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Combinatorial Hierarchy: Two Decades Later

Matti Pitkanen


Combinatorial Hierarchy (CH) is a hierarchy consisting of Mersenne integers M(n)= MM(n-1) =2M(n-1)-1and starting from M1=2.  The first members of the hierarchy are given by 2, 3, 7, 127, M127 =2127-1and are primes. The conjecture of Catalan is that the hierarchy continues to some finite prime.  It was proposed by Peter Noyes and Ted Bastin that the first levels of hierarchy up to M127 are important physically and correspond to various interactions.  I have proposed the levels of CH define a hierarchy of codes containing genetic code corresponding to M7 and also memetic code assignable to M127. In this article I consider the argument that the hierarchy ends at M127 and find that it should end already at M7 for which the condition used saturates and which corresponds to genetic code in TGD interpretation. The failure of condition at M127 level has interesting “Godelian interpretation".  I find also that in TGD Universe genetic code and its memetic counterpart are realized at the level of fundamental particles. Already earlier I have ended up with alternative realizations at the level of dark nucleons and sequences of 3 dark nucleons.

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