einsteinKappa
plain-language theorem explainer
The definition sets the Einstein coupling constant to κ = 8φ^5/π in Recognition Science units where c = 1. Researchers deriving the Einstein field equations from the J-cost gradient would cite this value for the source term coefficient. It is a direct noncomputable definition with no proof steps, relying only on the golden ratio fixed point and pi.
Claim. The Einstein coupling constant is defined by $κ = 8φ^5 / π$.
background
In the General Relativity from RS module the Einstein equations appear as G_μν + Λ g_μν = κ T_μν, with G_μν obtained from the gradient of the J-cost function. The module identifies κ with 8G/c^4 and states that five canonical GR effects (lensing, time dilation, perihelion precession, frame dragging, gravitational waves) correspond to configDim D = 5. The golden ratio φ enters as the self-similar fixed point forced by the T5–T6 steps of the unified forcing chain.
proof idea
One-line definition that directly assigns the expression 8 * phi ^ 5 / Real.pi to the constant.
why it matters
This supplies the explicit coupling for the GeneralRelativityCert structure, whose kappa_positive field records 0 < einsteinKappa, and for the separate positivity theorem einsteinKappa_pos. It completes the A4 Strong Field step that equates κ to 8G/c^4 while linking to the T8 spatial dimension and the Recognition Composition Law that fixes φ. No open scaffolding remains for this constant itself.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.