lambdaRS
plain-language theorem explainer
The Recognition Science prediction for the cosmological constant is Λ_RS = 8 φ^5 / 45 in native units. Cosmologists matching RS outputs to Planck data cite this for the dark energy density ratio Ω_Λ. The declaration is a direct noncomputable assignment using the golden ratio and its fifth power.
Claim. The Recognition Science cosmological constant is defined by $Λ_{RS} = 8 φ^5 / 45$, where $φ$ is the golden ratio satisfying $φ^2 = φ + 1$.
background
The golden ratio φ arises as the self-similar fixed point forced by J-uniqueness (T5) in the forcing chain, with powers obeying Fibonacci relations such as φ^5 = 5φ + 3. This module imports the core expression from OmegaLambdaBITKernelBand and supplies the RS-native form for Λ_RS, which evaluates to a value in (1.88, 2.03). The local setting is the derivation of the cosmological constant from RS, yielding the dimensionless ratio Ω_Λ = Λ_RS / (3 H_0^2) ≈ 0.685.
proof idea
This is a one-line definition that directly assigns the expression 8 * phi ^ 5 / 45. Downstream theorems unfold the definition and substitute the Fibonacci identity phi^5 = 5 * phi + 3 together with bounds on phi to certify the numerical interval and positivity.
why it matters
This definition supplies the core RS prediction for Λ that feeds into CosmologicalConstantCert, lambdaRS_band, and lambdaRS_pos. It realizes the T8 step fixing D = 3 and produces a numerical anchor in the alpha band that matches Planck Ω_Λ within 0.5 percent. The parent theorems in OmegaLambdaBITKernelBand and the present module close the loop from the Recognition Composition Law to observable cosmology.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.