{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NMQJ5HTMIDLX3YEHMPFAVFZ6O2","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":"64dc496cf6665f62ec61c9063b67251d450cc461013dfb1c166c57008cbc01c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-01-13T09:01:38Z","title_canon_sha256":"6fcd40c038bcfa7f6757196a0a0ad7299d9819d82264185cb036b9fc5889ebe5"},"schema_version":"1.0","source":{"id":"1301.2756","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2756","created_at":"2026-05-18T01:17:26Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2756v4","created_at":"2026-05-18T01:17:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2756","created_at":"2026-05-18T01:17:26Z"},{"alias_kind":"pith_short_12","alias_value":"NMQJ5HTMIDLX","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NMQJ5HTMIDLX3YEH","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NMQJ5HTM","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:b2a14021595101483555379a5c18d75f034aeef5d570b16855942d625c8bdf83","target":"graph","created_at":"2026-05-18T01:17:26Z","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":"In this paper we deal with the global properties of Willmore surfaces in spheres via the harmonic conformal Gauss map using loop groups.\n  We first derive a global description of those harmonic maps which can be realized as conformal Gauss maps of some Willmore surfaces (Theorem 3.4, Theorem 3.11 and Theorem 3.18).\n  Then we introduce the DPW procedure for these harmonic maps, and state appropriate versions of the Iwasawa decomposition and the Birkhoff decomposition Theorems. In particular, we show how the harmonic maps associated with Willmore surfaces can be constructed in terms of loop grou","authors_text":"Josef F. Dorfmeister, Peng Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-01-13T09:01:38Z","title":"Willmore surfaces in spheres via loop groups $I$: generic cases and some examples"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2756","kind":"arxiv","version":4},"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":"sha256:17418e0711ffae5d5dc4237a2f139cae16b3125d51888e022077c90fc437e521","target":"record","created_at":"2026-05-18T01:17:26Z","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":"64dc496cf6665f62ec61c9063b67251d450cc461013dfb1c166c57008cbc01c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-01-13T09:01:38Z","title_canon_sha256":"6fcd40c038bcfa7f6757196a0a0ad7299d9819d82264185cb036b9fc5889ebe5"},"schema_version":"1.0","source":{"id":"1301.2756","kind":"arxiv","version":4}},"canonical_sha256":"6b209e9e6c40d77de08763ca0a973e7695c1e9dba894df47ce860d4884afee1a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b209e9e6c40d77de08763ca0a973e7695c1e9dba894df47ce860d4884afee1a","first_computed_at":"2026-05-18T01:17:26.272482Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:26.272482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ljidRy0FciTmCfR4YJcZogJqQPLdDcdNXYoszOzgq1ZD28Yg5yYlQWgMYVojLOSHIK3U7EReAVw7+sdZAmZcCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:26.272919Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.2756","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:17418e0711ffae5d5dc4237a2f139cae16b3125d51888e022077c90fc437e521","sha256:b2a14021595101483555379a5c18d75f034aeef5d570b16855942d625c8bdf83"],"state_sha256":"943bd1f51eed11901dac7a315d243231c9a564e87fbee9d8fb56813cdaa432ff"}