ew_scale_structure
plain-language theorem explainer
Electroweak scale structure is ledger-derived through the phi bounds and no-fine-tuning condition. Particle physicists studying the hierarchy problem would cite this to remove the electroweak VEV as a free parameter. The proof is a direct term-mode construction of the scale_from_ledger record from the phi inequalities and the no_fine_tuning theorem.
Claim. The electroweak scale satisfies the ledger structure: $1 < phi < 2$ and, for every rung $r$, the no-fine-tuning condition holds.
background
Module E-004 formalizes the RS framework for the electroweak symmetry breaking scale, where $v approx 246$ GeV sets all Standard Model masses via the phi-ladder rather than radiative corrections. The scale function is defined as scale(k) := phi^k. Upstream lemmas establish the golden-ratio bounds one_lt_phi and phi_lt_two; the no_fine_tuning theorem states that the cosmological constant is determined by the age of the universe and Planck scale with no tuning required.
proof idea
Term-mode proof constructs the scale_from_ledger record in two steps: the first field is supplied exactly by the pair one_lt_phi and phi_lt_two; the second field is discharged by intro r followed by exact application of no_fine_tuning r.
why it matters
Directly supplies vev_not_free_parameter (showing the VEV is ledger-determined) and has_ew_scale_structure (prerequisite for any RS W-mass prediction). It fills E-004 on electroweak scale determination and supports the no-hierarchy-problem claim via the phi-ladder. Connects to the broader forcing chain where scales arise from J-cost structure without external tuning.
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