IndisputableMonolith.Jurisprudence.SentencingProportionalityFromJCost
The module defines sentencing proportionality ratios derived from J-cost, establishing the canonical punishment-to-harm ratio as the golden ratio φ. Legal theorists applying Recognition Science would reference these definitions for proportional sentencing models. It consists of a series of definitions and simple inequalities built directly on the imported Cost and Constants modules.
claimThe canonical punishment-to-harm ratio equals $φ$, with the proportionality ratio satisfying $r > 1$ and the adjacent severity ratio satisfying $s > 2$, where sentencing cost is proportional to harm via the J-cost function.
background
Recognition Science defines J-cost via the J-uniqueness function $J(x) = (x + x^{-1})/2 - 1$ in the Cost module. Constants supplies the base time quantum $τ_0 = 1$ tick as the RS-native unit. This module applies these to jurisprudence, introducing sentencing costs and certificates that enforce proportionality with ratio $φ$ drawn from the phi-ladder.
proof idea
This is a definition module, no proofs. It introduces proportionalityRatio, sentencingCost, SentencingCert and their basic properties as direct definitions and inequalities on top of the Cost and Constants imports.
why it matters in Recognition Science
The module supplies the proportionality foundation for jurisprudence applications in Recognition Science. It connects J-cost to sentencing via the phi-ladder, feeding into SentencingCert and related certificates. The canonical ratio $φ$ aligns with the self-similar fixed point in the forcing chain.
scope and limits
- Does not compute explicit sentence lengths for cases.
- Does not handle case-specific adjustments beyond the ratio.
- Does not validate against empirical legal data.
- Does not extend to non-J-cost metrics or alternative costs.