Transformational Unification through the Theory of Entropicity (ToE): A Reformulation of Quantum–Gravitational Correspondence via the Obidi Action and the Vuli-Ndlela Integral

The Theory of Entropicity (ToE) unifies Thermodynamics, Quantum mechanics, and General relativity under a single entropic variational principle. This paper reformulates the transformational framework of the ∆∞O meta-theory of Alexander Ngu and Amaya Odilon Kosso through the ToE formalism. Using the Obidi Action and the Vuli-Ndlela Integral, the analysis demonstrates that all transformation-based results claimed by the ∆∞O paper emerge naturally as entropic conse quences. The equivalence transformation program (T1–T6) shows that every major feature—unified operator, Planck-scale dispersion, and holographic entropy bounds—arises from entropic field dy namics governed by irreversible constraints and the finite rate of entropy rearrangement in ToE.