ABSTRACT: Deterministic particle transport closures such as diffusion and SPN approximations are widely used in nuclear transport analysis, but are typically derived under exponentially distributed free paths, implying Poisson collision statistics and the existence of all required free-path moments. In spatially correlated media, attenuation is generally nonexponential and may exhibit heavy-tailed behavior, raising the question of whether the corresponding closure coefficients remain well defined. This work uses a renewal-based formulation to identify when the moment-dependent coefficients of deterministic transport closures remain well-defined for correlated free-path statistics. Within this formulation, macroscopic equations arise as moment projections of an underlying renewal process, with closure coefficients determined explicitly by the hierarchy of free-path moments. Here, we recast the established moment dependence of nonclassical closure coefficients as an explicit coefficient-admissibility criterion for correlated renewal media whose free-path moment hierarchy may be finite. For the correlated survival-law family considered here, diffusion requires finite first and second free-path moments, while the one-dimensional isotropic SP2-level scalar closure developed in this work additionally requires the third free-path moment. The asymptotic renewal expansion shows how higher-order deterministic projections introduce successively higher free-path moments, but the coefficient-admissibility analysis is developed explicitly here for diffusion and the SP2-level closure. Boundary conditions are treated only as a scope limitation: rigorous boundary admissibility for correlated renewal transport would require a dedicated nonclassical half-space analysis and is left for future work. Classical transport is recovered in the exponential limit. Numerical solutions of the generalized linear Boltzmann equation are consistent with the predicted diffusion and SP2 coefficient thresholds and illustrate the resulting coefficient-admissibility limits within the correlated renewal family considered here.