Foundations of Quantum Resonant Gravity I: Emergent Metrics, Scalar Dynamics, and the Weak‑Field Limit

Quantum Resonant Gravity (QRG) models the vacuum as a Lorentz‑covariant resonant substrate supporting scalar and tensor excitations. The slowly varying envelope of the microscopic oscillatory field defines a scalar mode \Phi , which in turn determines the substrate rest frame through its normalized gradient. Matter and light couple to the substrate via polarization responses, giving rise to emergent matter and optical metrics. This paper develops the foundational structure of QRG, including: the microphysical origin of the scalar mode, the dynamical rest‑frame construction, the derivation of the optical metric from substrate polarization, the weak‑field limit and recovery of Newtonian gravity, the post‑Newtonian parameter \gamma =1, perturbative stability and preferred‑frame suppression, boosted‑frame PPN analysis, and an FRG derivation of the exponential infrared potential. The resulting framework is internally consistent, Solar‑System safe, and provides the theoretical basis for the phenomenological developments presented in Part II.