Editing Openai/6897769e-4ee4-800f-aba5-69cca34f701c (section)

==== (I) Local-to-global (aggregate) — Dirac / Mach route (recommended) ====
Compute the global QAT energy density uQATu_{\rm QAT}uQAT by integrating local shell event power over matter distribution (atoms, stars, plasma). Then insert uQATu_{\rm QAT}uQAT into cosmological relations (e.g. Friedmann equation H2=(8πG/3)ρH^2=(8\pi G/3)\rhoH2=(8πG/3)ρ) or Einstein scaling to see what value(s) of GGG are implied. This avoids assuming Planck units and is the least circular.

(II) Fundamental scale route (Planck-centric)
Assume QAT implies a microscopic length or time scale (e.g., δ\deltaδ or ν−1\nu^{-1}ν−1) that is independent of GGG. Then plug that into a local surface-curvature relation and solve for GGG. This is more ambitious: you must show QAT gives a fundamental scale (e.g., r0r_0r0 of order ℓP) from geometry alone. If you assume Planck-scale quantities up front, deriving GGG is circular because Planck scales already include GGG.