Scalar Coherence as a Unifying Principle in Quantum Gravity

We propose scalar coherence as a conserved structural quantity underlying both quantum mechanics and general relativity. Scalar coherence measures the degree of phase-aligned information present in a physical field configuration and is defined as a scalar functional invariant under a restricted class of coherence-preserving transformations. We show that scalar coherence admits a rigorous formulation on Sobolev spaces, possesses a covariantly conserved stress tensor derived from a variational principle, and naturally induces spacetime curvature. Two toy models—a 1+1 dimensional static geometry and a minisuperspace cosmology—demonstrate how gravitational dynamics emerge from coherence gradients without quantizing spacetime directly. This work is intended as a foundational, self-contained contribution suitable for subsequent submission to Classical and Quantum Gravity.