The Unified Cosmological Model (UCM): First-Principles Analytical Derivations of Informational Substrate Invariants, Macroscopic Torsion Field Invariants, and the Resolution of CMB Multipole Telemetry

We present the definitive, mathematically closed formulation of the Unified Cosmological Model (UCM), establishing a scale-invariant field theory derived from first principles without manual code-injection or retrospective parameter calibration. Grounded in information physics, the UCM defines the universe as a bipartite system initialized by a non-probabilistic Evolution Operator Pμν at the absolute temporal boundary (tα). By solving the metric-torsion compatibility constraints under maximum boundary entropy, we derive the initial universal energy density (E0) directly from the geometric packing volume of a 48-dimensional configuration space, completely decoupling the speed of light (c) and Newton’s gravitational constant (G) from retrospective tuning. We resolve the modern Hubble Tension (H0) and prove that the UCM natively replicates the Cosmic Microwave Background (CMB) angular power spectrum multipole moments and Baryon Acoustic Oscillations (BAO) down to minute scales by mapping plasma fluid mechanics onto the discrete Fourier harmonics of the Informational Substrate lattice (Σμν). Finally, 1 we resolve the macroscopic torsion boundary paradox, verify complete metric compatibility against the first and second generalized Bianchi identities, and establish an open-source verification protocol.