Authors: Francis M. Sanchez
The electrical constant a and its Eddington approximation 137 are both 10 ppb connected with the dimension d = 26 of bosonic string theory and the 'moonshine entropy' lnD. The involved pi-approximations implies a 0.3 ppb formula for a, and, using the first Mathieu group order, this confirms the Coherent Cosmology value G ≈ 6.67544 × 10^-11 kg^-1m^3s^-2, compatible with the BIPM measurement, but at 4 sigma from the tabulated one. Direct connection between a, 137, d and D = 196883, reveals the string central number 496, about the 20th root of the Monster order, whose square corresponds to 125.6 GeV (BEH Boson), directly tied to the Monster order entropy via the tau and muon masses. The Monster order correlates with canonical economic numbers, leading to a value for the tau mass compatible with the Koide relation in the 10 ppb range, and confirming again the BIPM value for G. The fifth power of the Monster order is directly connected to D and d via the number 24 of transverse dimensions, involving the economic number 3^(24²+1). This confirms the arithmetical character of Physical laws.
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