The Unified 4D Topological Substrate Theory (U4DTST): Geometry, Energy, and Dark Acceleration as Twist Dynamics

We present the Unified 4D Topological Substrate Theory (U4DTST), a covariant effective field theory in which spacetime curvature, matter, and cosmic acceleration emerge from a single twist field τ\tauτ defined on a four-dimensional manifold. The substrate supports three thermodynamic phases—positive twist (matter/curvature), neutral (background spacetime), and negative twist (anti-curvature)—and evolves through local untwisting at late times. In the homogeneous limit, the resulting pressure pτp_\taupτ and energy density ρτ\rho_\tauρτ yield an effective equation of state wτ≈−1w_\tau \approx -1wτ≈−1 without invoking a cosmological constant. The model is ghost-free, hyperbolic, and consistent with cT=1c_T=1cT=1 constraints from GW170817. It makes two near-term, falsifiable predictions: a small, suppressed weak-lensing convergence in stacked cosmic voids (“void anti-lensing”), and phase-coherent post-merger microstructure in gravitational-wave ringdowns when events are coherently stacked. This short paper summarises the theoretical framework, action, cosmological behaviour, and empirical predictions. Full derivations, proofs, and appendices are provided in the accompanying U4DTST Monograph (DOI: 10.5281/zenodo.17302718). Informally: The universe behaves as a 4D substrate that can twist; ordinary matter stores twist, while late-time untwisting acts like dark energy.