IndisputableMonolith.Unification.RegistryPredictionsProved
The module establishes that the Ω_Λ formula derived from the Recognition Science registry is well-defined and satisfies the bound Ω_Λ < 11/16. Cosmologists addressing the cosmological constant problem cite these certified inequalities. The argument assembles direct calculations from the imported phi-forcing, gap-weight, and alpha modules into a collection of explicit bounds.
claimThe dark energy density parameter satisfies $\Omega_\Lambda < 11/16$ with the defining formula well-defined in RS-native units.
background
This module operates in the Unification domain and imports the core RS constants (τ₀ = 1 tick), the alpha pipeline, the gap weight w₈ · ln(φ) from the 8-tick projection, and the PhiForcing module. The latter proves that φ is forced by self-similarity in a discrete ledger with J-cost structure. The module's siblings supply the concrete inequalities (omega_lambda_lt_11_16, omega_lambda_positive, phi_6_hierarchy_bounds) that together certify the registry prediction.
proof idea
The module is a collection of explicit inequality theorems. Each applies the phi-ladder and gap-weight definitions imported from PhiForcing and GapWeight to obtain the stated bounds on Ω_Λ; no single master tactic is used beyond direct algebraic reduction and numeric certification.
why it matters in Recognition Science
The module supplies the certified Ω_Λ bounds required by the downstream CosmologicalConstantDerivation module, which addresses registry item C-010 on the determination of Λ. It closes the gap between the phi-forcing foundation and the cosmological constant derivation.
scope and limits
- Does not compute a numerical value for Ω_Λ beyond the 11/16 upper bound.
- Does not resolve the full 10^120 discrepancy with QFT vacuum energy.
- Does not derive the cosmological constant from first principles without the registry.
- Does not address spatial curvature or other cosmological parameters.