SGF Paper 2 presents the mathematical backbone of the Spectral Gravitation Framework. It derives the modified Einstein equations, defines the entanglement and quantum‑foam fields, sketches one‑loop consistency, and explicitly states limitations and open questions on dynamics, EFT completion, and renormalization.

The Spectral Gravitation Framework (SGF) introduces a density‑responsive, entanglement‑based extension of general relativity. Paper 1 lays out the core ontology, unified action, three regimes, and falsifiable predictions, positioning SGF as a testable proposal for unifying gravity, quantum phenomena, and cosmology.