seam_ratio
plain-language theorem explainer
The seam ratio is the constant 103/102 that supplies the numerator for the curvature correction in the fine structure constant. Researchers deriving α^{-1} from the five-dimensional ledger phase space cite this value when accounting for the topological mismatch between spherical and cubic boundaries. It is introduced by direct assignment with no lemmas or reduction steps.
Claim. The seam ratio is the real number $103/102$, defined as the ratio of Euler closure (103) to the product of six faces and seventeen wallpaper groups (102), and serving as the prefactor for curvature stress integrated over five-dimensional configuration space.
background
The module derives the curvature correction δ_κ = -103/(102 π^5) in the fine structure constant expression α^{-1} = 4π·11 - f_gap - 103/(102 π^5). The five-dimensional configuration space consists of three spatial dimensions (forced by T8), one temporal dimension from the eight-tick cycle, and one dual-balance dimension from conservation. Each angular integration over a dimension contributes a factor of π, producing the π^5 denominator. The seam ratio quantifies the mismatch between smooth spherical and discrete cubic geometries, with 102 arising as 6 faces × 17 wallpaper groups and 103 as the Euler closure increment.
proof idea
This declaration is a direct definition that assigns the rational value 103/102. No lemmas are invoked and the body contains only the constant expression.
why it matters
The definition supplies the numerical coefficient required by the downstream theorem seam_ratio_from_topology, which rewrites the ratio using seam_numerator_at_D3 and seam_denominator_at_D3 at three spatial dimensions. It completes the topological accounting step in the curvature space derivation, linking the 5D phase space (three spatial plus temporal plus balance) to the correction term that appears in the Recognition Science expression for α^{-1}.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.