ZIPPED v3.0: An Elastic Spacetime Continuum Framework for Galactic Dynamics and Cluster Lensing Without Dark Matter

We present ZIPPED (v3.0), a covariant field theory that describes spacetime not as a passive Riemannian manifold, but as an elastic continuum (the Grid) with an intrinsic minimal tension coupled to the cosmic acceleration scale $a_0 = c H_0 / 2\pi$. By introducing an elastic strain potential and a non-local mass density gradient coupling into a unified action principle, ZIPPED simultaneously accounts for galactic rotation curves (the Radial Acceleration Relation, RAR) and cluster-scale gravitational lensing anomalies (such as the Bullet Cluster) without invoking cold dark matter particles or ad-hoc damping factors. We derive the complete field equations via the action variation, construct the symmetric Hilbert energy-momentum tensor $T^{\mu\nu}$, prove covariant energy-momentum conservation ($\nabla_\mu T^{\mu\nu} = 0$), and perform a linear perturbation analysis demonstrating that the framework is strictly free of ghosts ($Z_s > 0$) and tachyonic instabilities ($m_{\text{eff}}^2 \ge 0$).