Charge-Sector Construction of the Type-IIB Axion--Dilaton Wormhole Partition Function

I construct the Type-IIB axion--dilaton wormhole partition function from charge-sector data. In a chosen axion charge, equivalently form-field flux sector, the long-distance saddle calculation supplies a two-end operator term with coefficient matrix \(C^{ij}_\nu\). The labels \(i,j\) label end-insertion operators; the labels \(A,B\) label parent universes. Reduction data \(b\) convert this matrix into scalar coefficients \(W_\nu[b]\). The wormhole partition function in the theta variable is \(Z_{\rm wh}(\theta;b)=\sum_\nu W_\nu[b]\e^{i\nu\theta}\). I analyze properties and constraints this coefficients satisfy: discrete-symmetry covariance, phase, absolute bounds, moment positivity, Cauchy--Schwarz inequalities for the unreduced coefficient matrix, complex-\(\theta\) domains, charge-lattice tails, and the dilute Bessel/Skellam limit. The \(\theta\)-dependence of the wormhole partition function is the Fourier transform of the charge-sector scalar coefficients.