= Finite-cost optimal transport converse
An optimal <transport plan> of finite cost for a finite continuous cost <function> is <c-cyclically monotone>. A strict violation at finitely many support points persists in small product neighborhoods; subtracting small normalized pieces and inserting cyclically re-paired product <measures> preserves both marginals and strictly improves the finite cost. The finite-value hypothesis matters: if every competitor has infinite cost, a nonmonotone plan may still be an extended-value minimizer.
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