Errata:

-When in doubt: follow the project_code.s instructions!

-In 4.3 (minimax) $v0 returns the best score for that depth, unless depth equals zero, in which case it returns the tile position [0-8] of that best move.

-4.3.6 Return the min/max score if depth != 0.

-In 4.5 (update_board), $v0 returns the updated board

-In project_code.s main, the lines:
#    li $s0,  22180         # horizontal win in first row

#    li $s0, 133137

Do not correspond to a horizontal win in the first row. They did, at one point, but I then commenced to test a lot of other board states after that. :)