It is important to check if the Froissaron-Maximal Odderon (FMO) approach is the only model in agreement with the LHC data. We therefore generalized the FMO approach by relaxing the $ln^2s$ constraints both in the even-and odd-under-crossing amplitude. We show that, in spite of a considerable freedom of a large class of amplitudes, the best fits bring us back to the maximality of strong interaction. Moreover, if we leave Odderon Regge pole intercept $alpha_O(0)$ completely free we find a very good solution for $alpha_O(0)$ near -1 in agreement with the result of oddballs spectroscopy in QCD based on AdS/CFT correspondence.
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