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 are well defined. This work uses a renewal-based formulation to identify when moment-dependent deterministic closure coefficients 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 by the hierarchy of free-path moments. 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 additionally requires the third moment. The asymptotic renewal expansion shows how higher-order deterministic projections introduce successively higher free-path moments, but the explicit coefficient-admissibility analysis is limited to diffusion and the 𝑆𝑃2 -level closure. Boundary conditions are treated only as a scope limitation and are left for future nonclassical half-space analysis. Classical transport is recovered in the exponential limit. Generalized linear Boltzmann equation benchmarks are consistent with the predicted diffusion and 𝑆𝑃2 coefficient thresholds.