IndisputableMonolith.Cosmology.DarkEnergyEquationOfStateDepth
The Cosmology.DarkEnergyEquationOfStateDepth module sets the δ bound to 1/φ⁵ for dark energy equation of state depth, using the identity φ⁵ = 5φ + 3. Cosmologists working in RS-native units cite it when constraining the equation of state parameter via the phi ladder. The module consists of definitions and supporting lemmas that import the time quantum from Constants.
claim$\delta_{\rm bound} = \phi^{-5}$ where $\phi^5 = 5\phi + 3$.
background
Recognition Science derives all physics from the J-uniqueness forcing chain ending in T8 with D = 3. This module sits in the cosmology domain and imports Constants, whose sole documented content is the definition τ₀ = 1 tick as the RS-native time quantum. It introduces DarkEnergyModel together with deltaBound, phi5_eq, and the positivity and smallness lemmas for the bound.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the δ bound that supports DarkEnergyEoSDepthCert and the sibling declarations inside the same file. It supplies the concrete scaling needed to apply the phi-ladder mass formula and Recognition Composition Law to dark energy parameters.
scope and limits
- Does not derive the numerical value of the dark energy density parameter.
- Does not compute the equation of state parameter w itself.
- Does not connect the bound to observational constraints or data.
- Does not prove the underlying phi identities or the forcing chain steps.