The Complexity

We introduce a complex-metric theory of gravity founded on a single postulate: the spacetime metric tensor is complex-valued. Physical observables are real projections of complex quantities, so the measured speed of light remains Lorentz-invariant and special relativity is recovered in the zero-imaginary limit. The framework has one free parameter: the imaginary-to-real ratio α₀ at the present epoch. This is determined from the Planck CMB lensing anomaly (A_L = 6/5), and cross-checked by the Hubble tension; two internal consistency arguments — T-duality self-duality and the five-qubit quantum error-correcting code [[5,1,3]] — independently select the same value α₀ = 1/√5. From α₀ alone, with no additional free parameters, we derive: the matter density Ω_m = √30/18 ≈ 0.304 (1.5σ); the lensing amplitude A_lens = 6/5 = 1.200 (0.3σ); the Hubble tension resolved to 0.72σ; the FRB autocorrelation ratio to 0.8%; dark matter and dark energy as imaginary-sector condensates; black-hole singularity avoidance with T_BH = (2/5)T_Hawking; and galaxy spin parameter λ = (√5/3)λ_ΛCDM. The A_lens = 6/5 prediction simultaneously resolves the Planck lensing anomaly and, via Peng & Piao (2025), the DESI dark-energy preference to w₀ = −1. A complex Boltzmann simulation reduces the S₈ tension from 2.3σ to 0.65σ without new parameters. The theory predicts double-slit visibility V ≈ 0.937 for 0.49 < d/λ < 0.71 (discriminable at 20σ in a single BEC shot); twisted NbSe₂ bilayers at θ ≈ 0.6° superconducting at 275 K; and QRAM-free Grover search with O(1) memory.