I will get back to the translations of TGM posts in a bit, but I wanted again to look at why the golfer needs to aim above the apex of the break on breaking putts (for cup positions that are on a planar slope). Here's a great video showing this.
The red line shows where the golfer would be aiming if they aimed at the apex. This is incorrect and the red circles show where the ball actually goes and shows the putt being missed on the low side.
Conversely, the yellow line shows the golfer aiming ABOVE the apex of the curve and thus the putt goes on the intended line and rolls in the cup.