This mathematical exploration resolves the hierarchy problem in physics, suggesting a new understanding of mass ratios.
One axiom. One operation. Zero free parameters. The hierarchy problem — gravity’s vast weakness, the Planck mass sitting ~10¹⁹ proton masses above ordinary matter, and the conviction that such a ratio needs new physics to protect it — is dissolved here. The proton-to-Planck ratio is not fine-tuned; it is a forced span. At the forced covering depth seven (the same depth that fixes the fine-structure constant), the tower from the One down to its floor has linear size M_Planck/m_proton = 2^(127/2) ≈ 1.304×10¹⁹, matching the measured ratio (≈ 1.301×10¹⁹) to 0.24%, with zero free parameters. There is nothing to fine-tune and nothing to protect: the ratio is the number of doublings from the whole to the floor, counted. No supersymmetry, no extra dimensions. The only conventional quantity is the NAME of a unit, which carries no physics. Machine-checked; reproduces from one command. A standalone result within the Smithian Fold Theory of Everything (SFTOE). Full corpus, code, and the run-it-yourself VERIFY.md protocol: https://github.com/MettaMazza/Smithian-Fold-Theory
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Maria Smith (2026) studied this question.
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