An amaranth was a device created by the Time Lords to find unstable or discontinuous elements of the universe and to rebuild them along more rational lines, (PROSE: Christmas on a Rational Planet) along the lines of the established laws of the Spiral Politic. (PROSE: Against Nature)
The first amaranth was created by maintenance engineers on Gallifrey to help counteract the warping effects caused by the black hole on the spacetime continuum. It contained an emergency function to transport its user to a more stable part of space.
The Doctor once possessed an amaranth. The Seventh Doctor gave it to Daniel Tremayne while fighting the Carnival Queen; Tremayne left it in Woodwicke before heading to France. (PROSE: Christmas on a Rational Planet) In the 26th century, Randolph Bane recovered the "Egg" from the Grey Museum of the Shadow Directory. Bane intended to use it to modify the physical laws of the universe to ensure his own immortality, but Roz Forrester destroyed the Egg before he could complete his plan. (PROSE: Oblivion)