"Shall I look for errors, or terms needing more precise definition, or what? "
Both, plus overlooked structures, ambiguity...
I found that his whole system requires "complementarity" between the numbers (whatever they may be) in his set, with the numbers in his "unknown data added to make the set unique" (musical chairs 1?); and more complementarity from that complementarity (musical chairs 2?) to his further "added unknown data such that can subtract any item ("any" item gives yet more "musical chairs" like complementarity (join the dots (musical chairs 3?): what item must "dance" with the other selections for the thing to work).
I have just roughly hinted at what I'm uncovering: I think Alexander's "three compensating accelerations are almost perfect model of reality" is right here. (Acceleration:
rate of change of a rate of change)
QED seems implicit: his subtracted one unit involves all possible paths it can 'happen'(through the dances within his complementary: set, unknown data cloud, unknown data cloud).
M: "By "arbitrary," do we mean "randomly selected?"
I think so; he also says he ignores order if I recall right (but maybe fails to notice that his "making it unique" role that unknown data has for his set, means that order is not ignored inside his system.
Strictly: (5,5,5,5) is not absolutely exactly identical to (5,5,5,5) as one is there and one is over there. If they were identical in every way you couldn't count more than one (5,5,5,5) pattern.
M: "a) Were these unknowns added before, or after, the sequence of "observations" was put in their sequence?
b) If the unknowns are added before the sequencing, we have less of a problem. The other choice, "after," says we have added an unknown to an unknown and changed the sequence...and we now do not know what the sequence has become."
He disregards order in the sequences; only looks at frequency of numbers (have two sets got four fives each, so identical in that respect?)
But I think he overlooked the frequency complementarity that requires a balancing act or the "unknown data" added to one set might make it look just like another set (that previously looked different).
order is not being regarded; only content.
Only by selecting sample unknown data and set contents, can one uncover the complementarity he seems to have overlooked, it seems.