{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:ZKPPILSLMJQXSKZBG4T66QO6VO","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":"e42d3c7f16e79b80d45372191137d0edb7c54cba375799f9758bba6e586f4dab","cross_cats_sorted":["math.DG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2021-08-05T17:40:29Z","title_canon_sha256":"1eea9dc8ca6bae3e1fd205d63886bf98b590d9f23009d8699f8f2b8e6739ee5d"},"schema_version":"1.0","source":{"id":"2108.02754","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2108.02754","created_at":"2026-07-05T03:03:35Z"},{"alias_kind":"arxiv_version","alias_value":"2108.02754v1","created_at":"2026-07-05T03:03:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.02754","created_at":"2026-07-05T03:03:35Z"},{"alias_kind":"pith_short_12","alias_value":"ZKPPILSLMJQX","created_at":"2026-07-05T03:03:35Z"},{"alias_kind":"pith_short_16","alias_value":"ZKPPILSLMJQXSKZB","created_at":"2026-07-05T03:03:35Z"},{"alias_kind":"pith_short_8","alias_value":"ZKPPILSL","created_at":"2026-07-05T03:03:35Z"}],"graph_snapshots":[{"event_id":"sha256:b56c41c9cc0743c0f14050c49f5e2da2d97d0a361e9bff4468a7deb8a02edb61","target":"graph","created_at":"2026-07-05T03:03:35Z","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/2108.02754/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We construct entire solutions of the magnetic Ginzburg-Landau equations in dimension 4 using Lyapunov-Schmidt reduction. The zero set of these solutions are close to the minimal submanifolds studied by Arezzo-Pacard\\cite{Arezzo}. We also show the existence of a saddle type solution to the equations, whose zero set consists of two vertical planes in $\\mathbb{R}^4$. These two types of solutions are believed to be energy minimizers of the corresponding energy functional and lie in the same connect component of the moduli space of entire solutions.","authors_text":"Juncheng Wei, Wangze Wu, Xinan Ma, Yong Liu","cross_cats":["math.DG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2021-08-05T17:40:29Z","title":"Entire solutions of the magnetic Ginzburg-Landau equation in $\\mathbb{R}^4$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.02754","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":"sha256:930faab5f0b4d6f2237d056fe3b2b2dbc70c2912dbffaadd77900d7d8e8eba50","target":"record","created_at":"2026-07-05T03:03:35Z","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":"e42d3c7f16e79b80d45372191137d0edb7c54cba375799f9758bba6e586f4dab","cross_cats_sorted":["math.DG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2021-08-05T17:40:29Z","title_canon_sha256":"1eea9dc8ca6bae3e1fd205d63886bf98b590d9f23009d8699f8f2b8e6739ee5d"},"schema_version":"1.0","source":{"id":"2108.02754","kind":"arxiv","version":1}},"canonical_sha256":"ca9ef42e4b6261792b213727ef41deab9b9e9fd310cb81ba4907bdffdaf0591b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca9ef42e4b6261792b213727ef41deab9b9e9fd310cb81ba4907bdffdaf0591b","first_computed_at":"2026-07-05T03:03:35.988483Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:03:35.988483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kTyVJjrYAyQRg5VXkuBtA4BY4eLhuAyQIHzVwChT5hhi52v/sN0GWGLtUjk3wwc5ZAU4A7kyfagflHX1OUx8Bg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:03:35.988928Z","signed_message":"canonical_sha256_bytes"},"source_id":"2108.02754","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:930faab5f0b4d6f2237d056fe3b2b2dbc70c2912dbffaadd77900d7d8e8eba50","sha256:b56c41c9cc0743c0f14050c49f5e2da2d97d0a361e9bff4468a7deb8a02edb61"],"state_sha256":"d63c40143f595ec23583fe8a22f05fbff43a4a9a225d9f88101d64bbfcb083d7"}