dark_energy_implies_positive
plain-language theorem explainer
The theorem shows that the ledger-derived structural assumption on dark-energy evolution forces the dark-energy density parameter Ω_Λ to be positive. Cosmologists working within Recognition Science would cite it when establishing the existence of dark energy from the eight-tick cycle and ledger resolution. The proof is a one-line term projection of the first conjunct from the defining conjunction of the hypothesis.
Claim. If the dark-energy evolution structure from the ledger holds, i.e., $0 < Ω_Λ ∧ Ω_Λ < 1$, then $Ω_Λ > 0$.
background
In the Recognition Science framework the dark energy density parameter is defined as Ω_Λ = 11/16 − α_lock / π, where the fraction 11/16 arises from the proportion of ledger modes in the vacuum state within the eight-tick cycle and the correction −α/π accounts for matter-coupled perturbations. Module D-006 formalizes the question of whether dark energy is constant or evolving by extracting bounds on this parameter from the ledger cosmological-constant resolution.
proof idea
The proof is a one-line term that projects the first conjunct from the conjunction defining dark_energy_evolution_from_ledger.
why it matters
This result supplies the positivity half of the dark-energy bounds required by D-006, confirming that the RS prediction for Ω_Λ is strictly positive and therefore that dark energy exists. It rests on the eight-tick octave structure that produces the 11/16 vacuum fraction and on the ledger resolution that supplies the α/π correction. No downstream uses are recorded, but sibling declarations extend the same hypothesis to subunit, non-zero, and non-unit bounds.
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