Open. The site labels the problem OPEN (page last edited 1 February 2026). Neither the general fixed-$f$ power-gain question nor the stronger degree-scale question is resolved for every irreducible polynomial: the general subpower theorem and the special-family power bounds below fall short of both. Bhalla's conditional note of 2026-04-16 gives the degree-scale bound only under an unproved prime-values hypothesis. The special-family claims answer the first question for particular polynomials: accepted for $t^3+2$ (Heath-Brown, Irving), for even Klein-group quartics (de la Bretèche), for cyclic and dihedral quartics (Dartyge--Maynard) and for $t^2+1$ (Pascadi); pending for monic cubics (Ermoshin), for $at^2+h$ (Grimmelt--Merikoski) and for $t^2+1$ (Carella). None covers every irreducible polynomial, so both questions stay open.