Either 'noon' or 'midnight'

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Shacharis after chatzos

Is praying shacharis after chatzos (midday) permitted, and do you fulfill your obligation? If so, until when? Please give sources, preferably quoting the Mishna Berurah, Alter Rebbe of Lubavitch, or ...
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What is “חצות האמצעי”?

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 ...
5
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How is Chatzos Halayla (Halachic Midnight) calculated?

It seems pretty easy to calculate from the get-go that the formula is something like this: # a halachic hour is one twelfth of the time between sunrise and sunset halachicHour = (timeOfSunset - ...