Plain English: recidivismCost_reciprocal states that for any two positive real numbers (reoffense rate and baseline rate), the recidivism cost of their ratio equals the cost of the inverted ratio.
Relevance in Recognition Science: The result applies the reciprocal symmetry of the underlying J-cost to recidivism ratios. This symmetry is a structural feature of the recognition ledger: deviations above or below equilibrium incur identical recognition costs, restoring the cost floor symmetrically.
Reading the formal statement: The declaration takes two positive reals reoffense and baseline (witnessed by hr and hb), defines recidivismCost as Jcost (reoffense / baseline), and concludes equality after invoking the reciprocal property of Jcost and simplifying the division.
Visible dependencies and certificates: The proof unfolds recidivismCost and is bundled into the RecidivismCert structure (field cost_reciprocal) whose inhabitant is cert. The module also records the equilibrium and non-negativity properties as sibling theorems.
What it does not prove: The theorem establishes only the symmetry property; it supplies no numerical recidivism values, no empirical falsifiers, and no derivation of the J-cost function itself.