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### A Critical Re-examination of M8–H Duality: Part II

#### Abstract

This article is the second part of an article representing a critical re-examination of

*M*-^{8}*H*duality. This re-examination has yielded several surprises. The first surprise was that space-time surfaces in*M*must and can be co-associative so that they can be constructed also as images of a map defined by local^{8}*G*(octonionic automorphisms) transformation applied to co-associative sub-space_{2,c}*M*of complexified octonions^{4}*O*in which the complexified octonion norm squared reduces to the real_{c}*M*norm squared. An alternative manner to construct them would be as roots for the real part^{4 }*Re*of an octonionic algebraic continuation of a real polynomial_{Q(P)}*P*. The outcome was an explicit solution expressing space-time surfaces in terms of ordinary roots of the real polynomial defining the octonionic polynomials. The equations for*Re*=_{Q(P)}*0*reduce to simultaneous roots of the real polynomials defined by the odd and even parts of P having interpretation as complex values of mass squared mapped to light-cone proper time constant surfaces in*H*. The second surprise was that space-time surface in*M*can be mapped to^{8}*H*as a whole so that the strong form of holography (SH) is not needed at the level of*H*being replaced with much stronger number theoretic holography at the level of*M*.^{8}