dark_energy_w
plain-language theorem explainer
Recognition Science sets the dark energy equation of state parameter to negative one from the J-cost vacuum ground state. Cosmologists using the phi-ladder to model late-time acceleration would cite the result when deriving the scale-factor evolution. The proof reduces immediately to reflexivity on the module definition of the equation of state.
Claim. The dark energy equation of state satisfies $w = -1$.
background
The Cosmological Constant module derives Lambda from the J-cost ground state of the vacuum ledger. The equation of state is introduced as the constant -1, which encodes pressure equal to negative energy density and therefore drives accelerated expansion. This construction rests on the Recognition Composition Law and the T5-T8 forcing chain that fixes phi and three spatial dimensions.
proof idea
The proof is a one-line wrapper that applies reflexivity to the definition of the equation of state, which is set to -1 by construction.
why it matters
The result anchors the dark-energy component inside the RS resolution of the cosmological constant problem. It supplies the w = -1 behavior required for the accelerated-expansion phase on the phi-ladder and supports the claim that the coincidence problem is resolved by a specific rung transition. The module doc flags this as part of the major paper on the cosmological constant problem.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.