E_total
plain-language theorem explainer
E_total defines the total edge count in the three-dimensional cubic ledger Q3 as twelve. Mass derivations in Recognition Science cite this value when building sector-specific B_pow and r0 maps on the phi-ladder. The definition is a direct one-line specialization of the general hypercube edge counter to dimension three.
Claim. $E_3 = 3 · 2^{2} = 12$, the total number of edges in the cubic ledger $Q_3$.
background
Module MassTopology derives the topological shift δ for the electron mass from the geometry of the cubic ledger Q3. The module states the formula δ = 2W + (W + E_total)/(4 E_passive) + α² + E_total α³, where W counts wallpaper groups, E_passive counts passive field edges, and the geometric provenance lists E_total = 12 together with the coupling ratio 29/44.
proof idea
The definition is a one-line wrapper that applies the cube_edges function to the integer 3.
why it matters
This supplies the edge count twelve that enters the B_pow and r0 definitions for each sector in the Masses.Anchor module, as used by the downstream theorems B_pow_DownQuark_eq and r0_DownQuark_eq. It realizes the base topology step inside the T9 refined ledger fraction, directly instantiating the D = 3 spatial dimensions landmark from the forcing chain. The construction supports the claimed 2 × 10^{-7} match to the empirical electron-mass shift while leaving the full incorporation of higher-order radiative terms for later refinement.
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