I present the complete mathematical formalism for Harmonic Relational Theory (HRT), deriving how gravity emerges from coherence in a relational field rather than spacetime curvature. Starting from fields ψ and C governed by Hamiltonian Hψ, C, I derive field equations, extract an effective metric, prove relativistic covariance, and recover Einstein's equations in the appropriate limit. Key results: (1) Modified Einstein equations G_μν = 8πG₀⟨C⟩T_μν with coherence-scaled coupling, (2) Application to JADES-GS-z14-0 showing coherence feedback produces massive early galaxies faster than ΛCDM, (3) Rotation curve explanation without dark matter via morphological coherence, (4) Testable prediction: organized galaxies show stronger "dark matter" signatures than irregular galaxies of equal mass. Recent NANOGrav gravitational wave data (Chen et al. , 2026) disfavors dark matter spikes, consistent with HRT's smooth coherence gradients. Highest-priority test: morphology-dark matter correlation in SPARC database. Theoretical insights from Scott L. Costello, mathematical formalization assisted by Claude (Anthropic). Full disclosures in manuscript.
Scott Costello (Sun,) studied this question.