IndisputableMonolith.CriminalJustice.RecidivismFromJCost
The module applies the J-cost function to the recidivism ratio defined as reoffense rate over baseline rate. Criminal justice researchers working inside the Recognition Science framework would cite it when modeling reoffense costs. The module supplies the core definition together with elementary properties such as nonnegativity and equilibrium behavior.
claimRecidivism cost is given by $J(r/b)$ where $r$ is the reoffense rate, $b$ the baseline rate, and $J(x)=(x+x^{-1})/2-1$.
background
Recognition Science obtains the J function from the forcing chain T5 and the Recognition Composition Law. The imported Constants module fixes the native time unit at $ au_0=1$ tick. The Cost module supplies the general J-cost construction that this module specializes to the ratio of reoffense to baseline rates.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the recidivism-specific cost object used by the CriminalJustice domain. It feeds downstream properties such as equilibrium values and nonnegativity that appear in the sibling declarations.
scope and limits
- Does not contain empirical rate data.
- Does not model jurisdiction-specific parameters.
- Does not treat costs other than J-cost.