alpha_seed
plain-language theorem explainer
The geometric seed for the inverse fine-structure constant is defined as four pi times the passive edge count on the Q3 cube. Researchers deriving higher-order voxel-seam corrections to alpha inverse cite this as the baseline term before gap weights and curvature series. The definition is a direct abbreviation that substitutes the passive edge count obtained by subtracting active edges from total Q3 edges.
Claim. $α_{seed} = 4π ×$ (total Q3 edges minus active edges), where the passive edge count supplies the geometric baseline for the fine-structure series.
background
The module develops higher-order corrections to the fine-structure constant inverse, beginning with the geometric seed as the initial term in the additive and exponential formulas. Passive edges are defined as total Q3 edges minus active edges, where Q3 denotes the three-dimensional cube with its vertices, edges, faces, and wallpaper group pairings for voxel-seam combinatorics. The legacy seed from the Alpha module is four pi times eleven, representing baseline spherical closure cost over eleven-edge interaction paths.
proof idea
The declaration is a direct definition that computes the seed by multiplying four pi by the passive edges count, which itself subtracts active edges from total Q3 edges.
why it matters
This supplies the geometric seed used in alphaInv and alpha_components_derived, which unfold the exponential resummation alpha_seed times exp of minus f_gap over alpha_seed. It corresponds to the baseline in the Recognition Science derivation of alpha inverse, prior to the gap weight f_gap approximately 1.198 and the first curvature correction delta1. The definition supports the open computation of higher-order delta_n terms needed to close the residual to CODATA.
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