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Equation 15 · Part 4 · Comparing the Main Approaches to AI Agent Architecture

Symbol v

G=(V,E),v→v′ fires iff γ(v,v′)=1,G = (V, E), \qquad v \to v' \text{ fires iff } \gamma(v, v') = 1,
vv

What this part means

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

Its job in the formula

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

The passage around this formula

Formally, this pattern replaces the time-indexed loop with execution over a graph: G=(V,E),v→v′ fires iff γ(v,v′)=1G = (V, E), \qquad v \to v' \text{ fires iff } \gamma(v, v') = 1. where each node v ∈\in V is either a deterministic function or an invocation of some policy πv\pi_v , and γ\gamma is an explicit gate on the edge — a test, a validation check, or a human approval — that must pass before the transition is permitted. That is the structural reason human approval is a first-class primitive in this pattern rather than a wrapper bolted around it from outside: approval is just one kind of γ\gamma , attached to one particular edge, rather than a blanket condition on the whole run.

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

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