From Bit to Cosmos: Analytical Derivation of Planck CMB Parameters and Cross-Theoretical Extensions via the CBHIRT Framework

This paper presents a unified, parameter-free informational framework for early-universe cosmology by integrating the complete formal architecture of Cyclic Black Hole Information Reintegration Theory (CBHIRT). We demonstrate that primary cosmic microwave background (CMB) metrics can be derived analytically from pure quantum informational boundary conditions, bypassing the conceptual vulnerabilities of scalar-field cosmic inflation. We model the Hot Big Bang not as a singular geometric event, but as a global, irreversible thermodynamic phase transition driven by quantum phase decoherence. Utilizing Landauer’s principle, the primordial radiation plasma of standard CDM is derived directly as an emergent property of the logical erasure of highly entangled pre-geometric Page-time correlations surviving from precursor black hole ensembles. We show that the structural capacity of this transition is bounded by a rigid cosmic cycle invariant, = 4² (2) + 2/² 27. 56700, emerging from the holographic boundaries of a saturated pre-geometric phase space. Integrating this invariant through a relational log-normal information kernel, we analytically derive the scalar spectral index nₛ 0. 9662 and, via a non-commutative phase-space squeezing operator, a strict physical spectral running of ₛ^phys -0. 0024, showing sub-percent convergence with Planck 2018 legacy data. Concurrently, by evaluating the late-time scale-decoupling of the bulk capacity, the framework yields an exact theoretical dark energy coupling of c = 1/ 2 1. 201, landing squarely within the constraints issued by the Dark Energy Spectroscopic Instrument (DESI 2024). The framework naturally accounts for the large-scale CMB power deficit via an automatic ³ infrared suppression law and establishes a parameter-free mechanism for Dark Matter production via relic log-normal Primordial Black Holes (PBHs). Due to the strictly scalar-driven nature of the pre-geometric correlation mapping, the model predicts an absolute suppression of primordial tensor modes (r 10^-5), rendering the framework definitively falsifiable by upcoming CMB polarization experiments such as LiteBIRD and CMB-S4.