I don't know what you're trying to prove here. The reference point to any and all aiming systems changes whether it's contact point aiming, fractions, equal and opposite, etc.
It would be nice if all you had to do was aim at center OB for everything from 0 - 90 degrees and they all could go in. But it doesn't work that way. Obviously additional reference points are needed to create more acute cut angles. Try doing your tangent lines and diagrams when aligning CCB to COB or to 1/4 and 1/2 with varying degrees of an outside pivot adding throw into the equation. GOOD LUCK!
However with an offset and a varied amount of pivot, considerably fewer reference points are required to make the different shot angles. 90/90 is a pivot system that has the tip of the cue on the right or left outer limit of the CB, not just 1/2 or 1 tip away. It doesn't cover ALL angles which is when something else has to be done. Get Ron Vitello's DVD and system to find out how. Unfortunately, he passed away. See if anyone is willing to sell it.
Pivoting isn't the first and most important part of the aiming system. VISUAL ALIGNMENT is which then sets the eyes, head, body and stance from the INSIDE to an ever changing CENTER, IN BETWEEN CENTER AND EDGE, and EDGE of the two balls in relation to the pocket. We went through this yesterday when I had you place a ball 6-8" from the side pocket and move 12" at a time along the long rail to a corner pocket to see how the center and edges are in a constant state of change. From a straight on view behind the OB to pocket THAT COB is the NEVER CHANGING point of CONTACT for Contact Point Aiming or GB.
And just remember, Shiskabob and CTE are NOT the same. Shiskabob is using the tip and ferrule of the cue and CTE does not. CTE Pro1 also uses no manual pivot.
Your past history indicates when you go into the "trying to prove something" mode with math, diagrams, and what you deem as logic which is totally illogical because you're operating from a position of minimal or incorrect knowledge and technique, you're main goal is to DISPROVE what is being used to execute a system. I hope this isn't your goal again.
You're dragging this back into territory that has nothing to do with YOUR FRACTIONAL AIMING SYSTEM.
You should probably address how to acquire visuals in a way that's easier and fool proof when a cut demands more than a 1/2 ball hit besides tons of practice, HAMB, and figure it out for yourself.
Does that make sense? It does to me.