<p>We present a capillary connectivity spectrum framework for spontaneous imbibition in fractured porous media. The matrix is modeled as a continuum of capillary-accessible subdomains, each characterized by a local imbibition time scale, yielding a superposition of exponential relaxation processes. This formulation produces a recovery-kernel representation and an equivalent relaxation-spectrum description that connects macroscopic recovery dynamics to pore-scale accessibility. We show that the resulting recovery curves are bounded, monotone, and concave, while the recovery deficit is completely monotone. The inverse problem is formulated as a spectrum-inversion problem for reconstructing the underlying accessibility distribution from recovery observations. Conditions for identifiability are established, and the ill-posedness and intrinsic resolution limits of the inversion are analyzed. A regularized numerical implementation is developed for stable reconstruction. Synthetic and experimental results demonstrate accurate recovery of multiscale imbibition dynamics and improved performance relative to single- and bi-exponential models. The formulation provides a physically interpretable link between pore-scale connectivity and macroscopic recovery behavior while unifying classical exponential and multirate descriptions within a single continuum formulation.</p>