passive_edges
plain-language theorem explainer
The definition computes the number of passive edges on the three-cube as total edges minus the single active edge per tick. Researchers deriving higher-order voxel-seam corrections to the fine-structure constant cite this when building the geometric seed for α^{-1}. It is a direct subtraction of the two upstream constants Q3_edges and active_edges.
Claim. The number of passive edges on the three-cube is defined as the total edge count minus the active edge count: $N_{passive} := N_{edges} - N_{active}$.
background
In the module on higher-order voxel-seam corrections to α^{-1}, the three-cube Q₃ supplies the combinatorial base for the series. Q3_edges counts the twelve edges of the cube while active_edges counts the single active edge per tick. The module states the local setting as the geometric seed α_seed = 4π × passive_edges together with the gap weight and curvature corrections that target the CODATA value 137.035999206.
proof idea
This is a one-line definition that subtracts the constant active_edges from Q3_edges.
why it matters
This definition supplies the passive edge count required by the AlphaFrameworkCert structure and by the alpha_seed definition. It completes the geometric seed step in the Recognition Science derivation of α^{-1} = α_seed − f_gap + Σ δ_n, where α_seed ≈ 138.230. The framework remains open at the explicit computation of δ₂.
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