Puzzle #212: Magic Square

A 3-by-3 magic square contains the integers from 6 to 14.  (Each row, column, and diagonal adds up to the same number.)

Given the clues following, what integer is in each square?

The number in the top-right corner square is 10, 11, or 12.

The corner squares’ values are either all odd or all even.

The bottom-center number is 7, or 14, or maybe 13.

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, June 28, 2017 at noon Pacific Time. I will post the answer shortly after.