Volumetric Injection Framework (VIF): Resolving Hubble Tension via Modified Background Dynamics

We present the Volumetric Injection Framework (VIF) v15.0, combining a geometric null-junction sector with a phenomenological modified dark-energy background. A tripartite structure is adopted: a four-dimensional background (Region N), a neutral null interface (Sigma), and a reduced one-dimensional temporal channel (Region B). Using the Barrabès-Israel junction conditions for null shells on a generalized McVittie/Vaidya-type metric, we obtain a finite transverse expansion jump under asymmetric mass states (M_- != M_+). The background expansion is written without a z=0 normalization lock, H(z) = H_s * sqrt(Omega_m * (1+z)^3 + (1 - Omega_m) * w_0), so that the present rate H(0) = H_s * sqrt(Omega_m + (1 - Omega_m) * w_0) can differ from the early-time scale H_s when w_0 != 1. In the calibration adopted for this release (w_0 ~ 1.22, H_s ~ 67.4), one obtains H(0) ~ 72-73 km/s/Mpc, in the range of local distance-ladder determinations. Geometric junction results remain standard general relativity; the background factor w_0, the growth friction Q(z), and the one-dimensional regularisation of Region B are constitutive inputs of the phenomenological sector, not theorems derived from the junction alone.