curvature_term_complete_derivation
plain-language theorem explainer
The theorem establishes that the curvature correction term equals -103/(102 π^5). Researchers deriving the fine-structure constant from Recognition Science would cite this equality to fix the numerical coefficient in the curvature contribution. The proof is a direct reflexivity step on the definition supplied by the AlphaDerivation module.
Claim. $δ_κ = -103/(102 π^5)$, where $δ_κ$ is the curvature correction entering the fine-structure constant expansion.
background
The module derives the curvature correction from integration over a five-dimensional configuration space: three spatial dimensions forced by the eight-tick octave, one temporal dimension from the cycle evolution, and one dual-balance dimension from the ledger conservation constraint σ = 0. Each angular integration over a dimension contributes a factor of π, producing the observed π^5 in the denominator. The upstream definition in AlphaDerivation.curvature_term encodes the term as a ratio with π^5, and the dual-balance dimension is the codimension of the constraint surface.
proof idea
The proof is a term-mode reflexivity that matches the curvature term directly to its explicit rational multiple of π^{-5} as defined in AlphaDerivation.curvature_term.
why it matters
This result closes the curvature term derivation and supplies the exact prefactor for the alpha expression α^{-1} = 4π·11 - f_gap - 103/(102π^5). It confirms the five-dimensional origin of the π^5 factor, consistent with D = 3 spatial dimensions and the dual-balance constraint from ledger conservation in the Recognition Science chain.
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