{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:VFNVEMOVVFEXKZL3NIOHHL524Q","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":"ec0948da04ef0e0a96290b0ca11f8a01e2d9d56c9bc47caeec5f2a7491413aba","cross_cats_sorted":["math.AP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2023-10-30T17:58:22Z","title_canon_sha256":"fedd3678bc692f8b9dd2dc48e8c2eb6151f418ef1628b55915fe93a4510eeb4c"},"schema_version":"1.0","source":{"id":"2310.19860","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.19860","created_at":"2026-07-05T07:09:04Z"},{"alias_kind":"arxiv_version","alias_value":"2310.19860v2","created_at":"2026-07-05T07:09:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.19860","created_at":"2026-07-05T07:09:04Z"},{"alias_kind":"pith_short_12","alias_value":"VFNVEMOVVFEX","created_at":"2026-07-05T07:09:04Z"},{"alias_kind":"pith_short_16","alias_value":"VFNVEMOVVFEXKZL3","created_at":"2026-07-05T07:09:04Z"},{"alias_kind":"pith_short_8","alias_value":"VFNVEMOV","created_at":"2026-07-05T07:09:04Z"}],"graph_snapshots":[{"event_id":"sha256:9b1f5d6a54ed7f02e158f9d102f4328540f4ce15a4633f778a17d2ed098f7fa3","target":"graph","created_at":"2026-07-05T07:09:04Z","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/2310.19860/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In 1974, Federer proved that all area-minimizing hypersurfaces on orientable manifolds were calibrated by weakly closed differential forms. However, in this manuscript, we prove the contrary in higher codimensions: calibrated area-minimizers are non-generic. This is surprising given that almost all known examples of area-minimizing surfaces are confirmed to be minimizing via calibration. Let integers $d\\ge 1$ and $c\\ge 2$ denote dimensions and codimensions, respectively. Let $M^{d+c}$ denote a closed, orientable, smooth manifold of dimension $d+c$. For each $d$-dimensional integral homology cl","authors_text":"Zhenhua Liu","cross_cats":["math.AP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2023-10-30T17:58:22Z","title":"Homologically area-minimizing surfaces that cannot be calibrated"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.19860","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":"sha256:366d726c76ea8f2678d5382d6f30f7306d201553a882a8ec9369017e6bc33f23","target":"record","created_at":"2026-07-05T07:09:04Z","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":"ec0948da04ef0e0a96290b0ca11f8a01e2d9d56c9bc47caeec5f2a7491413aba","cross_cats_sorted":["math.AP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2023-10-30T17:58:22Z","title_canon_sha256":"fedd3678bc692f8b9dd2dc48e8c2eb6151f418ef1628b55915fe93a4510eeb4c"},"schema_version":"1.0","source":{"id":"2310.19860","kind":"arxiv","version":2}},"canonical_sha256":"a95b5231d5a94975657b6a1c73afbae418e9b2946bbab0fdb9ffda471c7bdcf3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a95b5231d5a94975657b6a1c73afbae418e9b2946bbab0fdb9ffda471c7bdcf3","first_computed_at":"2026-07-05T07:09:04.110882Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:09:04.110882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eG1GQmMkwPlgW7YSlulIdfASQzMBklVSiWvVwxJTl27tW0cyNJPtHf9tzDKJjJdDkyb9pNRRolrGw7uG9sxLCg==","signature_status":"signed_v1","signed_at":"2026-07-05T07:09:04.111283Z","signed_message":"canonical_sha256_bytes"},"source_id":"2310.19860","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:366d726c76ea8f2678d5382d6f30f7306d201553a882a8ec9369017e6bc33f23","sha256:9b1f5d6a54ed7f02e158f9d102f4328540f4ce15a4633f778a17d2ed098f7fa3"],"state_sha256":"09f245de42b406942c929c961f9ea6be52730944f4d3078598ac18c53e9170de"}