V(x) = k x²/2 has V'(0) = 0 and V''(x) = k (stationary-minimum signature)

Sympy-exact witness of the harmonic-PES stationary-point analysis. V(x) = k x²/2. First derivative dV/dx = kx, vanishing at x = 0 (first_deriv_at_0 = 0). Second derivative d²V/dx² = k (second_deriv = k); positive k ⇒ minimum. The zero…