Guide to RecidivismFromJCost

Purpose

The module IndisputableMonolith.CriminalJustice.RecidivismFromJCost casts recidivism into the structural framework of Recognition Science. It defines a MODEL where the recidivism ratio r = reoffense_rate / baseline_rate is evaluated through the J-cost function. The pre-intervention equilibrium sits at r = 1 with zero cost. The core HYPOTHESIS is that the minimum detectable intervention effect from effective rehabilitation (the "recognition threshold") corresponds to a one-φ-step departure in this ratio, resulting in a predicted J-cost of φ - 3/2 (approximately 0.118).

Main Declarations

• recidivismCost: The MODEL definition applying the fundamental J-cost to the ratio of reoffense to baseline rates.
• recidivismCost_at_equilibrium: THEOREM proving that an unchanged recidivism rate (r = 1) yields exactly zero cost.
• recidivismCost_nonneg: THEOREM proving that the cost is non-negative for any strictly positive rates.
• recidivismCost_reciprocal: THEOREM demonstrating that the cost is symmetric whether the ratio is evaluated as reoffense / baseline or baseline / reoffense.
• recidivismCost_phi_step: THEOREM establishing that evaluating the J-cost at φ exactly equals φ - 3/2.
• RecidivismCert and cert_inhabited: Structure and THEOREM confirming the formal properties of this model are fully realized without unresolved axioms.

Framework Integration

This module is an application of RS foundational principles to an empirical domain. The foundational theorems forcing the J-cost shape and deriving the constant φ establish the mathematical backbone. This module takes that structure and builds a falsifiable HYPOTHESIS for criminal justice: effective behavioral interventions must overcome the J(φ) threshold to register as a structural departure from baseline.

Outside the Canon

The module establishes the structural mathematics, but it contains no empirical datasets. Testing the HYPOTHESIS against actual large-N randomized controlled trials (such as cognitive-behavioral therapy outcomes from the Bureau of Justice Statistics) to verify if recidivism reductions respect the one-φ-step band is an empirical confirmation step outside the Lean formalization.