D9: Golden extremality (skeleton)

We provide a minimal optimization-style statement: given an admissible class and an objective, the golden operator is extremal (e.g. optimal) within that class. The precise objective and admissibility are deferred to later phases; here we only fix the API.

structure Frourio.ExtremalityContext : Type

Optimization context for 2-point Frourio operators.

• Adm : FrourioOperator 2 → Prop
• Obj : FrourioOperator 2 → ℝ

def Frourio.GoldenExtremality (C : ExtremalityContext) : Prop

Golden extremality statement: GoldenFrourioOperator minimizes the objective over the admissible class.

Equations

• Frourio.GoldenExtremality C = (C.Adm Frourio.GoldenFrourioOperator ∧ ∀ (op : Frourio.FrourioOperator 2), C.Adm op → C.Obj Frourio.GoldenFrourioOperator ≤ C.Obj op)