{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:VXI42DK3DZ75YKN2ITHHUH4FS3","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":"67470a838c2fb52fd34d5097e17ce2751ae3040aed900796813ca38c970301c2","cross_cats_sorted":["math.AP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2022-05-24T22:34:48Z","title_canon_sha256":"97fbdb56f21bf96b305622a061599862b6c9abaa03747bf64baed2f15023e2c6"},"schema_version":"1.0","source":{"id":"2205.12389","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2205.12389","created_at":"2026-07-05T04:26:25Z"},{"alias_kind":"arxiv_version","alias_value":"2205.12389v1","created_at":"2026-07-05T04:26:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.12389","created_at":"2026-07-05T04:26:25Z"},{"alias_kind":"pith_short_12","alias_value":"VXI42DK3DZ75","created_at":"2026-07-05T04:26:25Z"},{"alias_kind":"pith_short_16","alias_value":"VXI42DK3DZ75YKN2","created_at":"2026-07-05T04:26:25Z"},{"alias_kind":"pith_short_8","alias_value":"VXI42DK3","created_at":"2026-07-05T04:26:25Z"}],"graph_snapshots":[{"event_id":"sha256:781eebbf6add4bc0953a8d4b169fb186e3b0a80696450debea214e273558ecd0","target":"graph","created_at":"2026-07-05T04:26:25Z","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/2205.12389/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that every non-degenerate minimal submanifold of codimension two can be obtained as the energy concentration set of a family of critical maps for the (rescaled) Ginzburg-Landau functional. The proof is purely variational, and follows the strategy laid out by Jerrard and Sternberg, extending a recent result for geodesics by Colinet-Jerrard-Sternberg. The same proof applies also to the $U(1)$-Yang-Mills-Higgs and to the Allen-Cahn-Hilliard energies.","authors_text":"Alessandro Pigati, Guido De Philippis","cross_cats":["math.AP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2022-05-24T22:34:48Z","title":"Non-degenerate minimal submanifolds as energy concentration sets: a variational approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.12389","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":"sha256:7ff64fafe31335f0a130622b8d456041735720e0cce87642714ab880019896da","target":"record","created_at":"2026-07-05T04:26:25Z","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":"67470a838c2fb52fd34d5097e17ce2751ae3040aed900796813ca38c970301c2","cross_cats_sorted":["math.AP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2022-05-24T22:34:48Z","title_canon_sha256":"97fbdb56f21bf96b305622a061599862b6c9abaa03747bf64baed2f15023e2c6"},"schema_version":"1.0","source":{"id":"2205.12389","kind":"arxiv","version":1}},"canonical_sha256":"add1cd0d5b1e7fdc29ba44ce7a1f8596d14899c6f8d01c1e9c1e3bd96ba38461","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"add1cd0d5b1e7fdc29ba44ce7a1f8596d14899c6f8d01c1e9c1e3bd96ba38461","first_computed_at":"2026-07-05T04:26:25.230085Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:26:25.230085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0ATw7TKAfJU4TX2t/HhgEafIKukkfbSskyZzAoRMnzSX2IUpmUGuEDFtjpHW4PLYP8jz50/18X3hNgk/en20CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:26:25.230568Z","signed_message":"canonical_sha256_bytes"},"source_id":"2205.12389","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ff64fafe31335f0a130622b8d456041735720e0cce87642714ab880019896da","sha256:781eebbf6add4bc0953a8d4b169fb186e3b0a80696450debea214e273558ecd0"],"state_sha256":"7d6cad42ab053a391501831e1e37aa7eb55010ac2028667afe2985e53b29bd53"}