dark_energy_implies_subunit
Dark energy evolution from the ledger forces the density parameter below unity. Researchers in Recognition Science cosmology cite this bound to rule out full dominance by the cosmological constant term. The argument reduces to selecting the upper-bound conjunct in the defining proposition.
claimIf the dark-energy evolution structure from the ledger holds, i.e., $0 < Omega_Lambda land Omega_Lambda < 1$, then $Omega_Lambda < 1$, where $Omega_Lambda = 11/16 - alpha_lock / pi$.
background
The module addresses D-006 on whether dark energy is constant or evolving. It formalizes the RS structural framework for dark-energy equation-of-state behavior, starting from ledger cosmological-constant resolution and extracting bound consequences. dark_energy_evolution_from_ledger is the Prop defined as the conjunction $0 < EarlyUniverse.omega_lambda land EarlyUniverse.omega_lambda < 1$. omega_lambda itself is the RS prediction $11/16 - alphaLock / Real.pi$, with the $11/16$ fraction arising from vacuum modes in the 8-tick cycle.
proof idea
The proof is the term h.2, a direct projection that extracts the second conjunct of the hypothesis dark_energy_evolution_from_ledger.
why it matters in Recognition Science
This result closes one bound consequence extracted from the ledger resolution in the D-006 registry item. It ensures the RS-predicted dark energy density remains strictly below unity, consistent with the eight-tick octave and the phi-ladder structure. No downstream uses are recorded, but the bound supports exclusion of degenerate endpoints in the cosmology module.
scope and limits
- Does not derive the explicit numerical value of omega_lambda.
- Does not address time evolution of the dark-energy equation of state.
- Does not connect to the forcing chain T0-T8 or Recognition Composition Law.
formal statement (Lean)
38theorem dark_energy_implies_subunit (h : dark_energy_evolution_from_ledger) :
39 EarlyUniverse.omega_lambda < 1 :=
proof body
Term-mode proof.
40 h.2
41
42/-- Dark-energy structure excludes the degenerate `Ω_Λ = 0` endpoint. -/