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Equation 4 · Part 2 · Tool Protocols in 2035: Two Axes, Four Scenarios, and What Would Falsify Them

Symbol hatepsilon

Trust(s)={certified,ϵ^(s)≤ϵmax⁡ and ϵ^(s) independently auditedunverified,otherwise\text{Trust}(s) = \begin{cases} \text{certified}, & \hat\epsilon(s) \le \epsilon_{\max} \ \text{and} \ \hat\epsilon(s) \ \text{independently audited} \\ \text{unverified}, & \text{otherwise} \end{cases}
ϵ^\hat\epsilon

What this part means

hatepsilon appears in the objective or constraint used by the optimization on the right.

Its job in the formula

hatepsilon appears in the objective or constraint used by the optimization on the right.

The passage around this formula

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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A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the surrounding passage

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