"Jade Blue" by Edward Bryant

Available in Dozois' ebook, Magicats.  Also in Bryant's own collection, Cinnabar, a strange city of the far future.  The latter may be more useful for the author as he is enduring financial and health problems (see Friends of Ed Bryant).

Mr. Timnath Obregon is on the brink of inventing an APE or Articificial Probability Enhancer, a device which can edit time.  He demonstrates it to ladies but when they leave, a film canister is left behind.

Jade Blue is the catmother or governess who feeds her milk to George, a boy whose true parents tend to abandon him.  Statues greet him, but he needs to be comforted by his parents but Jade Blue will have to do. She has had children, but not real ones, computer-generated.  They use Obregon's machine.