Module Guide: IndisputableMonolith.CriminalJustice.RecidivismFromJCost

Purpose

This module formalizes recidivism modeling as an instance of J-cost applied to the ratio of reoffense rate to baseline rate. Pre-intervention equilibrium occurs at ratio = 1 (zero cost). Rehabilitation that reduces the ratio below 1 increases J-cost, restoring the recognition-cost floor. The module supplies a structural certificate and identifies a one-phi-step falsifier.

Main Declarations

• recidivismCost defines the cost as Jcost(reoffense / baseline).
• recidivismCost_at_equilibrium proves the cost vanishes exactly when reoffense equals baseline (for nonzero ratio).
• recidivismCost_nonneg establishes non-negativity under positive inputs.
• recidivismCost_reciprocal shows symmetry under ratio inversion.
• recidivismCost_phi_step evaluates the cost at the golden-ratio step.
• RecidivismCert bundles the four properties into a single certificate.
• cert constructs the concrete certificate instance.
• cert_inhabited proves the certificate type is inhabited.

Fit into Recognition Science

The module applies the J-cost structure (imported from Cost) to a domain ratio, mirroring the cost-to-recognition bridge. Equilibrium at ratio 1 recovers the zero-cost self-recognition case; the phi-step supplies a concrete, falsifiable departure. It sits downstream of the cost foundation and supplies a domain-specific certificate, consistent with the structural theorems already established for J.

What Remains Outside This Module

Empirical falsification via randomized controlled trials is stated only as a named falsifier, not formalized. No integration with the full forcing-chain theorems or ledger structures is carried out inside the module.