IndisputableMonolith.Unification.RegistryPredictionsProved
RegistryPredictionsProved collects Lean theorems that certify the dark energy density formula as well-defined and bounded above by 11/16 using the Recognition Science framework. Cosmologists deriving Λ from first principles without adjustable parameters would cite these results to anchor the C-010 registry item. The module structure consists of direct algebraic applications of the imported phi-forcing lemmas and gap-weight definitions to produce the listed bounds.
claimThe dark energy density parameter satisfies the well-defined formula with bound $0 < Ω_Λ ≤ 11/16$ in RS-native units derived from the phi-ladder and eight-tick structure.
background
The module sits in the unification domain and imports the RS time quantum τ₀ = 1 tick, the gap weight w₈ with closed form f_gap = w₈ · ln(φ) from GapWeight, and the proof that φ is forced by self-similarity on a discrete ledger equipped with J-cost from PhiForcing. J-cost obeys the Recognition Composition Law J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y) that generates the T5–T8 forcing chain. These imports supply the parameter-free constants and the phi-ladder needed to evaluate the Ω_Λ expression.
proof idea
The module is a collection of sibling theorems; each applies direct substitution of the forced φ value and the gap term into the Ω_Λ formula followed by algebraic simplification. Results such as omega_lambda_lt_11_16 follow from the phi-power hierarchy bounds already established upstream. No custom tactics beyond ring normalization and inequality chaining are required.
why it matters in Recognition Science
These proved bounds feed the CosmologicalConstantDerivation module that addresses registry item C-010 on the origin of Λ. The module thereby converts the abstract T5–T8 forcing chain and the eight-tick octave into a concrete upper limit on dark energy density, closing one link in the parameter-free derivation of the cosmological constant.
scope and limits
- Does not compute a specific numerical value for Ω_Λ inside the bound.
- Does not derive other cosmological parameters such as Ω_m or the Hubble constant.
- Does not relax the no-free-parameters assumption inherited from PhiForcing.