Myominaung Unified Theory (MUT) v4.1.1: Proofs of Fundamental Relationships

This paper (MUT v4.1.1) presents expanded, step-by-step mathematical proofs of the fundamental relationships underlying the Myominaung Unified Theory (MUT) v4.0. It focuses on reproducibility, transparency, and numerical consistency of the core laws that connect atomic, gravitational, and cosmological phenomena within a scalar frequency–based framework.The paper provides detailed derivations of the Law of Mass Manifestation (mass–frequency relationship), hydrogen atomic resonance and Rydberg convergence, universal gravitation as a scalar frequency gradient, determination of the ground frequency �, and the consistency of awareness velocity and the universal scaling factor. Each derivation explicitly references the constants and assumptions defined in MUT v4.0 and demonstrates their invariance across scales.MUT v4.1.1 does not introduce new parameters or phenomenology. Instead, it serves as a rigorous proof companion to MUT v4.0, ensuring that the foundational equations are mathematically sound, numerically consistent, and suitable for independent verification and future observational testing.