delta_n
plain-language theorem explainer
delta_n supplies the n-th order voxel-seam correction to the inverse fine-structure constant as the finite sum of weights over all n-fold face-wallpaper configurations on the cube Q3. Derivations of the Recognition Science series expansion for α^{-1} reference this summation to construct successive correction terms. The definition reduces to a direct aggregation over the index set Fin(n_fold_configs n).
Claim. $δ_n(n, w) = ∑_{i ∈ Fin(N_n)} w_i$, where $N_n$ is the number of ordered n-fold face-wallpaper configurations and $w$ is any weight assignment of type VoxelSeamCorrection n.
background
The module formalizes higher-order voxel-seam corrections that close the residual gap between the Recognition Science derivation of α^{-1} and CODATA. The base ingredients are the geometric seed α_seed = 4π × 11, the gap weight f_gap = w₈ · ln φ, and the first-order curvature term δ₁; the full series is then α^{-1} = α_seed − f_gap + Σ_{n=1}^∞ δ_n. VoxelSeamCorrection n is the type of maps Fin(n_fold_configs n) → ℝ, and n_fold_configs n equals the number of face-wallpaper pairs raised to the n-th power. Upstream structures establish the Q3 combinatorics that generate these configurations and the underlying J-cost and ledger factorization used to calibrate the weights.
proof idea
The definition is a one-line summation that aggregates the supplied weight vector over the finite index set of n-fold configurations.
why it matters
This definition supplies the general term in the infinite series that targets the ~8 ppm residual between the Recognition Science α^{-1} and CODATA. It supports the framework for arbitrary-order corrections on Q3, with explicit computation of δ₂ remaining open. The construction rests on the spectral emergence of Q3 that forces the gauge group content and the three-generation structure.
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