{"id":"hexagon/2611.00089","pdf":"https://hexagonmath.org/pdf/2611.00089v1","url":"https://hexagonmath.org/abs/2611.00089v1","tags":["math.RA","msc:03C60","msc:15A63","Hermitian form","inertia","model completeness","quantum measurement","real closed field","self-adjoint nilpotent operator"],"score":0,"title":"Inertia and Elementary Theories of Hermitian Nilpotent Operators","domain":"math.LO","source":"hexagon","authors":["Zhenyu Sun","Jilin Wang"],"reviews":0,"subject":"math.LO","summary":"Let \\(V\\) be a finite-dimensional Hermitian space over an algebraically closed field with a nonidentity involution, and suppose its form \\(h\\) is nondegenerate. For a self-adjoint nilpotent operator \\(N\\), we recover the multiplicity of each signed Jordan block from finite differences of the ranks and signature differences of the forms \\(h(x,N^j y)\\). On a fixed Hermitian space these inertias classify unitary conjugacy. Across scalar fields they classify elementary equivalence in the four-sorted language of scalars, vectors, endomorphisms, and projective points with \\(N\\) named. At fixed…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-11-04","reactions":{},"withdrawn":false,"authorship":"human","formalized":false,"human_understanding":"some"}