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Published equation contexts

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

Why this formula appears here

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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γ\gamma

Symbol gamma

an explicit gate on the edge — a test, a validation check, or a human approval — that must pass before the transition is permitted.

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Published contexts (1)

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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,

Equation 15 · AI Agents & Systems

Comparing the Main Approaches to AI Agent Architecture

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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.

Meanings in this article

  • VV: either a deterministic function or an invocation of some policy πv\pi_v.
  • γ\gamma: an explicit gate on the edge — a test, a validation check, or a human approval — that must pass before the transition is permitted.
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