While researching an answer to this question I stumbled across the term "חצות האמצעי".
What does it mean? Does it refer to halachic midday, i.e. halfway between netz hachama and shkias hachama, or something else? How does it differ from "חצות האמיתי"?
It refers to "mean noon," as opposed to "solar noon." True solar noon is when the sun crosses the imaginary meridian in the sky between east and west, i.e., when the sun is exactly in the south. The time this occurs varies slightly every day due to a number of factors; the variation is known as the "equation of time." (See here for an excellent explanation of this phenomenon.) The average time at which noon occurs is called the mean noon, and by definition it is at the same time every day. (Theoretically 12:00, but due to uniform time zones, it is usually off by a few minutes. In NYC, for example, it is at 11:56.)