IndisputableMonolith.CrossDomain.JEquilibriumUniversality
The module shows that Nash, market, and health equilibria each reduce to the single algebraic condition Jcost 1 = 0 when specialized to their domain labels. Cross-domain modelers cite it to demonstrate that distinct equilibrium notions share an identical core without extra hypotheses. The structure consists of direct specializations plus equality theorems linking the three cases.
claimNash equilibrium, market equilibrium, and health equilibrium each satisfy $J_ {cost}(1)=0$ under their respective domain labels, with the three statements identical as theorems.
background
The module imports the J-cost definition from the Cost module, where J-cost quantifies deviation from the self-similar fixed point under the Recognition Composition Law. Equilibrium occurs precisely when this cost vanishes at argument 1. The module then labels this condition for three domains and records the resulting propositions together with cross-domain equality statements.
proof idea
This is a definition module with no proofs. The three equilibrium propositions and their linking equalities are introduced as direct specializations of the base Jcost 1 = 0 identity to domain labels.
why it matters in Recognition Science
The module supplies the cross-domain universality layer that connects domain-specific equilibrium statements to the core J-uniqueness result in the forcing chain. It thereby supports unified treatment of equilibria across game theory, economics, and biology under a single functional equation.
scope and limits
- Does not compute numerical values for any concrete equilibrium.
- Does not treat dynamics, stability, or perturbations.
- Does not derive the underlying J-cost function.