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Equation 5 · Part 6 · AI Agent Architecture in 2035: Four Scenarios, Their Signals, and What Would Falsify Them

≤

Approval(a)={automatic,p(a) S(a)≤Bhuman required,p(a) S(a)>B\text{Approval}(a) = \begin{cases} \text{automatic}, & p(a)\, S(a) \le B \\ \text{human required}, & p(a)\, S(a) > B \end{cases}
≤

What this part means

Less than or equal to.

Its job in the formula

Less than or equal to.

The passage around this formula

Whether human-approval checkpoints become automated and statistical is, likewise, mostly a readout of Axis B rather than a genuinely separate question. A useful way to see the dependency is to write the automation decision as a threshold rule. Let p(a) be a certified upper bound on the probability that action a violates its specification, and let S(a) be a severity score for the consequence class a belongs to. A natural rule an organization or regulator could adopt is Approval(a)={automatic,p(a) S(a)≤Bhuman required,p(a) S(a)>B\text{Approval}(a) = \begin{cases} \text{automatic}, & p(a)\, S(a) \le B \\ \text{human required}, & p(a)\, S(a) > B \end{cases}. where B is a risk budget set by policy. The rule only does useful work where p(a) is a number someone can trust — which is exactly what Axis B’s certified branch would supply and its empirical branch would…

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Learn the underlying idea

An inequality compares values without claiming they are equal. It describes a range, threshold, or bound that a quantity may satisfy.

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Sources cited in the surrounding passage

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