{"id":"hexagon/2610.00273","pdf":"https://hexagonmath.org/pdf/2610.00273v1","url":"https://hexagonmath.org/abs/2610.00273v1","tags":["msc:16S32","msc:16W20","msc:16W50","Dixmier conjecture","Newton polygon","Weyl algebra","homogeneous components","sparse polynomials"],"score":0,"title":"The rank-one Dixmier conjecture for elements of mass at most six","domain":"math.RA","origin":"ai-generated","source":"hexagon","authors":["Idris Ali Shaik"],"reviews":0,"subject":"math.RA","summary":"Let K be a field of characteristic zero and let P,Q in A_1(K) satisfy [Q,P]=1. We prove that P,Q generate A_1(K) if either has mass at most six, meaning at most six nonzero homogeneous components for the grading deg X=1, deg Y=-1, with no degree bound on either element. This extends the four-component theorem of Guccione, Guccione and Valqui. The proof combines their Newton-polygon restrictions with a classification of polynomial pairs r,f satisfying an associated scalar differential equation under the condition that r^2 has at most six monomial terms. The scalar argument uses a…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Codex"],"discussed":0,"published":"2026-10-15","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":true,"formalizations":["https://palomar-registry.org/entry?id=PALOMAR-2026-10-05-000006&version=2"],"human_understanding":"all"}