Type IIB Axion--Dilaton Wormholes and the BPS Limit Hessian

I revisit Type-IIB axion--dilaton Euclidean saddles in a specified axion charge sector. In that sector, the solution with E=0 is the BPS instanton, while E>0 gives non-BPS wormholes with a smooth throat. The two cases solve the same radial equations but define different fluctuation problems. For the E=0 instanton, the Hamiltonian constraint, gauge quotient, charge-sector boundary condition, and removal of collective zero modes reduce the quadratic action to a physical Hessian. This Hessian factorizes, {cal H}_ν={mathcal Q}_ν^dagger{mathcal Q}_ν. I interpret this as an endpoint theorem, beyond a stability theorem for the full E>0 wormhole. This puts Type IIB wormhole spectra on firmer grounds. I also separate the connected two-ended wormhole throat from its long-distance two-end multipole operator term. Once the coefficient matrix C^ij is derived, the different-component and same-component placements of the two end insertions are terms in the same quadratic expression. Removing either term requires a genuine projection or cancellation.