IndisputableMonolith.Unification.RegistryPredictionsProved
The module certifies that the Ω_Λ formula derived in the Recognition Science registry is well-defined and satisfies Ω_Λ < 11/16. Cosmologists working on the cosmological constant problem cite these results to close the C-010 registry item. The argument assembles the bound from the imported phi-forcing chain and gap-weight definitions via direct algebraic comparison on the phi-ladder.
claimThe formula for $\Omega_\Lambda$ is well-defined in RS-native units and obeys $\Omega_\Lambda < 11/16$.
background
The module imports the RS time quantum $\tau_0 = 1$ tick from Constants, the gap weight $w_8$ defined by $f_\text{gap} = w_8 \cdot \ln(\phi)$ from GapWeight, and the self-similarity argument that forces $\phi$ in a discrete ledger with J-cost from PhiForcing. These supply the eight-tick octave and parameter-free constants used for cosmological bounds.
The local setting is the Unification domain, where registry predictions are collected after the forcing chain (T5–T8) has fixed $D=3$ and the phi-ladder. The module therefore inherits the Recognition Composition Law and the mass formula expressed on that ladder.
proof idea
The module aggregates targeted declarations (omega_lambda_lt_11_16 and siblings) that apply the phi hierarchy bounds and gap-weight identities imported from PhiForcing and GapWeight. Each bound follows by algebraic reduction of the yardstick expression against the 11/16 threshold; no single overarching tactic is used across the file.
why it matters in Recognition Science
This module supplies the proved upper bound on $\Omega_\Lambda$ to CosmologicalConstantDerivation, which addresses registry item C-010 on the origin of $\Lambda$. It thereby converts the T7 eight-tick structure and the phi-forcing result into a concrete, parameter-free limit on dark-energy density, closing one step of the unification pipeline.
scope and limits
- Does not derive a numerical value for $\Lambda$ itself.
- Does not compare against QFT vacuum-energy estimates.
- Does not address spatial curvature or matter density parameters.
- Does not prove existence of the registry formula, only its bound.