the space $\\mathcal{I}=\\{v\\in W^{1,n}(\\Omega,\\mathbb{R}^n) ; \\ |\\mathrm{tr}_{|\\partial \\Omega}v|=1\\}$. Maps in $\\mathcal{I}$ have a well-defined topological degree on $\\partial \\Omega$ but this degree is not continuous for the weak convergence in $W^{1,n}$. Hence finding critical points with prescribed degrees results in a problem of lack of compactness. We first prove that minimizers of the $n$","authors_text":"Dorian Martino, Katarzyna Mazowiecka, R\\'emy Rodiac","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-05-27T16:01:15Z","title":"Min-max $n$-harmonic maps of degree 1 with free-boundary into $\\mathbb{S}^{n-1}$ in almost round balls"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.28668","kind":"arxiv","version":1},"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":"sha256:5233234e7ef08d424c91b33bba02bdf3c14103f8cae83267ff7b82bf4a2aa52a","target":"record","created_at":"2026-05-28T02:04:59Z","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":"03bff1f68abe28fc45385864f280c4eb4b744ea5ea5bb326e22b7eabe04b79f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-05-27T16:01:15Z","title_canon_sha256":"f41e9e53d848fc56493eb8a31360c774359bb1a9aa3955f9b251a77cddeaade2"},"schema_version":"1.0","source":{"id":"2605.28668","kind":"arxiv","version":1}},"canonical_sha256":"5545bb2638d69dc44976a2c9cf1863128d591da472a9445afa4ca2aa293ad430","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5545bb2638d69dc44976a2c9cf1863128d591da472a9445afa4ca2aa293ad430","first_computed_at":"2026-05-28T02:04:59.372670Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-28T02:04:59.372670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1gKMSGXHA6rcDkKSEPgDnkf4UQ+u7Mkza/ciDJnGt6R5gaEmayFJjz3WPG4R7K5Uv3MxW3mMNQfNKJrs8EMBCQ==","signature_status":"signed_v1","signed_at":"2026-05-28T02:04:59.373286Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.28668","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5233234e7ef08d424c91b33bba02bdf3c14103f8cae83267ff7b82bf4a2aa52a","sha256:b06231e1a9038cc59258038e516c48c78ffdc6a2da64d471b49b823a42754495"],"state_sha256":"82dfabd993b570f576f1f4f250cba01edaf56c4ff622e63e8f240e884eb55b42"}