DensityParameter
The DensityParameter structure packages the cosmological density parameter Ω = ρ/ρ_c as a positive real value together with its uncertainty. Cosmologists working within Recognition Science cite it when instantiating the observed flatness Ω ≈ 1.0000 ± 0.0002. The definition is a direct record declaration with three fields and no lemmas.
claimA density parameter is a structure consisting of a real number value > 0 (the ratio of energy density to critical density), a real uncertainty, and the proposition that the value is positive.
background
The Cosmology.FlatnessProblem module treats the density parameter as the measure of spatial curvature. Observed value Ω = 1.0000 ± 0.0002 is an unstable fixed point in standard models, yet required by ledger structure in Recognition Science. The module states that Ω = 1 is the only value consistent with ledger structure, critical density follows from J-cost minimization, and φ-constraints lock the universe to flatness.
proof idea
This is a record definition that introduces the three fields value, uncertainty, and value_pos. No lemmas or tactics are applied; the declaration is a direct structure with a positivity constraint.
why it matters in Recognition Science
The structure supplies the type used by omega_observed to record the measured value. It anchors the RS solution to the flatness problem by providing the observed quantity that J-cost minimization and phi-ladder constraints must explain. It sits inside the broader forcing chain that derives D = 3 and the eight-tick octave from T5 J-uniqueness.
scope and limits
- Does not derive the value of Ω from the phi-ladder or J-cost.
- Does not prove that Ω = 1 minimizes curvature cost.
- Does not model the time evolution of |Ω - 1|.
- Does not connect the uncertainty to Recognition Science constants.
formal statement (Lean)
47structure DensityParameter where
48 value : ℝ
49 uncertainty : ℝ
50 value_pos : value > 0
51
52/-- Current observation: Ω = 1.0000 ± 0.0002 -/