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

==== - The Planck time tPt_PtP depends on GGG. So using tPt_PtP as an assumed QAT event rate while attempting to derive GGG makes the derivation circular. ====
* There are two non-circular strategies:

===== If QAT can predict a microscopic timescale τQAT\tau_{\rm QAT}τQAT and thickness δQAT\delta_{\rm QAT}δQAT from purely geometric or dimensionless relations (e.g. using α\alphaα, φ\varphiφ, electron charge eee, electron mass mem_eme, etc.), then you can plug those into the formula and solve for GGG without circularity. This is harder, but it’s the clean route. =====

===== Instead of trying to get GGG from a single atom, compute the collective QAT energy density of the Universe from the per-atom event budget times the number density of atoms and radiation, and then match that cosmic energy density to the curvature of the universe (Friedmann equations). This is the Dirac/Mach route — it links local geometry to global quantities and can yield G∝1/tG\propto 1/tG∝1/t or similar relations if the QAT budget evolves with cosmic time. This avoids direct Planck assumptions but trades for cosmological assumptions. =====