pith. sign in
def

active_edges

definition
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module
IndisputableMonolith.Constants.AlphaHigherOrder
domain
Constants
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plain-language theorem explainer

Active edges per tick is fixed at one inside the Q3 combinatorics that generate voxel-seam corrections to α^{-1}. Workers on the Recognition Science series for the fine-structure constant cite this constant when forming the curvature numerator that feeds δ₁. The assignment is a direct constant definition.

Claim. The number of active edges per tick equals $1$.

background

The module supplies the combinatorial scaffolding for higher-order voxel-seam corrections that close the residual gap between the Recognition Science α^{-1} formula and the CODATA value. The series is written α^{-1} = α_seed − f_gap + Σ δ_n, where each δ_n is a weighted sum over n-fold face-wallpaper pairs on the Q3 lattice under the Z₂^5 measure. Q3 is equipped with vertices, edges, faces and wallpaper groups as the primitive counts.

proof idea

Direct definition that assigns the constant 1.

why it matters

The value enters curvature_numerator := face_wallpaper_pairs + active_edges and is invoked in the proof that δ₁ < 0. It therefore participates in the alternating series that targets the interval (137.030, 137.039) and addresses the open ~8 ppm discrepancy left by the base geometric seed plus gap weight. The construction prepares the explicit framework for computing the next term δ₂.

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