lambdaRS
Definition sets Λ_RS to 8φ^5/45 in native units. Cosmologists working in the Recognition Science framework cite this expression when matching the predicted vacuum energy density against the observed Ω_Λ band. The definition is a direct noncomputable assignment of the real number expression.
claim$Λ_{RS} := 8 φ^5 / 45$
background
The module treats the cosmological constant in the BIT kernel band for S3 cosmology. The golden ratio φ is the self-similar fixed point forced by the T6 step of the unified forcing chain, and the identity φ^5 = 5φ + 3 is the Fibonacci relation used to evaluate powers. The definition is imported from CosmologicalConstantFromRS to support formal band certification.
proof idea
Direct definition that assigns the real number 8 * phi ^ 5 / 45. No lemmas are invoked inside the body; the supporting identity φ^5 = 5φ + 3 is recorded only in the documentation comment for downstream use.
why it matters in Recognition Science
The definition supplies the explicit RS form of Λ_RS that feeds lambdaRS_band (proving the interval (1.88, 2.03)) and the certificate structures OmegaLambdaBandCert and CosmologicalConstantCert. It realizes the RS structural prediction for the cosmological constant inside the phi-ladder and eight-tick octave framework.
scope and limits
- Does not derive the prefactor 8/45 from the Recognition Composition Law.
- Does not prove the numerical band membership without the phi^5 identity.
- Does not perform conversion to SI units or direct comparison with Planck data.
formal statement (Lean)
24noncomputable def lambdaRS : ℝ := 8 * phi ^ 5 / 45
proof body
Definition body.
25
26/-- φ⁵ = 5φ + 3. -/