delta_1
plain-language theorem explainer
delta_1 supplies the explicit first-order curvature correction in the Recognition Science series for the inverse fine-structure constant. Researchers closing the residual after the geometric seed and gap weight cite this term as the base case δ₁ ≈ -0.00330. The definition sets the value to the negated ratio of the curvature numerator over face-wallpaper pairs times pi to the fifth power. It is realized by direct substitution of the precomputed combinatorial counts from the Q3 cube.
Claim. $δ_1 = -N_c / (N_{fw} π^5)$, where $N_c$ is the curvature numerator (face-wallpaper pairs plus active edges), $N_{fw}$ is the number of face-wallpaper pairs, and the exponent 5 is the measure dimension (three spatial plus temporal plus conservation).
background
The module formalizes higher-order voxel-seam corrections to α^{-1} in Recognition Science. It sets up the series α^{-1} = α_seed - f_gap + Σ δ_n to address the open 8 ppm residual after the geometric seed 4π × 11 and gap weight w₈ ln φ. The first term δ₁ is the curvature correction on the Q3 cube.
proof idea
This is a direct definition. It negates the ratio obtained by casting the curvature numerator to real and dividing by the product of face-wallpaper pairs (cast to real) and pi raised to the measure dimension.
why it matters
delta_1 supplies the explicit base term required by the AlphaPrecisionHypothesis structure and the additive_residual computation that quantifies the remaining sum of δ_n. It realizes the curvature correction step in the module's alternating series for α^{-1}, drawing on the D=3 cube geometry from the forcing chain. The definition supports the AlphaFrameworkCert and the bounds on subsequent terms needed to reach CODATA.
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