delta_1_power
plain-language theorem explainer
The theorem asserts that the integration measure dimension equals five. Researchers computing higher-order voxel-seam corrections to the inverse fine-structure constant reference this equality when weighting combinatorial sums over Q3 face-wallpaper configurations. The proof is a direct term application of the reflexivity theorem on the definition measure_dimension := 3 + 1 + 1.
Claim. The integration measure dimension, defined as three spatial dimensions plus one temporal dimension plus one conservation dimension, equals five: $3 + 1 + 1 = 5$.
background
The module formalizes higher-order corrections to the fine-structure constant via the series α^{-1} = α_seed - f_gap + Σ_{n=1}^∞ δ_n, where each δ_n is a finite sum over n-fold face-wallpaper pairs on Q3 weighted by the Z_2^5 half-period integration measure. The integration measure dimension is introduced as D + 1 (temporal) + 1 (conservation) with D = 3. Upstream results establish measure_dimension := 3 + 1 + 1 and its equality to 5 by reflexivity.
proof idea
The proof is a one-line term wrapper that applies the reflexivity theorem measure_dimension_eq directly to the definition measure_dimension := 3 + 1 + 1.
why it matters
This equality supplies the weighting dimension for the δ_n series that targets the CODATA value 137.035999206 within the Recognition Science framework. It anchors the first-order correction δ_1 = -103/(102 π^5) and connects to the forced D = 3 at T8. The module leaves the explicit computation of δ_2 as the open deliverable.
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