lepton_R0_eq
plain-language theorem explainer
The lepton sector offset evaluates to 62. Researchers deriving the electron mass from cube geometry and crystallographic constants in Recognition Science cite this to fix the phi-ladder position for the first-generation lepton. The proof is a direct term simplification that substitutes the geometric constants and normalizes the arithmetic result.
Claim. The lepton sector offset satisfies $r_0 = 4W - (8 - r_b) = 62$, where $W = 17$ is the number of wallpaper groups and $r_b = 2$ is the baseline rung.
background
The T9 module derives lepton sector constants from cube geometry in three dimensions. Cube edges total 12 with one active transition per tick, leaving 11 passive edges that set the binary exponent scale. The offset is computed as four times the wallpaper groups count minus the octave adjustment from the baseline rung of 2. Upstream results supply the wallpaper groups definition as the crystallographic constant 17 and the octave period equality from the self-similar fixed point.
proof idea
The term proof unfolds the lepton offset definition and substitutes the sector binary exponent, spatial dimension, wallpaper groups value, octave period equality, and baseline rung, then applies numerical normalization to reach the integer 62.
why it matters
This equality supplies the rung offset used in the structural mass theorem, which expresses the electron mass as $2^{-22} phi^{51}$. It completes the geometric derivation step from D = 3 and the eight-tick octave to the mass formula. The result anchors the T9 chain linking cube geometry and wallpaper groups to the phi-ladder mass expression.
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