sentencingCost
plain-language theorem explainer
Sentencing cost evaluates the J-cost operator on the ratio of punishment to harm. Jurisprudence researchers formalizing Recognition Science predictions would cite it to ground proportionality claims in the cost function. The definition is realized by direct substitution of the ratio into Jcost.
Claim. For real numbers $p$ (punishment) and $h$ (harm), the sentencing cost is $J(p/h)$, where $J$ is the J-cost function satisfying $J(1)=0$.
background
The module develops sentencing proportionality by treating the punishment-to-harm ratio as an input to the J-cost function drawn from Recognition Science. J-cost quantifies departure from equilibrium for any positive ratio, with the unit property that cost vanishes exactly when the ratio equals one. The local theoretical setting states that the optimal ratio equals the golden ratio phi, matching the multiplicative scaling observed in sentencing guidelines such as base offense levels with adjustments.
proof idea
This is a one-line definition that applies the J-cost function directly to the quotient of its two real arguments.
why it matters
The definition supplies the cost measure required by the SentencingCert structure, which asserts that the ratio exceeds one, adjacent severity ratios exceed two, and cost vanishes when punishment equals harm. It embeds the J-cost into jurisprudence, supporting the framework prediction that the canonical ratio is phi and aligning with the eight-tick octave scaling in Recognition Science.
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