Propagation of True Randomness and the Meta-Necessity of Grand Unified Theory under Information Preservation

Grand Unified Theories (GUTs) have traditionally been treated as high-energy hypotheses that are difficult to verify directly. This paper proposes a meta-theoretical framework extending the perspective of "operational non-separability." By defining the universe as an information-processing system governed by state transformations (unitary or CPTP channels), this study investigates the propagation of true randomness from the early universe We demonstrate that if information is not arbitrarily erased, the currently fragmented four fundamental forces must necessarily converge into a higher unified structure via information-theoretic reverse inference. This conclusion suggests that GUT is not merely a model-dependent hypothesis (e.g., SU(5), SO(10)) but a "meta-necessity" required by the consistency of single-origin cosmology and information preservation principles