This manuscript formulates the emergent-gravity block of the TTOE framework as a mixed chain that fixes the scale A = c sqrt (G rhoᵥac) from the E8 structure, the Sakharov induced coupling, an FRG correction, and the observed cosmological input rhoᵥac. The numerical value a0 = (2/pi) A is presented only as a conditional result: it requires a sinusoidal time profile and a rectified L¹ observational functional. The possible evolution a0ₑff (z) proportional to H (z) is kept separate as a testable phenomenological hypothesis, not as a direct verification of the full chain.
O. F. C. (Tue,) studied this question.