cosmological_constant_resolution
plain-language theorem explainer
Recognition Science derives the dark energy density parameter to satisfy 0 < omega_lambda < 1. Cosmologists resolving the cosmological constant problem cite it to show the parameter is positive yet subunitary with no fine-tuning. The proof is a one-line term that pairs the positivity and upper-bound results from sibling declarations in the same module.
Claim. $0 < Ω_Λ < 1$, where $Ω_Λ$ is the fraction of vacuum modes in the ledger given by $11/16 - α/π$ in RS-native units.
background
The EarlyUniverse module formalizes RS derivations for early-universe conditions and the dark sector, covering EU-001 (initial state), D-002 (dark energy), and D-003 (cosmological constant size). omega_lambda is defined via ledger mode counting rather than QFT vacuum energy, so the 10^120 discrepancy is reclassified as a misidentification. The fundamental tick τ₀ = 1 supplies the discrete time quantum, and consistency predicates from complexity modules ensure ledger states remain compatible with the φ-ladder.
proof idea
The proof is the term ⟨omega_lambda_pos, omega_lambda_lt_one⟩. It is a one-line wrapper that directly combines the positivity theorem and the strict upper-bound theorem already established for omega_lambda in the same module.
why it matters
This theorem supplies the D-003 resolution: the cosmological constant is a ledger fraction, not a tunable vacuum energy, eliminating fine-tuning. It is invoked by the omega_lambda_bounded theorem in DarkEnergyEvolutionStructure, which supplies the structural placeholder for effective equation-of-state evolution. The result sits inside the T0-T8 forcing chain and the eight-tick octave, confirming D = 3 and the phi-ladder mass formula remain consistent with observed dark-energy density.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.