Runtime Spectral Theory (RST): The Spectral Foundation of Emergent Physics - Full Preprint

This record contains a preprint introducing Runtime Spectral Theory (RST) — a framework in which spacetime, gravity, and cosmology emerge from an underlying spectral structure of correlations. The fundamental object is a correlation graph equipped with a spectral measure dμ(ε), whose resolvent defines amplitudes and an effective geometric structure. Classical and relativistic dynamics arise from stationary phase conditions of spectral amplitudes, leading to an emergent Hamiltonian structure. A central result is that gravitational behavior at large scales is governed by the nonlocal structure of the resolvent operator K = (I - W)⁻¹, rather than by a modification of local dynamics. In the presence of long-range correlations, the infrared limit approaches a Green-function form KIR ~ (-Δ)⁻¹. The theory predicts a natural transition scale [ Lₜᵣₐₙₛ ~ {1}{√{σ ε0∞}} ] which falls within galactic scales (10–30 kpc) under observational constraints. In this regime, flat rotation curves and Tully–Fisher scaling v^4 ∝ M emerge without invoking dark matter. RST provides a unified description linking local gravitational tests (e.g. pulsars) with galactic dynamics through a single spectral parameter. The framework yields falsifiable predictions across multiple scales, while a full derivation of the spectral measure from the underlying graph remains an open problem. This record includes: • Full preprint (PDF) • Conceptual visualization of the theory Feedback and discussion are welcome.