Geometric Complexity Theory VI: The flip via positivity

Geometric complexity theory (GCT) is an approach towards the P vs. NP and related problems. The article [GCTflip] describes its defining strategy, called the flip, to resolve the self referential paradox, which is the root difficulty in these problems. This article describes an approach based on positivity hypotheses in algebraic geometry and representation theory to implement the flip and thereby resolve the self referential paradox in the arithmetic setting wherein the underlying field of computation has characteristic zero. The main result here is the Decomposition Theorem that decomposes the arithmetic P vs. NP and permanent vs. determinant problems into such positivity hypotheses and easier hardness hypotheses, all without the self referential difficulty.