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Equation 13 · Part 3 · Reliable AI Agents Are Control Systems, Not Chatbots

=

pi=pp_i=p
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

If one makes the deliberately crude assumption pip_i=p , a 98% reliable stage repeated 50 times yields 0.98^{50}≈\approx0.364 . Real agent steps are neither independent nor identically distributed: an early mistake can corrupt later observations, while a test can expose and reverse it. The simple product is useful because it reveals the architecture’s burden. Long tasks require mechanisms that change conditional probabilities after observing evidence , not merely a model with a flattering average.

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the article section

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