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I will report on my progress, joint with David Reutter, to construct and analyze the algebraic closure of nVec --- in other words, the universal n-category of framed nD TQFTs. The invertibles are Pontryagin dual to the stable homotopy groups of spheres. The Galois group is almost, but not quite, the stable orthogonal group. And an invertible TQFT can be condensed from the vacuum if and only if it is in the Pontryagin dual to the cokernel of the J-homomorphism.

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