Numerical Reconstruction of Organized Temporal-Torque Domains and Simulated Residual Cosmic Birefringence Maps

Numerical Reconstruction of Organized Temporal-Torque Domains and Simulated Residual Cosmic Birefringence Maps This paper is Paper 4 in the Temporal Torque Memory and Aether Organization series. Papers 1 through 3 established temporal torque memory, Aether tomography, and a QMU-native definition of temporal-torque density. The present paper develops a numerical implementation of Aether tomography using simulated residual cosmic birefringence maps and HEALPix sky discretization. The five-dimensional chronogeometric framework is based on the coordinate structure (x,y,z,τᵥ,τₜ), where τᵥ represents chronovibration and τₜ represents chronotorsion. The birefringence field is decomposed as β(θ,φ)=β₀+δβ(θ,φ), with the universal component β₀=1/16π². The residual birefringence field is modeled by the Aether tomography projection relation δβ(θ,φ)=κ∫LOSΩₜ(x),ds, where Ωₜ(x) denotes temporal-torque density. Paper 3 derived the QMU-native temporal-torque density expression Ωₜ=ηFq²AᵤλC, equivalent to Ωₜ=/volm. The present paper implements normalized HEALPix simulations at Nside=64, corresponding to Nₚᵢₓ=12Nside²=49,152 equal-area sky pixels. Representative temporal-torque domains are simulated for dipole, quadrupole, spiral, filamentary, and mixed hierarchical organization. The resulting residual sky maps are expanded as δβ(θ,φ)=∑,maₘYₘ(θ,φ), with angular power spectra C₌1/2+1∑ₘ |aₘ|² and handedness statistic H=∑ₘ m|aₘ|². The simulations show that dipole and quadrupole models concentrate power in low-order harmonics, while spiral, filamentary, and hierarchical models distribute power across multiple angular scales. An idealized low-order HEALPix reconstruction using ≤2 recovers the input temporal-torque field with relative reconstruction error ε=2.14×10⁻¹⁶, consistent with machine-precision recovery for the idealized low-order case. This work converts Aether tomography from a conceptual inverse problem into a computationally implementable framework. It provides simulated residual birefringence maps, harmonic diagnostics, and reconstruction tests that may be compared with future CMB polarization surveys.