has_ew_scale_structure
plain-language theorem explainer
The electroweak scale satisfies the phi bounds and ladder consistency required for RS W-mass predictions. Cosmologists examining the CDF anomaly would cite this to treat the measured value as the ledger-derived scale rather than a beyond-Standard-Model signal. The proof is a direct one-line application of the electroweak scale theorem.
Claim. The electroweak scale satisfies $1 < phi < 2$ and every mass lies on a phi-ladder rung with no separate fine-tuning.
background
Recognition Science resolves the electroweak scale problem by placing the vacuum expectation value on the phi-ladder: the scale is E_coh times phi to an integer power, eliminating the need for a separate Higgs VEV tuning. The proposition scale_from_ledger encodes exactly this: phi lies strictly between 1 and 2, and the mass hierarchy is self-consistent across all rungs. The present module (T-005) frames the CDF W-mass anomaly as a possible direct readout of that RS scale rather than a discrepancy with the Standard Model Higgs fit.
proof idea
The proof is a one-line wrapper that applies the theorem ew_scale_structure. That theorem constructs scale_from_ledger by pairing the bounds one_lt_phi and phi_lt_two with the no_fine_tuning lemma applied to every rung.
why it matters
This result supplies the electroweak-scale input required by the downstream theorem w_mass_anomaly_structure, which states that the anomaly follows from the ledger. It completes the structural prerequisite in T-005 by confirming that the scale emerges from the same phi-ladder that fixes all other masses, consistent with the eight-tick octave and D = 3. The open experimental question of whether the CDF excess survives future measurements is left untouched.
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