This analysis reveals a new formula for the hierarchy problem, suggesting gravity's perceived weakness is due to its distance in the tower's structure.
The hierarchy problem —why gravity is ∼ 1016 times weaker than the electroweak force— has driven beyond-Standard-Model physics for 50 years, motivating supersymmetry, extra dimensions, and fine-tuning arguments. We show that MPl/v = 3kEW where kEW = 35 = 5 × 7, derived from the GF(3k) tower structure. The electroweak scale v = 35 + 3 = 246 GeV and the Planck scale MPl = v × 335 ≈ 1.22 × 1019 GeV. The refined formula v = MPl × 112/(111 × 335) = 246.22 GeV matches the PDG value 246.22 GeV to 0.001%. The factorization kEW = 5 × 7 connects the hierarchy to the tower’s Galois structure. No SUSY, no extra dimensions, no fine-tuning: gravity is not weak—it is 35 tower levels away.
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Daniel Florin Cherloaba (2026) studied this question.
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