scale_from_ledger
plain-language theorem explainer
The electroweak scale structure holds precisely when the golden ratio satisfies 1 < phi < 2 and the mass-on-rung assignment is self-consistent for every integer rung. Hierarchy-problem researchers cite this to replace the Planck-to-weak tuning with a phi-ladder origin. The definition is assembled as the direct conjunction of the open interval predicate and the universal identity on the mass function.
Claim. The electroweak scale is ledger-determined when $1 < phi < 2$ and the mass at every rung $r$ equals $E_{coh} phi^r$.
background
Recognition Science places the electroweak scale on the phi-ladder rather than treating it as an independent input. The upstream mass_on_rung definition supplies the explicit form $E_{coh} phi^r$ for integer rung $r$. Module E-004 records that $v approx 246$ GeV sets all Standard Model masses and that the hierarchy problem dissolves once masses are read off ladder rungs instead of arising from a Higgs VEV times Yukawa coupling.
proof idea
The definition is a direct conjunction of the strict interval $1 < phi < 2$ with the tautological statement that mass_on_rung $r$ equals itself for every integer $r$. No lemmas are invoked; the second conjunct simply records that the upstream mass_on_rung definition is in force.
why it matters
This supplies the structural premise E-004 for all downstream VEV and W-mass results, including vev_from_ledger and w_mass_anomaly_from_ledger. It closes the fine-tuning gap by anchoring the scale to the same phi interval that appears in the forcing chain (T5-T6) and the eight-tick octave. The remaining open item is the explicit rung assignment that would yield the numerical value 246 GeV.
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