Real spectral quantization for the self-dual mass-deformed local F0 operator

At ℏ = 2π and positive real logarithmic mass, we prove that Zakany's period condition characterizes the spectrum of the Friedrichs realization of the local F0 quantum mirror curve. Starting with the known inverse kernel, we characterize its full eigenspace by a scalar boundary problem on an elliptic curve. A product identity determines the allowed zeros and poles. We compare the two period multipliers with those of the physical curve, including the endpoint identification on an unramified double cover. The resulting real quantization condition is necessary and sufficient, and the eigenvalues are simple.