The Fredholm determinant of the symmetric self-dual local F0 operator

We fix the symmetric mass and ℏ = 2π for local F0. We define the closed-string grand potential by taking the removable finite part of the combined instanton contribution in each curve class before summation. Using the rank-two blowup identities, we prove normal convergence in the exterior region and identify the resulting Jacobi theta expression. We continue this function through its three degenerate parameters and match its complete zero divisor with the spectrum of the Friedrichs realization of the mirror-curve operator. An order-zero bound then identifies the entire continuation with the Fredholm determinant. The statement uses a fixed coefficientwise prescription at the self-dual point.