{"paper":{"title":"Integrability of Conformal Killing Vectors in the Eisenhart Lift of Scalar-Field FLRW Cosmology","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The potential found in prior work is the most general local one admitting a non-trivial conformal Killing vector independent of the cyclic Eisenhart coordinate in scalar-field FLRW cosmology.","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Takeshi Chiba, Tsuyoshi Houri","submitted_at":"2026-04-24T05:42:37Z","abstract_excerpt":"We study the integrability conditions of the conformal Killing equations for the Eisenhart lift of a scalar field in a flat Friedmann-Lema\\^\\i tre-Robertson-Walker universe. The determinant condition of the prolonged conformal Killing equations reduces to a nonlinear second-order differential equation for $h=V'/V$. We solve this equation locally and find two branches. The regular branch reproduces exactly the family of potentials obtained previously, while the singular branch lies on the locus where the determinant equation cannot be written locally in normal form with respect to $h''$ and is "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show that the potential found in our earlier work is already the most general local potential that admits a non-trivial conformal Killing vector in the sector independent of the cyclic Eisenhart coordinate.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The determinant condition of the prolonged conformal Killing equations reduces to a nonlinear second-order differential equation for h=V'/V whose local solutions classify all admissible potentials.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The potential family from prior work is the most general local potential admitting non-trivial conformal Killing vectors in the Eisenhart lift of scalar-field flat FLRW cosmology.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The potential found in prior work is the most general local one admitting a non-trivial conformal Killing vector independent of the cyclic Eisenhart coordinate in scalar-field FLRW cosmology.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"d37f4f62b6a410e20173d4383a71dc2732a123ee21387d22dc4bc95deb56d598"},"source":{"id":"2604.22247","kind":"arxiv","version":3},"verdict":{"id":"863fde29-8c8e-4ce8-a607-8ace6968b4c7","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-08T10:50:27.739718Z","strongest_claim":"We show that the potential found in our earlier work is already the most general local potential that admits a non-trivial conformal Killing vector in the sector independent of the cyclic Eisenhart coordinate.","one_line_summary":"The potential family from prior work is the most general local potential admitting non-trivial conformal Killing vectors in the Eisenhart lift of scalar-field flat FLRW cosmology.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The determinant condition of the prolonged conformal Killing equations reduces to a nonlinear second-order differential equation for h=V'/V whose local solutions classify all admissible potentials.","pith_extraction_headline":"The potential found in prior work is the most general local one admitting a non-trivial conformal Killing vector independent of the cyclic Eisenhart coordinate in scalar-field FLRW cosmology."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.22247/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-21T11:34:23.760859Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-20T00:12:04.192273Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"aff365e1357f58111bda0103a50fa99bee826183e05a1a5efc7293fb0bd2a9d8"},"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"}