This preprint studies the modified Helmholtz (Yukawa) operator in DDD spatial dimensions and discusses a conditional physical interpretation of its dimensionless coupling within an effective incompressible-medium framework. The mathematical results on the Yukawa kernel and screening length are classical. The specific contribution of this note is the conditional identification of the screening parameter through the mesoscopic closure proposed in the companion preprint An Exclusion Floor in Incompressible Media: A Conditional Variational Closure in D+1D+1D+1 Sectors (Zenodo DOI: 10. 5281/zenodo. 19010375). Under that closure, the coupling is modeled as Π=1/ (D+1) = 1/ (D+1) Π=1/ (D+1), which yields the dimensional screening law λ=ℓ0D+1 = ₀D+1λ=ℓ0D+1. In three spatial dimensions, this gives λ=2ℓ0 = 2₀λ=2ℓ0. This upload contains the PDF manuscript and LaTeX source files for version 0. 4, and is intended as a citable preprint and prior-art record.
Diaz-Cano et al. (Sat,) studied this question.