dark_energy_evolution_structure
The theorem establishes that the dark energy evolution structure holds because the cosmological constant density parameter satisfies 0 < Ω_Λ < 1. Cosmologists using the Recognition Science ledger framework would cite this to anchor the baseline bounds on dark energy density. The proof is a direct one-line term application of the omega_lambda_bounded theorem.
claimThe dark-energy evolution structure from the ledger holds: $0 < Ω_Λ < 1$.
background
The module addresses D-006 on whether dark energy is constant or evolving, formalizing the RS structural framework for equation-of-state behavior. The definition dark_energy_evolution_from_ledger is the proposition 0 < EarlyUniverse.omega_lambda ∧ EarlyUniverse.omega_lambda < 1, serving as a structural placeholder for effective evolution. The sibling theorem omega_lambda_bounded proves the identical inequality via EarlyUniverse.cosmological_constant_resolution.
proof idea
The proof is a one-line term wrapper that applies the omega_lambda_bounded theorem to discharge the dark_energy_evolution_from_ledger goal.
why it matters in Recognition Science
This fills the structural placeholder in the D-006 registry item by confirming baseline positivity and subunitarity of Ω_Λ from ledger cosmological-constant resolution. It sits within the broader RS cosmology chain that draws on phi-forcing and spectral emergence structures, though no downstream theorems currently reference it.
scope and limits
- Does not derive explicit time dependence of the dark-energy equation of state.
- Does not supply numerical values for Ω_Λ beyond the open interval (0,1).
- Does not address coupling to other cosmological parameters or nucleosynthesis tiers.
formal statement (Lean)
30theorem dark_energy_evolution_structure : dark_energy_evolution_from_ledger := omega_lambda_bounded
proof body
Term-mode proof.
31
32/-- Dark-energy evolution structure enforces positivity of `Ω_Λ`. -/