Cosmic miracle: gravitational Compton length of Sagittarius A* is equal to the Bohr radius for Earth like planets

I noticed an extremely intriguing coincidence - if it is a coincidence. The gravitational Compton length for Sagittarius A^*, the galactic blackhole in the center of the Milky Way is equal to the solar Bohr radius in the Nottale model reproducing planetary orbits rather satisfactorily.

1. The values of the ℏ_eff could correspond to the values of ℏ_gr= GMm/β₀, where M is the mass of the galactic blackhole, m is the particle mass, and β₀=v₀/c<1 is velocity parameter. These values of h_eff are gigantic . The gravitational Compton length Λ_gr is GM/β₀= r_S/2β₀ and for β₀=1 it is equal to one half of the Scwartschild radius of the galactic blackhole, which in the range (10⁶--10⁹)× r_S(Sun), r_S(Sun)= 3 km. Note that the distance of Earth to Sun is AU=.15 × 10⁹ km and is in this range.
2. The gravitational Bohr radius for Sun in the Nottale model with β₀≈ 2^-11 is obtained from the radius of Earth's orbit with principal quantum number n=5 as a_0,gr= AU/5≈ .6× 10⁷ km (see this). The gravitational Compton length for the Sagittarius A^* is Λ_gr= r_S/2= .62 × 10⁷ km for β₀=1 and is equal to the solar Bohr radius! Is this a mere coincidence or is there strong coupling between the galactic quantum dynamics and solar quantum dynamics and does this coincidence reflect the very special role of the Earth in the galactic biosphere?
3. In the TGD inspired quantum biology, living matter is controlled by phases with a large value of ℏ_gr, in particular those associated with the gravitational flux tubes of Earth and Sun and quantum gravitation plays a key role in metabolism. This, and the fact that h_eff/h₀ serves as a kind of IQ for living matter, strongly suggests that galactic blackholes are living super intelligent systems controlling matter in very long scales.

See the article Magnetic Bubbles in TGD Universe: Part I or the chapter with the same title.

For a summary of earlier postings see Latest progress in TGD.