IndisputableMonolith.Cosmology.DarkEnergyEquationOfStateDepth
The module establishes the depth parameter bound δ = 1/φ^5 for the dark energy equation of state in Recognition Science cosmology, using the algebraic identity φ^5 = 5φ + 3. RS cosmologists cite it when bounding deviations from w = -1. The module consists of definitions and elementary properties of the bound together with model counts and positivity checks.
claim$\delta_{\rm bound} = \phi^{-5}$ where $\phi^5 = 5\phi + 3$.
background
The module imports IndisputableMonolith.Constants, whose doc-comment states: "The fundamental RS time quantum (RS-native). τ₀ = 1 tick." It introduces the DarkEnergyModel together with the delta bound, its positivity, and smallness statements. The setting is the cosmology domain of Recognition Science, where φ denotes the self-similar fixed point and the phi-ladder supplies mass and energy scales.
proof idea
This is a definition module, no proofs. It collects the central equality phi5_eq, the definition deltaBound, and the derived statements deltaBound_pos and deltaBound_small.
why it matters in Recognition Science
The module supplies the δ bound that enters the DarkEnergyEoSDepthCert certification and the associated model count. It fills the numerical depth slot required by the RS cosmology chain after the forcing steps T5–T8.
scope and limits
- Does not derive the equation of state from the Recognition Composition Law.
- Does not connect δ to observational Hubble data.
- Does not prove that the bound is the unique value permitted by the phi-ladder.
- Does not address spatial dimension D = 3 or the eight-tick octave.