The Hubble Tension May Have a Direction

Natural Evolution of Actuality (NEA) starts from two independently lawful abstract parentalresponsibilities M and F, and primitive Ω as consequential joining, comparison, admissibility, confirmation and retained History. The developed gravitational and optical response of a realised cosmicnetwork is not an additional primitive. Existing NEA work proposes a localised retarded responsewhose late-time interior approximation is b(z, µ) = C(z)eκ(z)µ, with µ = nˆ ·pˆ, coupled to an operationalexpansion readout Hread = Href/(1 + εb). We retain the selected finite-speed parent equation andcarefully distinguish the interior Gaussian approximation from its causal front. We first derive the exactfull-sky monopole, dipole and quadrupole, including the source-owned small-concentration relationQ2M/D21 → 1/3. New conditional results include a monotone relation permitting κ to be recovered fromthe dipole-to-monopole ratio; a new weak-concentration octupole invariant; an exact nonperturbativeantipodal-product and log-affine identity for the inverse expansion readout; a closed-form nonlinear skymean and its positivity domain; and cross-redshift consistency relations tying angular concentration todistance and causal-response age. A selected fixed-age radial envelope has a unique maximum, whilethe full past-light-cone prediction requires an independently determined T(z) and a finite-speed arrivalcondition. We also identify sky-mask mixing, signed source orientation, and observational transferrequirements. These identities provide a constrained, internally consistent NEA investigation of adirectional expansion discrepancy. They do not calculate an observed Hubble tension, prove a GreatAttractor boundary, or independently derive the optical coupling and cosmic-source parameters fromthe primitives.