Dilaton-Axion Wormhole Partition Function Away from the BPS Endpoint

I determine the leading finite-radius correction to the two-boundary response of a charged axion wormhole near its BPS endpoint. With $\delta =a_{\ast }^2$, exact radial matching in a product axion–dilaton/saxion system gives a boundary eigenvalue that vanishes as $O(\delta )$ and an off-diagonal Hessian entry of order $O({\delta }^2)$. Their combination produces a cross-boundary covariance linear in $\delta$, with a negative first sub-leading correction on the branch studied here. I determine the semiclassical range in which the quadratic approximation remains controlled and identify the first finite-radius angular resonance, ${\delta }^2\log (\delta \mathrm{/}{\delta }_0)$. Under a uniform rescaling of all active charges, the coefficient of the linear cross-boundary response scales as the inverse square of the charge scale. I then average the inverse response over the chiral Gaussian ensemble describing the BPS endpoint. Boundary reduction preserves the hard-edge index. Multiplication by the matched BPS sector weight converts the normalized response into the leading finite-radius two-source coefficient.