ew_rung
plain-language theorem explainer
Integer rung 51 places the electroweak scale on the Recognition Science φ-ladder. Cosmologists and particle theorists cite it when fixing T_EW = φ^51 and the Z-mass sector formula. The declaration is a bare integer definition, not a derived theorem.
Claim. The electroweak φ-ladder rung is the integer $51$. In the EW-sector mass formula this means $m_Z = 2\,\varphi^{51}/10^6\,\mathrm{MeV}$, and the phase-transition temperature is taken as $T_{\mathrm{EW}} = \varphi^{51}$ in RS-native units (sector prefactors absorbed into the unit choice).
background
Recognition Science places particle and cosmological scales on a discrete φ-ladder: masses and temperatures appear as yardstick times φ raised to an integer rung (with small gap corrections). The golden ratio φ is forced earlier in the foundation chain as the self-similar fixed point (T6).
This module is an RS-native-unit scaffold for the electroweak phase transition. The Z boson sits at EW-sector rung 51 via the ElectroweakMasses prediction $m_Z = 2\times\varphi^{51}/10^6,\mathrm{MeV}$. Standard EW baryogenesis takes $T_{\mathrm{EW}}\sim m_Z\sim 100,\mathrm{GeV}$; in RS-native units only the φ-power matters for dimensionless ratios, so $T_{\mathrm{EW}}=\varphi^{51}$.
Downstream quantities (Hubble rate at the transition, sphaleron-to-Hubble washout scaffold) all pin this same rung. The module explicitly does not feed the washout ratio into the Planck-matched η_B formula.
proof idea
No proof: a definition equating the electroweak rung constant to the integer literal 51. Downstream certificates simply pattern-match or rewrite with this equality.
why it matters
Fixes the single integer that anchors every EW-scale quantity in the module: $T_{\mathrm{EW}}$, $H^2(T_{\mathrm{EW}})$, and the sphaleron washout scaffold. The certificate structure EWTransitionCert requires ew_rung = 51 as its first field, so any complete EW-transition witness must cite this definition.
In the broader framework it is the cosmological counterpart of the mass-ladder rung for the Z boson, tying the radiation-era Friedmann combination at the electroweak epoch to the same φ-power used in ElectroweakMasses. It does not close the open Boltzmann-transport path to η_B; the module status remains MODEL scaffold pending a genuine washout calculation.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.