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Equation 3 · Part 2 · Typed Tools: Protocols as an Agent's Action Alphabet

subscript

Rt\mathcal{R}_t
subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

The passage around this formula

Rt\mathcal{R}_t is the result type : what the caller is told. The second Σ\Sigma is the side effect : what changed. These two are separate, and conflating them is the origin of most agent unreliability. A tool that returns {"status": "ok"} has a result type carrying roughly one bit while its effect on Σ\Sigma may be arbitrarily large. The caller — model and harness alike — has no way to verify that the bit is true.

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

Sources cited in the article section

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