Einstein--Skyrme Theory on a Planck-Scale Causal Lattice

We propose a UV-complete theory of gravity by placing the Einstein--Skyrme system on a Planck-scale causal lattice. The Skyrme field ($SU(2)$) provides a topological regulator via $\pi_3(SU(2))=\mathbb{Z}$, setting a cutoff $\Lambda_{\rm UV}=2\pi/\ell_{\rm Pl}$. The model passes solar-system tests via Vainshtein screening and predicts a chiral primordial gravitational-wave background peaking at $f=2.87\pm0.03\,\text{mHz}$ ($\Omega_{\rm GW} h^2 \sim 10^{-12}$), detectable by LISA. The tensor-tensor-tensor non-Gaussianity is enhanced, $f_{\rm NL}^{\rm GW} \sim \mathcal{O}(10)$. This theory not only builds a connecting path for the unification of quantum gravity and classical gravity, but also provides physical predictions that can be tested by gravitational wave observations, opening new avenues for addressing fundamental issues such as the nature of spacetime and cosmic evolution.