Quantum Formalization of the Entropic Reset: Unification of Infrared Cutoff Evidence in the CMB

This paper presents a unified quantum-gravitational solution to the cyclic entropy paradox and the CMB low-power anomaly (ℓ<30). We formalize the Quantum Entropic Reset mechanism at the contracting singularity (a→0, the Big O state) through Non-Commutative Geometry (NCG). The core mechanism—\textbf{Absolute Quantum Certainty} (ΔxΔp→0)—degenerates the Heisenberg algebra (ℏeff(a)∝a2), forcing the Bekenstein-Hawking entropy (SBH) to vanish, thereby ensuring thermodynamic consistency (ΔSCycle=0) and unitarity. This fundamental suppression induces an \textbf{Infrared (IR) cutoff} in the primordial power spectrum, which significantly improves the fit to Planck 2018 data, yielding Δχ2≈19.1 and strong Bayesian evidence (ΔlogE≈9.5) over ΛCDM. The model predicts a stochastic Gravitational Wave (GW) background (ΩGWh2∼10−12) detectable by LISA (SNR ≳15), offering a direct, verifiable test of the quantum bounce dynamics.