omega_lambda_bounded
plain-language theorem explainer
The RS dark energy density parameter lies strictly between zero and one. Researchers deriving the structural evolution of dark energy within the Recognition Science ledger framework cite this bound as the starting point for equation-of-state analysis. The proof consists of a direct one-line application of the cosmological constant resolution theorem from the EarlyUniverse module.
Claim. $0 < Ω_Λ < 1$ where $Ω_Λ := 11/16 - α_{lock}/π$ denotes the Recognition Science dark energy density parameter.
background
Module D-006 formalizes the RS structural framework for dark-energy equation-of-state behavior and begins with ledger-based bounds on Ω_Λ. The definition omega_lambda sets Ω_Λ = 11/16 − α_lock / π, where the leading term is the fraction of vacuum modes in the 8-tick cycle and the correction accounts for matter-coupled modes. The upstream cosmological_constant_resolution theorem states: D-003 Resolution: The cosmological constant is NOT the vacuum energy of QFT. It is the fraction of vacuum modes in the ledger. The actual Ω_Λ comes from ledger mode counting: 11/16 − α/π.
proof idea
The proof is a one-line wrapper that applies the cosmological_constant_resolution theorem from EarlyUniverse.
why it matters
This bound feeds directly into the dark_energy_evolution_structure theorem, which sets dark_energy_evolution_from_ledger equal to the present result. It closes the initial step of D-006 by importing the ledger resolution of the cosmological constant (D-003). Within the framework it anchors the positivity of dark energy density to the 8-tick octave and ledger mode counting.
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