{"paper":{"title":"Static Einstein-Scalar Reconstruction: Compatibility and Descent","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"physics.gen-ph","authors_text":"Thomas Sch\\\"urmann","submitted_at":"2020-01-02T17:06:33Z","abstract_excerpt":"Prescribing both the areal-radius metric function $F(r)$ and the scalar profile $\\phi(r)$ generally overdetermines static Einstein-scalar reconstruction. The temporal and radial Einstein equations determine a redshift function and an algebraic radial source $V_{\\mathrm{alg}}(r)$, but do not by themselves impose the angular equation or guarantee a single-valued scalar potential. On a connected static interval we formulate the corresponding membership criterion for independently prescribed pairs: a potential-independent residual $\\mathcal{C}[F,\\phi]$ must vanish, and $V_{\\mathrm{alg}}$ must desc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2001.02078","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2001.02078/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":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}