cert_inhabited
plain-language theorem explainer
The result establishes that a certificate bundling the J-cost properties for recidivism ratios is inhabited by direct construction of an explicit witness. Criminologists modeling intervention effects inside Recognition Science would cite it to anchor their cost structure. The proof is a one-line term that supplies the witness from the sibling certificate definition.
Claim. The type of certificates for recidivism costs is nonempty, where each certificate consists of proofs that the cost function vanishes when the reoffense-to-baseline ratio equals itself, is nonnegative for positive arguments, is symmetric under interchange of arguments, and satisfies the phi-step identity on the J-cost function.
background
Recognition Science models recidivism via the J-cost applied to the ratio r of reoffense rate to baseline rate. Equilibrium before intervention sits at r = 1 with zero cost; effective rehabilitation drives r below 1 and raises the cost, restoring the recognition floor. The module packages these requirements into a certificate structure whose four fields are equilibrium vanishing, nonnegativity, reciprocity, and the explicit phi-step value of the J-cost function.
proof idea
The proof is a one-line term that directly constructs the inhabitant of the nonempty type by supplying the explicit certificate defined in the sibling declaration.
why it matters
This declaration completes the structural theorem for the recidivism J-cost model by confirming existence of the required certificate. It supports the module prediction that the minimum detectable reduction occurs at a one-phi-step departure with J-cost approximately 0.118. In the framework it instantiates the J-uniqueness and phi fixed-point landmarks for the criminal-justice application; the falsifier is any large-N randomized trial showing recidivism reduction outside the predicted J-cost band.
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