Version 4.0 validates the bulk-sector mapping of the logarithmic strain framework by deriving the Shapiro radar-echo time delay in the weak-field regime. Using a consistent isotropic bulk coupling, null propagation reproduces the standard logarithmic delay with the correct scaling and two-way geometry dependence. This version completes the weak-field validation set of the constitutive representation without modifying Einstein’s equations.
Matthew Alexander Firtl (2026) studied this question.