{"paper":{"title":"Local Origin of Hidden Symmetry in Rotating Spacetimes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The kinematical core of Kerr geometry is fixed locally by the Einstein equations.","cross_cats":["astro-ph.HE","hep-th"],"primary_cat":"gr-qc","authors_text":"Hyeong-Chan Kim","submitted_at":"2026-03-09T14:04:28Z","abstract_excerpt":"We show that, within a broad stationary-axisymmetric class, Kerr-type separability and hidden symmetry arise as a local consequence of the Einstein equations. Without assuming separability, algebraic speciality, Killing--Yano symmetry, or global boundary conditions, we analyze stationary and axisymmetric geometries in a locally non-rotating orthonormal frame and impose a minimal local equilibrium condition, namely the absence of mixed energy-momentum fluxes. We find that the mixed Einstein equations enforce a rigid projective alignment between radial and angular sectors, uniquely characterized"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"the kinematical core of Kerr geometry is already fixed locally, and the Schwarzian structure provides the local origin of Kerr rigidity.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"the minimal local equilibrium condition of absent mixed energy-momentum fluxes together with the choice of a locally non-rotating orthonormal frame; the paper states this is imposed without assuming separability, algebraic speciality, or Killing-Yano symmetry.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The mixed Einstein equations in stationary-axisymmetric geometries with absent mixed fluxes enforce a constant-Schwarzian constraint whose global-regularity branch is precisely the Kerr sector.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The kinematical core of Kerr geometry is fixed locally by the Einstein equations.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"0523f3a2c010459ba4eed186f7d907379c21a8a430e41c06c6d4409c4d7233f0"},"source":{"id":"2603.08408","kind":"arxiv","version":3},"verdict":{"id":"16969b29-10e2-41ab-8061-57a5122ac6cd","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T15:05:15.457853Z","strongest_claim":"the kinematical core of Kerr geometry is already fixed locally, and the Schwarzian structure provides the local origin of Kerr rigidity.","one_line_summary":"The mixed Einstein equations in stationary-axisymmetric geometries with absent mixed fluxes enforce a constant-Schwarzian constraint whose global-regularity branch is precisely the Kerr sector.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"the minimal local equilibrium condition of absent mixed energy-momentum fluxes together with the choice of a locally non-rotating orthonormal frame; the paper states this is imposed without assuming separability, algebraic speciality, or Killing-Yano symmetry.","pith_extraction_headline":"The kinematical core of Kerr geometry is fixed locally by the Einstein equations."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.08408/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"a0d469428033ef26f03f16eb758212c05a3df899793c59c1fa0e4b4d290ba20d"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}