Foundations of Quantum Resonant Gravity I: An Effective Field Theory of Metric Response and Scalar Dynamics

This record contains the final submission version of Foundations of Quantum Resonant Gravity I: An Effective Field Theory of Metric Response and Scalar Dynamics. The paper develops the EFT foundations of Quantum Resonant Gravity (QRG), a scalar–tensor framework in which a dimensionless scalar field defines a dynamical preferred direction and couples to matter through a restricted disformal metric. The construction is fully EFT‑consistent: degrees of freedom and symmetries are explicit, operator truncation is justified, and the regulator ε is given a physical interpretation as a coherence‑length scale. The weak‑field limit reproduces Newtonian gravity and the post‑Newtonian parameter γ = 1, while naturally suppressing preferred‑frame parameters. A distinctive, sign‑definite, and observationally testable prediction for the gravitational slip parameter (η − 1 ≈ −10⁻³ to −10⁻²) is derived and contextualized with current and near‑future lensing surveys. The paper also clarifies how Part I constrains the nonlinear kinetic sector developed in Part II. A shortened FRG appendix motivates the exponential potential used in the cosmological extension. This version incorporates minor editorial refinements requested by a final‑round referee and is intended as the definitive public version