A common route to discreteness in physics is to postulate a Hilbert-space operator and then solveits eigenvalue problem. Here a different, stability-based route is formulated. The starting pointis a variational stability principle: a physically realized stationary state is required not only tosatisfy the stationarity condition δS = 0, but also to be stable with respect to the second variation,δ2S ≥ 0, understood as a positive stability form. Under standard assumptions on the secondvariation–symmetry, closedness, lower semiboundedness, and coercivity after a shift–this form definesa self-adjoint stability operator. If the physical boundary conditions make the relevant embeddingcompact, the stability operator has compact resolvent and therefore a discrete spectrum. In thissense, discreteness is not introduced as an independent quantum postulate; it arises as a spectralconsequence of the second variation together with stability and boundary conditions. The result isstated as a theorem and proved using the representation theorem for closed semibounded forms andcompactness of the Sobolev embedding. The physical meaning is clarified by distinguishing threelevels of discreteness: discrete stability modes, discreteness of action variables, and quantum-typeenergy quantization. Periodic classical systems, including bounded orbital motion, naturally givediscrete stability modes, whereas quantization of energies requires an additional minimal action scaleand a single-valued phase condition.