Jordan spectra of nilpotent derivations from scalar geometry

We determine the complete Jordan spectrum of nilpotent derivations of a nonabelian class-two Lie algebra I over a characteristic-zero field. We assume that its scalar bracket space has a decomposable basis over the ground field and that its reduced geometric decomposable locus admits no nontrivial additive-group action. A plane-preserver algebra and a hyperplane arrangement determine the horizontal rank set R; an integer criterion then decides every full Jordan type. Every admitted type occurs over the ground field, and the spectrum remains unchanged under field extension. For u = dim(I/Z(I)), d = dim I′, f = dim(Z(I)/I′), and r = max R, the greatest partition is (2^r, 1^(u-2r)) + (f) + (1^d), with componentwise addition. The full spectrum recovers R and is a dominance order ideal exactly when R has no gaps. For fixed free central dimension f, finite scalar loci with identical support-sum rank functions can have different spectra; support dimension six is minimal. A family has Jordan strata and commuting varieties whose component dimensions differ without bound. Geometric consequences include a smooth rational greatest-type stratum, a crepant resolution, and a classification of nilpotent linear spaces of largest dimension. Hall polynomials give uniform Jordan-stratum point counts at almost all places for number-field models. Source repository: https://github.com/eulogica/jordan-spectra-nilpotent-derivations ChatGPT by OpenAI, OpenAI Codex, and Claude by Anthropic were used during the preparation and revision of this manuscript for mathematical exploration, proof development, source retrieval, editorial and structural revision, and to assist in checking proofs, notation, terminology, internal consistency, cross-references, and bibliographic citations.