Remark: An exact real specification is not a rounded decimal

Equation (eq:pstar), its isolating interval, and uniqueness name one exact real number. The rational midpoint $p_0$ is not asserted to equal $p^{\star }$. A generic optimizer need not have a finite algebraic expression. The explicitly written algebraic pair (eq:finite-pair) is supplied when a finite preparation description with a certified information loss is preferred.