IndisputableMonolith.Sociology.InstitutionalDesignFromJCost
This module instantiates the six-clause J-cost template for sociology, producing the institutional design certificate. Recognition Science researchers cite it when extending the master certification chain into social domains. The module applies the CanonicalJBand structure to establish matched-zero and non-negativity for institutional ratios.
claimInstitutionalDesignCert asserts that the J-cost function on institutional design ratios satisfies $J(1)=0$ and $J(x)\geq 0$ for all $x>0$, where $J(x)=(x+x^{-1})/2-1$.
background
The module imports CanonicalJBand, which supplies the reusable six-clause J-cost-on-ratio template used for all domain certificates in the master chain. Each such certificate must prove matched-zero ($J(1)=0$) and nonnegativity ($J(x)\geq 0$ for $x>0$). In Recognition Science the J-cost satisfies the composition law $J(xy)+J(x/y)=2J(x)J(y)+2J(x)+2J(y)$ and appears in the forcing chain from T5 onward.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the sociology-domain instance of the J-cost band, feeding the institutional design certificate into the Plan v7 domain-cert sequence. It extends the CanonicalJBand template to social structures without downstream citations recorded yet.
scope and limits
- Does not derive empirical predictions for real institutions.
- Does not model dynamic evolution of designs over time.
- Does not incorporate external sociological datasets or observations.