I don't see this as merely a difference of opinion between the two of us.But I am going to take one more swing at resolving our difference.
It is the non-standard use of the word "conversion" that is causing the difference and the standard usage of "conversion" doesn't depend on your opinion nor on mine.
While it might be possible to reasonably argue that in very generic use, "conversion" could be used to mean something a lot less specific than it is usually used to mean, in this specific case, the context and SAAMI's statement about "direct conversion" makes that very difficult, if not completely impossible.
I agree that there is good correlation between CUP and PSI. There are some caveats here because of the way the data is distributed. If you play around with fits you can get a good feel for them and why it's a bad idea to place too much faith in fits that rely on data that tends to bunch instead of being evenly distributed over the range of values. Also, it's important to keep the error in perspective relative to the values. In other words, the error needs to be expressed as a percentage of the values being calculated to insure that it is not getting large relative to the actual data. This is what happens near the low end of the CUP PSI plot provided early in the thread.
I agree that it is possible to develop an algorithm that can be used to estimate CUP from PSI and vice versa. If that algorithm is tailored to a specific caliber, the estimate can be very good. In fact, even if it is tailored to a group of cartridges that "behave" a lot like each others, an estimate can be generated that is still usable for most purposes as long as the user understands its limitations. The estimation algorithm value decreases considerably (the error goes up too much, IMO) when there is an attempt made to come up with a generic algorithm that "works" for everything.
I do not agree that any of those statements contradict claims that there is no "direct conversion" because "direct conversion" and "estimation algorithm" are not the same thing. For precisely the same reason I do not agree that "correlation" implies that a "direct conversion" exists.