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Equation 40 · Part 2 · AI Feeds on the Distance Between an Intention and an Outcome

subscript

dtd_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

Here qtrq_{tr} is supplied input-context length in tokens, not tokens consumed after the agent has begun acting; using post-attempt expenditure would contaminate the predictor with behavior. The term dtd_t is a predeclared ordinary benchmark-difficulty score based only on endpoint-side, redaction-invariant features such as repository size band, static dependency reach, test-suite scope, and selected task-family label. It is deliberately conventional and admittedly imperfect. The terms urepo(t)u_{\mathrm{repo}(t)} and utu_t are repository and task random effects, while αm\alpha_m represents model or agent-configuration identity. The baseline includes model identity, token length, ordinary difficulty, and task…

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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

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