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Equation 3 · Tool Protocols in 2035: Two Axes, Four Scenarios, and What Would Falsify Them

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ϵmax⁡\epsilon_{\max}

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ϵmax⁡\epsilon_{\max}

Symbol epsilon_max

epsilonmn_max is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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subscript

subscript

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A convenient way to see what a resolved Axis B would actually require is to write the registry’s listing decision as a threshold rule. Let ϵ^(s)\hat\epsilon(s) be an estimate of the probability that a listed tool or server s behaves differently from what its description claims once it is actually invoked, and let ϵmax⁡\epsilon_{\max} be the error tolerance a registry operator or a downstream client is willing to accept. A defensible rule is

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