r_electron
plain-language theorem explainer
The electron occupies rung 2 on the φ-ladder that generates fermion masses. Researchers deriving lepton mass ratios from the Recognition Science framework cite this baseline when eliminating Yukawa parameters. The proof is a one-line term that extracts the first conjunct from the theorem verifying all lepton rung assignments.
Claim. The rung integer for the electron lepton satisfies $r_e = 2$.
background
Recognition Science places each charged lepton at a fixed rung on the φ-ladder, so its mass scales as φ to the power of that integer. The assignment map sends the electron to rung 2, the muon to rung 13, and the tau to rung 19; these integers come from the Anchor definitions that encode cube geometry and passive field edges. The module formalizes P-002, which asks what fixes the fermion mass hierarchy and answers that the hierarchy is purely geometric.
proof idea
The proof is a one-line term that selects the first conjunct of the conjunction in the rung verification theorem.
why it matters
This baseline supplies the electron reference for the lepton hierarchy theorem, which proves the geometric ratios m_μ/m_e = φ^11 and m_τ/m_μ = φ^6 and resolves P-002. It aligns with the φ-ladder and eight-tick octave of the framework by fixing the lowest rung without free parameters.
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