IndisputableMonolith.Sociology.InstitutionalDesignFromJCost
This module certifies institutional designs in sociology by applying the J-cost framework to social structure ratios. Researchers extending Recognition Science to institutional and social systems would cite it within the domain certification series. The module follows the reusable six-clause J-cost template from CanonicalJBand to establish matched-zero and nonnegativity.
claimThe module supplies $InstitutionalDesignCert$ asserting that institutional designs satisfy $J(1)=0$ and $J(x)≥0$ for all $x>0$, where $J$ is the canonical cost functional on positive ratios.
background
Recognition Science applies the J-functional, defined by J-uniqueness as $J(x)=(x+x^{-1})/2-1$, across domains via the Recognition Composition Law. This sociology module imports the CanonicalJBand template, which supplies the six-clause structure proving matched-zero at unity and nonnegativity for positive arguments. The local setting extends the forcing chain landmarks (T5 J-uniqueness, T6 phi fixed point) to institutional ratios without new derivations.
proof idea
This is a definition module, no proofs. It declares the certification objects InstitutionalDesignCert and institutionalDesignCert by direct instantiation of the imported CanonicalJBand template for the sociology domain.
why it matters in Recognition Science
The module contributes to the master cert chain for B-tier whole-science openings as one of the Plan v7 domain certs. It applies the J-cost template to institutional design, linking upstream J-uniqueness results to downstream social applications within the unified framework.