Ab Initio Derivation of MOND and Dark Matter Profiles: Causal Decoherence and Visco-Elastic Wakes in the KEFE Framework

We present an ab initio derivation of Modified Newtonian Dynamics (MOND) and galactic dark matter profiles strictly from the continuum mechanics of the Kinemetric-Extended Field Equations (KEFE). By shifting the physical ontology of the universe from a passive geometric background to a macroscopic, relativistic elastoviscoplastic vacuum governed by causal Müller-Israel-Stewart (MIS) hydrodynamics, inertial mass emerges not as an intrinsic scalar, but as a reactive boundary-layer drag dictated by the Green-Kubo time-correlation of vacuum fluctuations. We demonstrate that this visco-elastic vacuum memory is subject to two independent causal truncation limits: the local Rindler horizon of the accelerating particle and the global Hubble horizon of the expanding universe. Evaluating this decoherence integral analytically yields the MOND "Simple Interpolating Function" and derives the fundamental acceleration scale a0=cH0 without phenomenological fine-tuning. Crucially, this derivation natively predicts the cosmic evolution of the acceleration threshold (a0(z)=cH(z)), offering a highly falsifiable kinematic scaling law for high-redshift galaxies currently probed by JWST. Furthermore, we establish a strict mathematical duality between modified inertia and dark matter. The geometric Bianchi identities mandate that radial gradients in this vacuum drag generate an active, non-geodesic fifth force, natively reproducing the extended spatial profiles of apparent dark matter halos and formally deriving the External Field Effect (EFE) from the causal decoherence limits of continuum mechanics. Finally, we resolve the Bullet Cluster anomaly — historically MOND's greatest vulnerability. We demonstrate that violent cluster collisions induce kinematic quenching and spectral partitioning. The rapidly decelerating intra-cluster plasma transfers its macroscopic momentum directly into the vacuum fluid, where it is governed by the non-linear Vorticity Transport Equation. This injected momentum forms a stable, sub-luminal "Visco-Elastic Wake" (a macroscopic vortex ring). Topo-elastically anchored by the moving vacuum gradients of the surviving collisionless galaxies, this wake perfectly mimics the weak-lensing spatial offsets of collisionless particulate dark matter. Key Contributions: Ab Initio MOND Derivation: Derives the MOND interpolating function and acceleration scale (a0=cH0) directly from the causal truncation of Green-Kubo vacuum fluctuations. Cosmic Evolution of a0: Predicts a redshift-dependent acceleration threshold (a0(z)=cH(z)), providing a strict, falsifiable scaling law for high-redshift galactic rotation curves. Dark Matter as Vacuum Drag: Proves that spatial gradients in vacuum viscosity mathematically mandate a non-geodesic fifth force via the Bianchi identities, replicating dark matter halos and the External Field Effect (EFE). Bullet Cluster Resolution: Solves the spatial decoupling of mass and gravity using pure fluid dynamics, modeling the apparent dark matter offset as a sub-luminal visco-elastic vortex ring anchored to collisionless galaxies. The KEFE Framework Suite:This manuscript is part of a comprehensive suite of papers demonstrating the universal application of the Kinemetric-Extended Field Equations (KEFE). By modeling the quantum vacuum as a causal, elastoviscoplastic continuum, the framework resolves major crises across disparate scales without dark sectors: Foundations: The Kinemetric-Extended Field Equations (KEFE): A Unified Effective Field Theory of Vacuum Rheology and Cosmological Evolution, https://doi.org/10.5281/zenodo.19333013 Cosmology: Ab Initio Resolution of the Hubble Tension: Visco-Elastic Cosmology and Conformal Degeneracy, https://doi.org/10.5281/zenodo.20254714 Galactic Astrophysics: Ab Initio Derivation of MOND and Dark Matter Profiles: Causal Decoherence and Visco-Elastic Wakes, https://doi.org/10.5281/zenodo.20254928 Quantum Gravity: Ab Initio Resolution of the Black Hole Information Paradox: Asymptotic Mass Freedom and Visco-Elastic Sublimation , https://doi.org/10.5281/zenodo.20254954