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After some more reflection, I have discarded by "epsilon-alpha hypothesis" about the interpolation of the finitely-indexed hyperoperator sequence and the aleph numbers. Although this increases the implicit semiotic scale of the universe of sets (on my model), it has the drawback of eliminating a particularly nice example of advergence and also makes my representation of a generalized glyphic index harder to handle (versus the classical/mainstream fixed-point notation, in this context). Of course, this is really just the fact that the reality is harder to handle, here.
So anyway I have no more solution to the first triangle operation or the first hypertower, to say nothing of my notion of a xatrix cardinal!