Horndeski Minimal Model: A Unified Framework for Gravity, Cosmology, and Quantum Structure

This work develops a minimal and self-consistent formulation of Horndeski gravity, showing that a single scalar degree of freedom is sufficient to unify gravitational dynamics, cosmological evolution, and quantum structure. The model is constructed from first principles, without introducing arbitrary potentials or free functions, and recovers General Relativity as a limiting case. At cosmological scales, the theory naturally produces accelerated expansion without dark energy, while at quantum scales it provides a geometric interpretation of wavefunction collapse and entanglement. The resulting framework is mathematically compact, physically transparent, and capable of connecting classical and quantum regimes within a single coherent structure.