← All parts of this equation

Equation 15 · Part 6 · Comparing the Main Approaches to AI Agent Architecture

=

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,
=

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

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

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.

Open the illustrated equality: what the equals sign claims guide →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.