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Equation 9 · Part 10 · The Hardest Unsolved Problems in AI Agent Architecture

Starting index or lower bound: s

b′(s′)=η O(o∣s′,a)∑sT(s′∣s,a) b(s),b'(s') = \eta \, O(o \mid s', a) \sum_{s} T(s' \mid s, a)\, b(s),
ss

What this part means

This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.

Its job in the formula

s appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

The passage around this formula

…of a single observation channel in their own worked example forces a much larger plan graph, and a correspondingly larger memory requirement, just to stay confident [ 4 ] . Applied to a long-running LLM agent, s is everything true about the task — every file changed, every external call made, every fact established — and b is whatever the agent’s context window currently represents. The update above is exact only if the full state and its full history are kept; an agent cannot keep them, because the…

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Learn the underlying idea

Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.

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Sources cited in the surrounding passage

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