{"paper":{"title":"Biharmonic rotational surfaces in the four-dimensional Euclidean space are minimal","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"Any biharmonic simple rotational surface in four-dimensional Euclidean space is minimal.","cross_cats":[],"primary_cat":"math.DG","authors_text":"Shun Maeta","submitted_at":"2026-05-10T14:58:36Z","abstract_excerpt":"In this paper, we show that any biharmonic simple rotational surface in the four-dimensional Euclidean space is minimal. The proof is based on reducing the biharmonic equation to a system of ordinary differential equations for the profile curve and then excluding all possible non-minimal branches. This is a partial affirmative answer to Chen's conjecture."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Any biharmonic simple rotational surface in the four-dimensional Euclidean space is minimal.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The surface is assumed to be a simple rotational surface whose profile curve lies in a fixed 2-plane, allowing the biharmonic equation to reduce cleanly to an ODE system without additional curvature or torsion terms.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Biharmonic simple rotational surfaces in R^4 are minimal.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Any biharmonic simple rotational surface in four-dimensional Euclidean space is minimal.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"b853d7a539c484c646a5be987d5f8585761455e96c57282e04c7062d044e7525"},"source":{"id":"2605.09587","kind":"arxiv","version":2},"verdict":{"id":"0f5d60cd-5d45-4c3d-a9fd-8c550520a141","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T18:07:49.079528Z","strongest_claim":"Any biharmonic simple rotational surface in the four-dimensional Euclidean space is minimal.","one_line_summary":"Biharmonic simple rotational surfaces in R^4 are minimal.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The surface is assumed to be a simple rotational surface whose profile curve lies in a fixed 2-plane, allowing the biharmonic equation to reduce cleanly to an ODE system without additional curvature or torsion terms.","pith_extraction_headline":"Any biharmonic simple rotational surface in four-dimensional Euclidean space is minimal."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.09587/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T16:39:16.283421Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T13:01:17.391114Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T10:07:57.335298Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"f56afd338050a338ff76648b7c9e9a40dafa5e05ef5cabfe2cd9ee362e853e1f"},"references":{"count":23,"sample":[{"doi":"","year":2013,"title":"K. 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