@article {AltChe26SCIII,
      author={Jason M. Altschuler and Sinho Chewi},
      title={Shifted composition {III}: local error framework for {KL} divergence}, 
   JOURNAL = {Found. Comput. Math.},
  FJOURNAL = {Foundations of Computational Mathematics. The Journal of the
              Society for the Foundations of Computational Mathematics},
      YEAR = {2026},
     PAGES = {},
}