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, ᵥ, ₜ), where ᵥ represents chronovibration and ₜ represents chronotorsion. The birefringence field is decomposed as (, ) =₀+ (, ), with the universal component ₀=116². The residual birefringence field is modeled by the Aether tomography projection relation (, ) =₋₎ₒₜ (x), ds, where ₜ (x) denotes temporal-torque density. Paper 3 derived the QMU-native temporal-torque density expression ₜ=Fq^{2}{AᵤC}, equivalent to ₜ=volm. The present paper implements normalized HEALPix simulations at Nₒ₈₃₄=64, corresponding to N₏₈ₗ=12Nₒ₈₃₄²=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 (, ) =, ₌a ₌Y ₌ (, ), with angular power spectra C_=12+1ₘ |a ₌|² and handedness statistic H=ₘ m|a ₌|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 =2. 1410^-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.