IndisputableMonolith.Cosmology.DarkEnergyEquationOfStateDepth
This module defines the dark energy equation of state depth bound in Recognition Science cosmology as δ = 1/φ^5. It supplies the model, the explicit bound, positivity and smallness lemmas, and the certification object. Cosmologists using RS-native units cite it for the equation-of-state deviation controlled by the phi-ladder. The module is built from a short chain of definitions and elementary lemmas that apply the identity φ^5 = 5φ + 3.
claimThe dark energy model satisfies a depth bound $|w + 1| \leq \delta$ with $\delta = \phi^{-5}$ where $\phi^5 = 5\phi + 3$.
background
Recognition Science places cosmology on the same J-cost and phi-ladder used for particle masses and constants. The imported Constants module fixes the fundamental time quantum as τ₀ = 1 tick. The present module introduces DarkEnergyModel together with the explicit δ bound, the auxiliary equation phi5_eq, and the certified object DarkEnergyEoSDepthCert. All constructions remain inside the eight-tick octave and D = 3 spatial dimensions fixed by the upstream forcing chain.
proof idea
This is a definition module, no proofs. It declares the model, states the bound δ = 1/φ^5 via phi5_eq, then records the two elementary lemmas deltaBound_pos and deltaBound_small that establish positivity and the numerical smallness of the bound.
why it matters in Recognition Science
The module supplies the δ bound required for any RS-native treatment of the dark energy equation of state. It directly implements the doc-comment claim that δ bound = 1/φ^5 using φ^5 = 5φ + 3, thereby connecting the cosmological sector to the same phi-ladder that yields G = φ^5 / π and the alpha band. No downstream uses are recorded yet.
scope and limits
- Does not derive a numerical value for the cosmological constant.
- Does not incorporate observational constraints on w.
- Does not address the coincidence problem or fine-tuning issues.
- Does not extend the bound to modified gravity or extra dimensions.