Phase-Coherent Spacetime: A Resonance-Driven Extension to General Relativity

This revised theoretical preprint develops Phase-Coherent Spacetime as a candidate resonance-driven extension to general relativity. The associated framework, referred to as Coherence-Induced Gravity, formulates structured phase coherence as a possible effective contribution to metric behavior, geodesic evolution, gravitational-wave propagation, and large-scale gravitational signatures. The model is introduced as an effective correction class rather than as a replacement of general relativity, an additional empirical interaction, or an operational control scheme. Its central ansatz represents the effective metric as: g_μν = ḡ_μν + εΨ_μν where g_μν denotes the effective metric, ḡ_μν denotes the background metric associated with the standard relativistic comparison regime, Ψ_μν denotes a resonance-induced metric correction tensor, and ε denotes a perturbative coupling parameter. The standard relativistic regime is recovered when ε tends to zero. The preprint also introduces a local resonance-flow descriptor, β (λ), to represent scale-dependent coherence behavior within the correction class. The framework identifies candidate observational and experimental signatures, including gravitational-wave phase deviations, ringdown residuals, polarization and dispersion constraints, weak- and strong-lensing deviations, pulsar-timing residuals, galaxy-scale and large-scale-structure constraints, and laboratory-scale coherence-sensitive bounds. The scope of the paper is restricted to effective formulation, formal comparison, and observational constraint. Detection of compatible residuals would support further restriction and development of the correction class after competing explanations are bounded. Non-detection would constrain the magnitude, scale, or domain of applicability of the proposed correction. The paper explicitly distinguishes model formulation, observational readability, empirical constraint, external realization, and operational control.