We pick the tanh because it gives us the maximum possible slope of thing we have to measure, and the more slope the more marks our yardstick, when we count things in sets of X. X is either the frequency or the wavelength (up or down) of one particular marking quant, Qk. It looks like b^[m*Q], all f(X) having the exponential form. If f(X) are solutions to Tanh(X) polynomials of small order, then Tanh(X) can be b^[m*Q], I think. Or better yet forms like:
b^[n] + b^[-n].
So lets count exponent m up in frequency then the Shannon condition is:
[m*Q]/[b^[mQ] all be less than one, then m can grow without bound, I think.
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