{"id":"palomar/PALOMAR-2026-09-03-000004","url":"https://github.com/stalex444/radial-harmonic-classification/tree/74e9b3ea7f204fba2e84e546c80457bcca5c6268","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-03-000004-v1.json","repo":"https://github.com/stalex444/radial-harmonic-classification","tags":["math.CA","math.AP","math-ph","physics.class-ph","msc:31B05","msc:35J05","msc:34A05","msc:70F05","msc:70H14","msc:70K20"],"score":0,"title":"Radial harmonic functions on a real inner product space: the classification, the Laplacian of radial functions, and the stability of circular orbits for power-law central forces; Ehrenfest's dimensionality argument (1917) as the application","trust":"high","domain":"math.CA","source":"palomar","authors":["Stephanie Alexander"],"reviews":0,"subject":"math.CA","summary":"GENERAL THEOREMS FIRST. Throughout, E is a finite-dimensional real inner product space of dimension n, Δ is Mathlib's coordinate-free Laplacian, HarmonicOnNhd its harmonic functions, and f : ℝ → ℝ is twice differentiable on (0, ∞) (two HasDerivAt hypotheses, with derivatives f', f''). (I) THE CLASSIFICATION OF RADIAL HARMONIC FUNCTIONS: (1) for n ≠ 2 and E ≠ 0, the radial function f ∘ ‖·‖ is harmonic on E ∖ {0} if and only if f(r) = a + b r^(2−n) on (0, ∞) for some real a, b; (2) for n = 2, if and only if f(r) = a + b log r — every radial harmonic function with a twice-differentiable profile…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-03","reactions":{},"formalized":true}