Quantized Vacuum Attenuation: Resolving the Hubble Tension via Third-Order Nonlinear Susceptibility in a Discrete Manifold

Abstract The standard Lambda-CDM cosmological model is currently challenged by a 5-sigma discrepancy in Hubble Constant (H0) measurements and observations of mature galaxies at z > 10 that defy hierarchical formation timelines. We present a formal validation of the Quantized Vacuum Attenuation model, which defines the vacuum as a Discrete Manifold acting as a Logical System, distinct from the physical fields (Space) that execute within it. Utilizing an attenuation coefficient of alpha approx. 8. 26 x 10^-27 m^-1 derived from information-theoretic limits, our model resolves three primary tensions: The Velocity Budget & Time Dilation: By divorcing logical addressing from physical execution, we derive a "Velocity Budget" where time dilation is a mechanical consequence of the manifold’s finite refresh rate (c). This replaces geometric spacetime warping with a signal-processing constraint: c² = v² + vt². Early Galaxy Paradox: The model removes the Big Bang singularity, reinterpreting high-redshift galaxies (e. g. , JADES-GS-z13) as objects seen through approx. 35 Gyr of static vacuum transmission. This provides an infinite timeline for the chemical maturation observed by JWST. Little Red Dots: The angular diameter distance in a discrete, static manifold correctly predicts the compact morphologies of high-redshift objects, resolving the conflict with the angular magnification predicted by expanding metric models. We conclude that the observed universe is consistent with a static, infinite, and dissipative logical manifold where cosmological redshift is a non-scattering energy loss inherent to photon propagation across discrete coordinates.