Entropy-Originated Topological Framework for a Unified Theory of Matter and Gravity

We propose an entropic–topological projection framework that unifies matter and gravity within a single conceptual structure. The central object is a diagram Hilbert space, from which physical sectors are selected via projective operators constrained by topological invariants and entropic consistency conditions. This dual projection mechanism simultaneously generates particle masses through effective symmetry reduction and yields emergent gravitational dynamics as an entropic force. Renormalization group (RG) flows of gauge couplings indicate a natural tendency toward convergence, modified by entropic–topological corrections that stabilize unification without requiring fine-tuned thresholds. The framework embeds quantum chromodynamics (QCD) and the Standard Model (SM), provides space for neutrino physics, and suggests distinct experimental signatures such as proton decay, neutrinoless double beta decay, and cosmological imprints. The novelty lies in achieving unification through projection, rather than introducing exotic new fields.