Distortion Gravity: A Complete Proof of Ghost-Free Unitarity With Full Analytical and Numerical Verification

We present a complete and rigorous proof that Distortion Gravity (DG), a metric-affine framework where the affine connection is promoted to a dynamical field, is ghost-free and unitary. Starting from the irreducible decomposition of the distortion tensor, we show that the original Fierz–Pauli kinetic term contains a ghost in the axial torsion sector. Attempts to cure this via Yang–Mills actions lead to kinetic mixing ghosts. The solution is to postulate independent Proca Lagrangians for the trace vector and the axial torsion vector. We subject this theory to eight independent tests—including stochastic spectral analysis (290,000 random configurations), Lyapunov stability, Fourier mode analysis, polarization completeness, Wigner–Eckart covariance, and Källén–Lehmann spectral positivity. All tests confirm the absence of ghosts. We derive the complete field equations, the physical implications for dark energy and dark matter, and the gravitational-wave signatures. The final theory propagates a massless graviton and two massive vectors, providing a unitary and phenomenologically rich extension of General Relativity.