{"paper":{"title":"The Framed Beltrami-Vekua Normal Form and its Pseudo-Analytic Mass","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":"2026-06-26T10:46:05Z","abstract_excerpt":"We normalize a first-order real planar elliptic system, by pointwise algebra, to a framed Beltrami-Vekua equation $\\Phi(w_{\\bar z} - \\mu w_z) + \\Psi(\\overline{w_z} - \\mu\\,\\overline{w_{\\bar z}}) + \\mathfrak{a} w + \\mathfrak{b} \\bar w = \\mathfrak{f}$, with $|\\mu| < 1$ and $|\\Phi| > |\\Psi|$, and compute the closed transformation laws of its data under the recombination of unknowns $w \\mapsto \\varphi w + \\psi \\bar w$ and under orientation-preserving $C^1$ changes of variables. The 2-form $\\Theta = \\frac{\\bigl|\\,\\Phi\\,\\mathfrak{b} - \\Psi\\,\\mathfrak{a} - (\\Phi\\, L\\Psi - \\Psi\\, L\\Phi)\\,\\bigr|^2}{\\big"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27950","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/2606.27950/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"}