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

A unified framework is formulated in which gravity and gauge interactions emerge from an entropic–topological operator structure acting in a diagram Hilbert space. The fundamental variables are projection operators that encode topological sectors of quantum fields. Entropy is defined as an operator functional relating geometric and matter densities, leading to a renormalizable action that yields Einstein gravity and Yang–Mills dynamics in the low-coupling limit. Within this formalism, effective mass spectra for elementary particles arise as eigenvalues of projective operators constrained by entropic minimization. The framework provides a continuous bridge between quantum chromodynamics, the Standard Model, and entropic gravity, predicting coupling unification under renormalization-group flow.