Degenerate
plain-language theorem explainer
Degeneracy of a configuration c holds when its possibility set contains at least two distinct elements sharing the same minimal J-cost. Recognition Science modal analyses cite this definition to locate the source of contingency. The definition is supplied directly as an existential predicate over the possibility set with no auxiliary lemmas.
Claim. A configuration $c$ is degenerate if there exist distinct $y,z$ in the possibility set of $c$ such that the J-cost of $y$ equals the J-cost of $z$ and this common value is minimal over the entire possibility set of $c$.
background
The J-cost function satisfies the Recognition Composition Law $J(xy)+J(x/y)=2J(x)J(y)+2J(x)+2J(y)$ and is given explicitly by $J(x)=(x+x^{-1})/2-1$. The possibility set of $c$ collects all configurations reachable from $c$ under the forcing chain. Config is the structure carrying physical parameters such as upsilonStar and the epsilons from the ILG gravity model.
proof idea
The definition is given explicitly by the existential quantification requiring two distinct minimal-J-cost elements inside the possibility set. No lemmas are invoked; the predicate itself constitutes the complete definition.
why it matters
Degenerate supplies the key predicate used by Contingent in the same module to mark properties that could have been otherwise. It realizes the origin of contingency in the Recognition Science framework by identifying equal J-cost minima on the phi-ladder, connecting directly to the self-similar fixed point and eight-tick octave in the T5-T8 forcing chain.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.