{"id":"palomar/PALOMAR-2026-10-05-000006","url":"https://github.com/shaikidris/DixmierMassSix-Palomar/tree/61783d52b6ae44cd2d8d20ad6cb798e7bbbce3ff","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-05-000006-v2.json","repo":"https://github.com/shaikidris/DixmierMassSix-Palomar","tags":["math.RA","msc:16S32","msc:16W20","msc:16W50","ring-theory","weyl-algebra","dixmier-conjecture","lean-formalization"],"score":0,"title":"The rank-one Dixmier conjecture for elements of mass at most six","trust":"high","domain":"math.RA","source":"palomar","authors":["Idris Ali Shaik"],"reviews":0,"subject":"math.RA","summary":"Over any characteristic-zero field, two elements P and Q of the first Weyl algebra satisfying QP-PQ=1 generate the algebra when P has at most six nonzero homogeneous components for deg X=1 and deg Y=-1. The degree, order and mass of Q are unrestricted. The proof combines sparse-polynomial rigidity with internally proved Newton and Weyl-algebra structural results.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-05","reactions":{},"formalized":true,"formalizes":[{"title":"The rank-one Dixmier conjecture for elements of mass at most six","identifier":"https://doi.org/10.5281/zenodo.23161793","relationship":"formalizes"}]}