An operadic spectrum acts as a control parameter for a norm-analytic functor calculus, delivering criteria for polynomial behavior, exponential convergence bounds on Taylor towers, and a reconstruction theorem from derivative data via operadic plethysm.
Calculus I: The first derivative of a homotopy functor,
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Spectral Operadic Calculus: Norm-Analytic Functor Calculus
An operadic spectrum acts as a control parameter for a norm-analytic functor calculus, delivering criteria for polynomial behavior, exponential convergence bounds on Taylor towers, and a reconstruction theorem from derivative data via operadic plethysm.