{"paper":{"title":"The Absorption Theorem for the Beltrami-Vekua Normal Form","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CV","authors_text":"Daniel Alay\\'on-Solarz","submitted_at":"2026-06-16T17:40:46Z","abstract_excerpt":"The Beltrami-Vekua normal form assigns to every smooth first-order real planar elliptic system a complex equation $w_{\\bar z}-\\mu w_z+\\mathcal{A}w+\\mathcal{B}\\bar w=\\mathcal{F}$ by an explicit pipeline. A companion paper showed that the density $\\Theta=|\\mathcal{B}|^2/(1-|\\mu|^2)\\,dx\\,dy$ and its total mass are invariants under multiplicative gauges $w\\mapsto\\phi w$ and orientation-preserving diffeomorphisms. The real system carries a larger symmetry: its unknowns may be recombined by any pointwise invertible real-linear substitution $w=\\varphi v'+\\psi\\bar v'$, the complex gauges being the cas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.18211","kind":"arxiv","version":1},"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/2606.18211/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"}