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 Witten 'moonshine entropy' lnD, with D = 196883 = 59(59²-12²). 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 controversial tabulated one. The monstrous fifth number in the fractional development of pi is clearly involved. Direct connection between a, 137, d and D, implies the string central number 496, very close to 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, which are connected by an holographic relation, confirming the Eddington tau-proton symmetry and the symmetrical Koide relation. The Monster order correlates with canonical economic numbers, leading to a value for the tau mass, from its approximation 59²me, so directly tied to D, and compatible with the Koide relation in the 10 ppb range, 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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