DarkEnergyModel
plain-language theorem explainer
This inductive definition enumerates five dark energy models for Recognition Science cosmology. Workers classifying equation-of-state deviations from w = -1 in the BIT framework cite it when counting models or certifying baseline behavior. The declaration is a direct inductive type that derives decidable equality and finite cardinality with no further computation.
Claim. The dark energy models comprise the cosmological constant, quintessence, phantom energy, quintom, and holographic dark energy.
background
The module treats the dark energy equation of state in S3 cosmology depth. Recognition Science predicts that the BIT correction deviates from w = -1 by an amount bounded by the J-cost J(φ) ≈ 0.118, so that w_0 lies in (-1 - J(φ), -1). The upstream cosmologicalConstant definition identifies the tension energy density with 3 H_0² in natural units. A parallel inductive enumeration in the depth module uses a different labeling (lambdaCDM, wCDM, etc.) while preserving the same cardinality.
proof idea
The declaration is a direct inductive type with five constructors. It derives DecidableEq, Repr, BEq, and Fintype instances by standard automation; no lemmas are applied beyond the inductive definition itself.
why it matters
The enumeration feeds the certification structure DarkEnergyEoSCert, which records exactly five models together with the baseline wLambda = -1. It supplies the model list required by the depth-module certificate that adds the relation phi^5 = 5 phi + 3 and the bound deltaBound < 0.1. The definition therefore closes the step from the forcing-chain landmarks (T5 J-uniqueness, T6 phi fixed point) to the observable prediction |w_0 + 1| ≤ J(φ) in RS-native units.
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