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Equation 5 · Part 2 · AI Agent Architecture in 2035: Four Scenarios, Their Signals, and What Would Falsify Them

Symbol p

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}
pp

What this part means

p is an input to the expression that computes the quantity on the left.

Its job in the formula

p is an input to the expression that computes the quantity on the left.

The passage around this formula

…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…

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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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