Gravity from the Structural Intensity Field ρ: A Real-Time Spectral Framework

We present a precise, coordinate-free definition of the structural intensity field
 ρ and use it as the primary geometric variable in real time, yielding a compact curvature
 identity and an Euler–Lagrange equation for σ from the spectral action. The construction
 is supported by three pillars: (i) an adiabatic twistor collapse that selects the anti-self
dual sector and reduces the spectral action to four dimensions; (ii) a noncommutative
 Penrose–Ward correspondence identifying ASD gauge data with holomorphic modules on
 the twistor bundle; and (iii) a time–space no-go theorem enforcing θ0i = 0 under antiunitary
 time reversal and Hadamard spectral regularity. Together they ensure causal, Lorentzian
 consistency and organize gauge contributions while ρ drives the effective metric via R =
 −6ρ−1/2□ρ1/2 . In the late-Universe linear regime this implies cT = 1, αM = 0, and no
 gravitational slip, and the framework extends to nonunital noncommutative manifolds by
 locality of the heat kernel and spectral compactness-by-localization.