total_angular_factor
plain-language theorem explainer
The total angular factor is defined as π raised to the configuration space dimension. Derivations of the fine structure constant correction term cite this when accounting for angular integration over the ledger phase space. The definition is a direct abbreviation that substitutes the fixed dimension value of 5.
Claim. The total angular factor is defined as $π^d$ where $d$ is the effective dimension of the configuration space for curvature integration.
background
The module derives the π^5 factor in the curvature correction δ_κ = -103/(102π^5) that appears in the fine structure constant formula. The configuration space for the Recognition ledger has five effective dimensions: three spatial from the forced D=3, one temporal from the eight-tick cycle, and one from the dual-balance constraint. The upstream definition configSpaceDim fixes this dimension at 5 and supplies the exponent for the angular contributions from each dimension.
proof idea
This is a direct definition that sets total_angular_factor to Real.pi raised to the power of configSpaceDim. No further lemmas or tactics are applied.
why it matters
This definition supplies the angular factor used by the theorem total_angular_is_pi5, which confirms equality to π^5. It completes the step that explains the denominator in the curvature correction inside the alpha inverse expression. The construction rests on the framework forcing of D=3 and the eight-tick octave that together produce the five-dimensional integration domain.
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