IndisputableMonolith.Physics.FineStructureConstantFromRS
The module derives the fine structure constant from Recognition Science by defining rung factors on the phi-ladder and incorporating the gauge loop area. It introduces alphaRung and rsAlphaFactor to reach FineStructureCert. The structure consists of algebraic definitions and bound checks that rest on the imported RS time quantum τ₀ = 1 tick.
claimThe RS inverse fine structure constant satisfies $α^{-1} = 44π · rsAlphaFactor(φ, τ₀)$ where $44π$ is the gauge loop area denominator.
background
The module operates in the Physics domain and imports the fundamental RS time quantum τ₀ = 1 tick from IndisputableMonolith.Constants. It extends the Recognition Science framework by placing the fine structure constant on the phi-ladder via rung-specific factors. The setting uses the J-cost function and self-similar fixed point from the upstream forcing chain.
proof idea
This is a definition module, no proofs. It consists of successive definitions for alphaRung, rsAlphaFactor, and related positivity lemmas that culminate in the FineStructureCert object.
why it matters in Recognition Science
The module supplies the fine structure constant derivation that supports the Recognition Science prediction of α^{-1} inside (137.030, 137.039). It feeds the constant-certification step that closes the electromagnetic sector from T5 J-uniqueness and T6 phi fixed point.
scope and limits
- Does not derive 44π from the forcing chain.
- Does not compute numerical α beyond the algebraic expression.
- Does not address renormalization or higher-order corrections.
- Does not connect to other gauge groups or particle spectra.