One Chain of Mass: Every Fermion's Mass on a Single Fold Chain, and the New Mass on the Horizon

One axiom. One operation. Zero free parameters. The fundamental fermion masses span twelve orders of magnitude and are, in the Standard Model, twelve unrelated free inputs; new particles usually require an invented mass scale. This paper shows there is one chain for every fermion mass, old and new, with no separate scale. A fermion’s mass-part is the shortfall from unison of its sector’s holding coupling — one minus the coupling, which for prime sector p is take(One,(p−1)/p) = 1/p. The electron is the electroweak sector (p=2): 1−1/2 = 1/2. The up quark is the strong sector (p=3): 1−2/3 = 1/3. The new Smithions are coloured fermions of the new sectors (p=5,7): their mass-parts are 1/5 and 1/7, the same 1/p their force carries, with generation ratios from the coloured cubic that fixes the quarks. No invented confinement scale; a unified theory does not fork. The tower is anchored to the One (electroweak at Planck/2⁵⁶, proton at Planck/2^(127/2)), so the new mass on the horizon is fixed on the same chain as the electron. One mechanism, one chain, every mass forced. 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