optimizationProblemTypeCount
plain-language theorem explainer
Recognition Science optimization theory counts exactly five problem types via the finite inductive definition. Researchers certifying RS-derived optimization results reference this cardinality. The proof applies the decide tactic to the Fintype instance.
Claim. The set consisting of the linear, nonlinear, combinatorial, convex, and stochastic optimization problem types has cardinality five.
background
The module derives optimization results from Recognition Science by defining an inductive type whose five constructors are the canonical classes linear, nonlinear, combinatorial, convex, and stochastic. This count equals configDim D = 5 and matches the five KKT constraint-active conditions. All optimization reduces to J-cost minimization with global minimum at J = 0.
proof idea
One-line wrapper applying the decide tactic to evaluate the cardinality of the finite inductive type with five constructors.
why it matters
This cardinality populates the five_types component of the downstream optimizationTheoryCert definition that assembles the full certification. It implements the module claim that five types equal configDim D = 5 and connects to J-cost minimization in the RS framework.
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