phi_27
plain-language theorem explainer
This definition isolates the constant obtained by raising the self-similar fixed point to the 27th power, which Recognition Science equates to the ratio of the Higgs vacuum expectation value to the electron mass. Electroweak model builders and mass-hierarchy analysts cite it to anchor the electroweak scale on the phi-ladder. The declaration is a direct exponentiation with no lemmas or hypotheses.
Claim. Define the real number obtained by raising the self-similar fixed point to the 27th power; this quantity satisfies the numerical relation VEV over electron mass approximately equal to 4.8 times 10 to the 5.
background
The module derives W and Z boson masses from the Higgs mechanism under Recognition Science, where electroweak symmetry breaking corresponds to a J-cost minimum and the vacuum expectation value sits at a definite rung on the phi-ladder. The local setting treats the Weinberg angle and mass ratio m_Z equals m_W over cos theta_W as geometric consequences of the gauge embedding, with all scales fixed by powers of the self-similar fixed point. This definition extracts the specific power that matches the observed VEV to electron-mass ratio, consistent with the general mass formula yardstick times phi to the power of rung minus 8 plus gap.
proof idea
The declaration is a one-line definition that applies the exponentiation operation directly to the imported self-similar fixed point.
why it matters
The constant supplies the scaling factor for the Higgs vacuum expectation value in the electroweak sector and supports the numerical predictions m_W approximately 80.38 GeV and m_Z approximately 91.19 GeV listed in the module. It realizes the phi-ladder placement step of the mass hierarchy and connects to the T6 forcing of the self-similar fixed point. No downstream theorems are recorded, leaving open the explicit insertion of this rung into the full boson-mass derivations.
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