KIR-QER-Nezirov - Supplement I Formal Derivations & Field Equations

This Supplement I provides the formal mathematical foundation for the Theory of Kinetically-Induced Spacetime (KIR-Nezirov). While the main treatise establishes the conceptual framework, this document focuses on the rigorous derivation of the field equations from first principles of kinetic interaction. The mathematical exposition includes: The Scalar Interaction Field: Formal definition of the density field and its coupling to photon flux. Kinetic Derivation of Metrics: A step-by-step derivation showing how the Gordon metric emerges from local density gradients, providing a refractive-index-based alternative to the Schwarzschild metric. Equations of Motion: Derivation of the modified geodesic equations, accounting for position-dependent inertia and the resulting non-Newtonian dynamics in galactic scales. Consistency Proofs: Mathematical verification that KIR reproduces the classical results of General Relativity (such as light deflection and perihelion precession) in the limit of weak fields, while diverging at high-density thresholds to avoid singularities. This supplement is intended for readers requiring the technical proof of the KIR theory’s internal consistency and its quantitative predictive power. KIR-QER-Nezirov: Kinetically Induced Spacetime and Quantum Field Emergence of Reality — Complete Theoretical Framework with Supplements. Zenodo. https: //doi. org/10. 5281/zenodo. 18943890