IndisputableMonolith.CriminalJustice.RecidivismFromJCost
This module defines the J-cost applied to the recidivism ratio, reoffense_rate divided by baseline_rate. Recognition Science researchers extending the framework to social systems would cite these definitions when quantifying costs in criminal justice models. The module consists of direct definitions and elementary properties such as non-negativity and equilibrium behavior.
claimDefine recidivismCost as $J(r/b)$ where $r$ is the reoffense rate, $b$ the baseline rate, and $J(x) = (x + x^{-1})/2 - 1$. Additional declarations establish non-negativity, reciprocal symmetry, and phi-step increments for this quantity.
background
The module imports the RS time quantum τ₀ = 1 tick from Constants and the J-cost operator from the Cost module. J-cost measures deviation from unity via the functional equation J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y). RecidivismCost applies this operator to the ratio of reoffense to baseline rates, with sibling declarations handling equilibrium cases and phi-ladder steps.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module populates the CriminalJustice domain by translating J-cost into recidivism metrics, supporting extensions of the forcing chain (T5 J-uniqueness through T8 D=3) to social observables. It supplies the basic objects used by any downstream theorem that incorporates equilibrium or phi-step properties in this domain.
scope and limits
- Does not incorporate empirical criminal justice statistics.
- Does not model multi-factor interactions beyond the single ratio.
- Does not derive equilibrium existence from first principles.
- Does not address time evolution or dynamic trajectories.