g = 2 from a spinor — two with no middle, without relativity

Stern–Gerlach uses silver, whose active electron is L = 0 (spherical, no orbital current). A scalar charge density then has no moment and cannot split — yet the beam splits into two. Give the electron's domain a two-component spinor with a σ·p kinetic term, and squaring it produces the −q σ·B Zeeman coupling automatically: two levels ±μBB, no middle, with g = 2 — and, by Lévy-Leblond, entirely non-relativistically.
An L = 0 electron through a field gradient. Scalar: one undeflected spot. Spinor: two spots, no middle, separating as B grows.
Moment vs angular momentum: the slope is g. Orbital (g = 1) reaches μ = ±μB only at ±1 unit; spin (g = 2) reaches it already at ±½ — twice the moment per unit of angular momentum.
L = 0 outcome —
number of spots 1
middle beam? —
g-factor —
splitting 0
A scalar density with orbital circulation can only split into an odd number 2l+1 (with a middle), and for L = 0 it does not split at all. Only the spinor gives exactly two.
How g = 2 emerges. Writing the kinetic term as (σ·D)²/2m with D = p − qA and using (σ·D)² = D²𝟙 − q σ·B gives the g = 2 Zeeman term automatically — it is not inserted by hand (single-electron grid test: identity holds to ~10⁻³, O(dx²)). The “2” is the SU(2) double cover, geometry not relativity.