total_angular_is_pi5
plain-language theorem explainer
The result shows that the total angular factor from integration over the five-dimensional ledger configuration space equals pi to the fifth power. Researchers deriving the curvature correction in the fine-structure constant within Recognition Science would cite this to justify the pi^5 denominator. The proof is a direct unfolding of the factor definition and the dimension constant followed by reflexivity.
Claim. The total angular integration factor over the five-dimensional configuration space equals $pi^5$.
background
This module derives the curvature correction term in the fine-structure constant formula as delta_kappa = -103/(102 pi^5). The configuration space has five effective dimensions: three spatial from the forced D=3, one temporal from the eight-tick cycle, and one from the dual-balance conservation constraint. Each dimension contributes a pi factor from its angular integration, producing the overall pi^5 scaling for the mismatch integral between spherical and cubic geometries.
proof idea
The proof is a one-line wrapper that unfolds the definitions of the total angular factor and the configuration space dimension, then applies reflexivity.
why it matters
This theorem closes the angular contribution step in the curvature space derivation, directly supporting the pi^5 term in the alpha inverse expression alpha^{-1} = 4 pi * 11 - f_gap - 103/(102 pi^5). It rests on the five-dimensional phase space that incorporates T8 spatial dimensions, the T7 eight-tick octave for time, and the ledger balance constraint. The result anchors the topological stress measure 103/102 within the Recognition framework's constant derivations.
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