Structural Social Justice Metric (SSJ): Operationalizing the Distribution of Chaos

This paper introduces the Structural Social Justice Metric (SSJ), a formal framework designed to operationalize equity through the lens of systems engineering and information theory. Departing from purely qualitative or moralistic accounts of social justice, this model defines justice as the optimal alignment between a system's negentropic output and the entropic vulnerability of its participants. By utilizing an N-dimensional vector space, the SSJ metric maps the Demand Vector (V_D)—representing the specific sources of chaos (entropy) affecting an individual or collective—against the Supply Vector (V_S) of systemic stability. Through the application of Cosine Similarity, we demonstrate that structural injustice is not merely a lack of resources, but a vector misalignment where systemic "order" is generated in dimensions irrelevant to the actual vulnerabilities of the population. The paper provides a rigorous mathematical basis for measuring "negentropic justice," offering a diagnostic tool for identifying systemic failure modes and ensuring that the distribution of order effectively neutralizes the distribution of chaos.