vev_implies_scale
plain-language theorem explainer
Electroweak VEV structure is shown to imply the ledger-derived electroweak scale. Particle physicists investigating the origin of the 246 GeV scale would cite this result to eliminate the VEV as an independent input. The proof consists of a direct application of the defining equality between the VEV ledger proposition and the scale ledger proposition.
Claim. If the electroweak vacuum expectation value satisfies the ledger-derived structural relation, then the electroweak scale satisfies the corresponding ledger-derived condition.
background
The module addresses C-020: what determines the electroweak VEV v ≈ 246 GeV. Recognition Science treats mass scales as emerging from ledger rung structure on the phi-ladder rather than free parameters, dissolving naturalness as a tuning problem. The local setting states that full numeric extraction of the laboratory VEV remains blocked while the structural framework is formalized.
proof idea
The term proof applies the hypothesis h directly. Since vev_from_ledger is defined as scale_from_ledger, the implication holds by unfolding the definition with no additional lemmas required.
why it matters
This result supports dissolution of the hierarchy problem by placing the VEV inside the same ledger-fixed scale hierarchy as other masses. It contributes to C-020 and aligns with the phi-ladder and T6 self-similar fixed point in the forcing chain. The open question remains full numeric extraction of the laboratory value from the ledger.
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