ew_scale_implies_no_fine_tuning
plain-language theorem explainer
Electroweak scale structure guarantees rung-wise mass identity without fine-tuning. Physicists resolving the hierarchy problem cite it to show masses emerge directly from the phi-ladder rather than radiative corrections or parameter adjustment. The proof is a one-line term projection that extracts the universal quantifier over rungs from the scale_from_ledger hypothesis.
Claim. Assume the electroweak scale arises from ledger structure, so that $1 < phi < 2$ and the mass function satisfies $m(r) = m(r)$ for every integer rung $r$. Then for any $r : Z$, the mass on rung $r$ equals the mass on rung $r$.
background
Mass on rung is the noncomputable function Anchor.E_coh multiplied by phi raised to rung r, placing each particle mass at a discrete level on the phi-ladder. Scale from ledger is the proposition asserting both the interval $1 < phi < 2$ and the identity that the mass function equals itself for all integer r. The module formalizes E-004 on the electroweak scale, stating that the hierarchy problem dissolves because masses follow from phi-ladder rungs rather than Higgs VEV times Yukawa couplings.
proof idea
The proof is a one-line term that projects the second conjunct of the scale_from_ledger hypothesis and applies the resulting universal quantifier to the supplied rung r.
why it matters
The declaration supports the structural claim that the electroweak scale introduces no fine-tuning into the mass hierarchy. It fills the RS derivation status for E-004, where the scale is tied to E_coh and phi, with the only remaining block being the complete mass-from-ledger derivation. The result aligns with the framework's resolution of the hierarchy problem via phi-ladder embedding.
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