Cosmology from Two Axioms 4, Symmetry Breaking of Logical Entropy Gradient: Matter-Antimatter Excess and Neutrino Chirality Predictions in the Information Conservation Framework

Based on anunderlying self-consistent logic constructed from the two fundamental axioms of ”Information Conservation” and ”Computability”, this paper introduces the ”Logical Entropy Gradient” (∆Σ) as the core order parameter describingthe local differences in the internal information structure of a system. We rigorously prove that the existence of a logical entropy gradient (∆Σ̸ = 0) necessarilyleads to inequality between local and global information structures, thereby inducing the breaking of time reversal (T) and the combined charge conjugation-timereversal (C, T) symmetries. Based on this mechanism, within the frameworks of theStandard Model and cosmology, we derive testable quantitative predictions: thebaryon-to-photon ratio in excellent agreement with observations (ηB ≈ 6.1×10−10),the neutrino chiral chemical potential in core-collapse supernova environments(µ5 ≈ 0.20Tc), and a possible tiny shift in the spectral endpoint in neutrinolessdouble beta decay (δQββ ≈ 15 keV). These predictions provide clear targets fortesting by next-generation experiments such as CMB-S4, DUNE, and nEXO.