{"paper":{"title":"Co-rotating Vortices on Surfaces of Variable Negative Curvature: Hamiltonian Structure and Curvature-Induced Drift","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Two identical vortices on a catenoid rotate rigidly at fixed latitude with speed set by the curvature gradient","cross_cats":["cond-mat.quant-gas","math.MP","nlin.SI","physics.flu-dyn"],"primary_cat":"math-ph","authors_text":"Gaurang Mangesh Joshi, Rickmoy Samanta","submitted_at":"2026-04-28T14:12:29Z","abstract_excerpt":"Vortices in fluids and superfluids are fundamental to phenomena ranging from Bose-Einstein condensates and superfluid films to neutron stars and hydrodynamic micro-rotors, where background geometry often plays an important role. Curvature can induce vortex motion distinct from planar domains. We study Hamiltonian vortex motion on a catenoid, a minimal surface of variable negative curvature, and derive explicit equations of motion and conserved quantities for co-rotating vortex pairs. For two identical vortices we find an exact analytic solution in which the pair rotates rigidly at fixed latitu"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"For two identical vortices we find an exact antipodal solution in which the pair rotates rigidly at fixed latitude, with angular velocity Ω=(Γ/16π) K'(V)/√(-K(V)), where K(V) is the Gaussian curvature. Thus the motion is governed by the curvature gradient rather than the curvature itself. The symmetric state is linearly unstable, with growth rate λ=√3|Ω|.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The point-vortex idealization and the specific Hamiltonian structure derived from the Biot-Savart law or Green's function on the catenoid metric remain valid for the co-rotating pairs; the derivation assumes the surface is minimal and the vortices are identical in strength and sign.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Co-rotating vortex pairs on a catenoid rotate rigidly at fixed latitude driven by curvature gradient rather than curvature value, with the symmetric state linearly unstable at growth rate √3|Ω| and generic pairs reducing to bounded oscillations plus secular drift.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Two identical vortices on a catenoid rotate rigidly at fixed latitude with speed set by the curvature gradient","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"e8a9ff4ca99e3753cea6aeed50fd2e43bf396e93ab9312811cac8474db950b37"},"source":{"id":"2604.25682","kind":"arxiv","version":2},"verdict":{"id":"727c1bf4-35a4-4973-8a9e-a3c09feb4a7e","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-07T14:25:44.197791Z","strongest_claim":"For two identical vortices we find an exact antipodal solution in which the pair rotates rigidly at fixed latitude, with angular velocity Ω=(Γ/16π) K'(V)/√(-K(V)), where K(V) is the Gaussian curvature. Thus the motion is governed by the curvature gradient rather than the curvature itself. The symmetric state is linearly unstable, with growth rate λ=√3|Ω|.","one_line_summary":"Co-rotating vortex pairs on a catenoid rotate rigidly at fixed latitude driven by curvature gradient rather than curvature value, with the symmetric state linearly unstable at growth rate √3|Ω| and generic pairs reducing to bounded oscillations plus secular drift.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The point-vortex idealization and the specific Hamiltonian structure derived from the Biot-Savart law or Green's function on the catenoid metric remain valid for the co-rotating pairs; the derivation assumes the surface is minimal and the vortices are identical in strength and sign.","pith_extraction_headline":"Two identical vortices on a catenoid rotate rigidly at fixed latitude with speed set by the curvature gradient"},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.25682/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_compliance","ran_at":"2026-05-19T20:52:28.626791Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"21ff1e832e10b939efe2636c4b8955eb8bf1c567332779bb2e7a09511488ba72"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}