Mastering a ritual means that mana you contribute to said ritual is doubled. So if Joe Empire has 2 ranks of Autumn Lore, is at the Imperial Regio and wants to solo perform Mantle of the Golden Orator (Magnitude 7), and has mastered it, what is the “effective” Magnitude? 3 or 4? Does it round down or up? I did look to see whether such a question had already been asked, but couldn’t see such a thread.

You need to expend enough mana to cover the magnitude. This means Joe needs to spend 4 crystals, for a magnitude of 8, which means he can’t do this on his own.
However, if Joe was joined by a fellow autumn ritualist from his coven who didn’t have it mastered, Joe could spend 3 crystals for 6 magnitude and his buddy can expend 1 crystal for 1 magnitude, giving them the required 7.

Magnitude never* changes. Don’t ever divide the magnitude - it’s just misleading. Instead, multiply the mana crystals.

Each contributor can put in a number of crystals equal to their lore level (including regio, etc).

If they have the ritual mastered, those crystals count for 2 magnitude each. Otherwise, they count for 1 each.

Then count up, and stop once you have equalled or exceeded the magnitude of the ritual. It’s most efficient to start with all the mastered contributors, and then add unmastered contributors if necessary.

With Joe, he has Lore 2, plus 1 from the regio, making lore 3. His 3 mana crystals count for 2 magnitude each, meaning he only hits 6 and cannot cast the ritual.

*Unless you are using something which has the explicit effect of reducing magnitude.