electron_structural_mass
plain-language theorem explainer
The electron structural mass is defined as the lepton yardstick scaled by phi to the power of the electron rung minus the octave period. Researchers deriving lepton masses from Recognition Science first principles cite this to obtain the base structural component on the phi-ladder. It is a direct one-line composition of the pre-derived yardstick, rung value 2, and octave period 8.
Claim. $m_ {struct} := Y · φ^{r_e - 8}$ where $Y$ is the lepton yardstick, $r_e = 2$ is the baseline lepton rung, and the octave period equals 8.
background
This definition sits in the T9 Electron Mass Definitions module, which separates core mass expressions from theorems to avoid import cycles. The module derives lepton constants from D = 3 cube geometry: 12 total edges, one active edge per tick, yielding 11 passive edges and B = -22; wallpaper groups fix R0 = 62. The electron rung is the baseline generation-1 value 2. The lepton yardstick is Y = 2^{-22} · E_coh · φ^{62}. The octave period is 8, obtained as cube_vertices D with D = 3 from the unified forcing chain T6-T8.
proof idea
One-line definition that multiplies lepton_yardstick by phi raised to the integer difference of electron_rung and octave_period.
why it matters
This supplies the structural mass input to alphaG_pred_eq, row_alphaG_pred, and alphaG_pred_closed in the AlphaGScoreCard, which express G m_struct² / (hbar c) and related predictions. It realizes the T9 mass formula m_struct = Y · φ^(r-8) inside the Recognition framework, connecting the phi-ladder scaling (T5-T6) and eight-tick octave (T7) to the electron scale after D = 3 is fixed (T8). It closes the structural part of the first-principles chain before residue corrections are applied.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.