Cybernetics of AI Companies

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Parameter jets, a neural tangent hierarchy, and an input-jet tangent kernel describe distinct extensions. Every extensional optimizer on smooth objectives factors through their global holonomic jet representation, with runtime and oracle state retained; factorization through a jet at one point has a separate locality condition. A smooth manifold is a Hausdorff, second-countable space covered by Euclidean charts with smooth transition maps; smooth maps are smooth in those charts.

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