phi_23
plain-language theorem explainer
φ²³ supplies the phi-ladder rung that approximates the W boson to electron mass ratio in Recognition Science electroweak derivations. Physicists computing m_W from the J-cost minimum and phi-ladder placement would cite this constant when matching the predicted 80.38 GeV scale. The declaration is a direct power abbreviation that follows the upstream scale(k) := phi^k pattern without additional computation.
Claim. Let φ denote the self-similar fixed point. Define φ²³ as the scaling factor on the phi-ladder that approximates the W boson to electron mass ratio.
background
The module derives W and Z boson masses from electroweak symmetry breaking in RS, where the Higgs VEV sits at a J-cost minimum and boson masses occupy specific rungs on the phi-ladder. Upstream scale(k) := phi^k from Cosmology.LargeScaleStructureFromRS supplies the general ladder construction; phi_23 specializes it to exponent 23 for the W/e ratio. Anchor.Z from Masses.Anchor provides the integer map used in mass formulas, while the module notes that m_W ≈ 80.38 GeV and m_Z ≈ 91.19 GeV emerge once the rung is fixed.
proof idea
One-line definition that directly applies the power operation to phi, mirroring the scale function in the upstream Cosmology result.
why it matters
This definition supplies the explicit rung for W boson mass predictions in the electroweak sector and feeds sibling declarations such as wBosonMass_GeV and wz_mass_ratio. It implements the phi-ladder placement step in the module's RS mechanism for P-015 and P-016, connecting to the T6 phi fixed point and the eight-tick octave structure in the forcing chain.
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