{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:PUEGNWE34B3UPFTE2W7UW3UUHE","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":"ac9bf9c31f2a4876e1209ecfbdf191ec115ec9db0da023bf579acc09867c0e21","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-07-22T18:46:00Z","title_canon_sha256":"1b814c0c73e48f78d97904bacf509ce051c5eba5dddc21e4eae0d7b4b18e336b"},"schema_version":"1.0","source":{"id":"1007.3967","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.3967","created_at":"2026-05-18T04:40:09Z"},{"alias_kind":"arxiv_version","alias_value":"1007.3967v2","created_at":"2026-05-18T04:40:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.3967","created_at":"2026-05-18T04:40:09Z"},{"alias_kind":"pith_short_12","alias_value":"PUEGNWE34B3U","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"PUEGNWE34B3UPFTE","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"PUEGNWE3","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:f7fdd1f65f0acf2e0bcf2eee69121d975c03d56bbff3cdf585c537a853bca7ea","target":"graph","created_at":"2026-05-18T04:40:09Z","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"},"paper":{"abstract_excerpt":"We study sequences $f_k:\\Sigma_k \\to \\R^n$ of conformally immersed, compact Riemann surfaces with fixed genus and Willmore energy ${\\cal W}(f) \\leq \\Lambda$. Assume that $\\Sigma_k$ converges to $\\Sigma$ in moduli space, i.e. $\\phi_k^\\ast(\\Sigma_k) \\to \\Sigma$ as complex structures for diffeomorphisms $\\phi_k$. Then we construct a branched conformal immersion $f:\\Sigma \\to \\R^n$ and M\\\"obius transformations $\\sigma_k$, such that for a subsequence $\\sigma_k \\circ f_k \\circ \\phi_k \\to f$ weakly in $W^{2,2}_{loc}$ away from finitely many points. For $\\Lambda < 8\\pi$ the map $f$ is unbranched. If t","authors_text":"Ernst Kuwert, Yuxiang Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-07-22T18:46:00Z","title":"$W^{2,2}$-conformal immersions of a closed Riemann surface into $\\R^n$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.3967","kind":"arxiv","version":2},"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":"sha256:2a8fc5bd735776563c57130ff030501eefe3fc649eb5b4f5685dcfcddf455664","target":"record","created_at":"2026-05-18T04:40:09Z","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":"ac9bf9c31f2a4876e1209ecfbdf191ec115ec9db0da023bf579acc09867c0e21","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-07-22T18:46:00Z","title_canon_sha256":"1b814c0c73e48f78d97904bacf509ce051c5eba5dddc21e4eae0d7b4b18e336b"},"schema_version":"1.0","source":{"id":"1007.3967","kind":"arxiv","version":2}},"canonical_sha256":"7d0866d89be077479664d5bf4b6e9439306b0a7805d3025025b5fcb63e125338","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d0866d89be077479664d5bf4b6e9439306b0a7805d3025025b5fcb63e125338","first_computed_at":"2026-05-18T04:40:09.268817Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:09.268817Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"re1cmsVFS3tpYfT3I7N5vbupZ7lyDkDdT/SwFp+XyrEg9zYUbiH6yUKUz81nUvGzMD5xujoF4ckgOIsw/NptBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:09.269242Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.3967","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a8fc5bd735776563c57130ff030501eefe3fc649eb5b4f5685dcfcddf455664","sha256:f7fdd1f65f0acf2e0bcf2eee69121d975c03d56bbff3cdf585c537a853bca7ea"],"state_sha256":"7ecd65cf8274b9555c7e537631b0b2ce041f741caa7e86865841221c6665adc1"}