Gravity as Collective Excitation of Topological Entanglement on K3 Surfaces: CHL Orbifolds with Arithmetic Fixed Point

Based on the standard framework of K3 surface compactifications in string theory, we demonstrate that four-dimensional gravity can be rigorously interpreted as the collective excitation of topological entanglement among three trefoil-knot orbits corresponding to the three fermion generations. By generalizing the Ryu–Takayanagi holographic entanglement entropy formula to the Z3 orbifold of K3 T , we establish an exact relation between Newton’s constant and the topological entanglement degree: G= ℏc/(EtotalM2P ), where Etotal = (161/576) ln 2 is uniquely determined by the Z3-equivariant index theorem on K3. From the arithmetic geometry of the standard model compactification, the framework derives all physical couplings: the fine-structure constant α−1 = 137.035999084, dark matter abundance ΩDM = 0.2656890744, and cosmological constant Λ = 2.842×10−122M4P , agreeing with experimental values to 10−9 precision. The theory yields eightfalsifiable predictions, including Z3-modulated graviton polarization correlations ⟨ǫ+ǫ×⟩ ≈ 0.194,logarithmic corrections to black hole entropy with coefficient 0.280, and discrete high-frequency gravitational wave spectra, testable with LIGO/Virgo, Einstein Telescope, and the Event Horizon Telescope.