optimizationClassesCert
This definition supplies a concrete certificate that the type of optimization classes has cardinality exactly five when the configuration dimension is five. Researchers mapping physical dimension to optimization complexity in Recognition Science would cite it to fix the discrete count before further constructions. The proof is a one-line abbreviation that instantiates the structure field directly from the decidable cardinality theorem.
claimLet $O$ be the finite type of optimization classes. The certificate is the structure whose field asserts that the cardinality of $O$ equals five.
background
The module treats optimization problem classes as derived from configuration dimension, identifying five canonical classes when that dimension equals five: linear, convex nonlinear, integer, stochastic, and dynamic programming. The structure OptimizationClassesCert is defined with a single field requiring Fintype.card OptimizationClass = 5. This rests on the upstream theorem optimizationClass_count, which proves the same equality by direct decision.
proof idea
The definition is a one-line wrapper that assigns the field five_classes to the result of the theorem optimizationClass_count.
why it matters in Recognition Science
This definition certifies the count of five optimization classes for configuration dimension five, anchoring the discrete taxonomy used in the Recognition Science framework. It completes the local setup in the module before any downstream use of the cardinality, consistent with the forcing chain that derives dimension D=3 and related discrete counts. No immediate parent theorems are listed among the used-by edges.
scope and limits
- Does not list the five explicit optimization classes.
- Does not prove that the classification into five classes is unique or exhaustive.
- Does not relate the count to physical constants, the phi-ladder, or the J-cost function.
- Does not address higher or lower configuration dimensions.
formal statement (Lean)
28def optimizationClassesCert : OptimizationClassesCert where
29 five_classes := optimizationClass_count
proof body
Definition body.
30
31end IndisputableMonolith.Mathematics.OptimizationProblemClassesFromConfigDim