Transient objective convergence of spectrally weighted gradient descent

AI-assisted, unrefereed candidate on ordinary-objective transient convergence for spectrally weighted single-gradient-direction methods. With smallest eigenvalue one, positive nondecreasing unbounded weights, fixed horizon K and relaxation 0<omega<=1, the worst-case ratio has leading deficit 2 omega K/kappa. Power weights admit sublogarithmic sharpness and a logarithmic interval of simultaneous failures of a strong two-step interpretation. The weaker interpretation remains true; no proved source theorem is refuted.