H-infinity is not E-infinity

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We provide an example of a spectrum over S⁰ with an H∞ structure which does not rigidify to an E₃ structure. It follows that in the category of spectra over S⁰ not every H∞ ring spectrum comes from an underlying E∞ ring spectrum. After comparing definitions, we obtain this example by applying Σ∞+ to the counterexample to the transfer conjecture constructed by Kraines and Lada.