optimal_solution
plain-language theorem explainer
The result establishes that the recognition cost function attains zero at unit scale. Operations researchers applying Recognition Science to optimization problems cite it to anchor the minimum-cost point. The proof is a direct one-line reduction to the unit lemma for the cost function.
Claim. $J(1) = 0$, where $J(x) = (x-1)^2/(2x)$ is the recognition cost.
background
In the Recognition Science treatment of operations research, optimization is defined as minimization of J-cost over the decision space, with the global minimum occurring at J = 0. The J-cost is the squared-ratio function J(x) = (x-1)^2/(2x) that quantifies recognition cost for a scale factor x. The module maps the five canonical OR methods (linear programming, dynamic programming, game theory, queuing theory, simulation) onto a five-dimensional configuration space whose optimum is the zero-cost point.
proof idea
The proof is a one-line wrapper that applies the lemma Jcost_unit0, which itself follows by direct simplification of the J-cost definition.
why it matters
This supplies the optimal-solution field inside the operationsResearchCert definition that certifies the five-method correspondence. It instantiates the RS claim that the minimum recognition cost is zero, consistent with the fixed-point structure of the forcing chain. The result closes the abstract optimization step before concrete method encodings are introduced.
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