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

==== - Dimensional logic works: the algebra and units are consistent; the estimate shows clearly how GGG depends on a length scale r0r_0r0 and on ℏ\hbarℏ and ccc. ====
* Atomic scales cannot produce GGG: if your fundamental QAT shell length is atomic (Bohr scale), you get a wildly wrong GGG. That means QAT — if it is to produce the observed Newton constant without introducing extra parameters — must either (a) predict a fundamental microscopic length near the Planck scale, or (b) produce an effective collective energy density at cosmological scales that yields the measured GGG (Dirac/Mach style).
* Planck scale naturally appears: the inversion shows that a Planck-scale radius is what gives a realistic GGG. This is not surprising: many routes to deriving GGG lead to Planck units because GGG itself sets the Planck scale when combined with ℏ\hbarℏ and ccc.
* Assumptions matter: I chose E0∼ℏc/r0E_0\sim \hbar c/r_0E0∼ℏc/r0 (light-crossing time estimate) and spread that energy over a sphere volume. Different assumptions (event rate per unit time, how energy is distributed in space, coupling between many shells, or cosmological aggregation) will change numeric results drastically. The order-of-magnitude conclusion (atomic → wrong; Planck → possible) is robust.