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Equation 3 · Part 8 · Ten Failure Modes That Define Production Claude Code Use

subscript

T50(t)≈T50(t0)⋅2 (t−t0)/d,d≈7 months,T_{50}(t) \approx T_{50}(t_0) \cdot 2^{\,(t - t_0)/d}, \qquad d \approx 7\ \text{months},
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

It is intuitive to expect an agentic session to improve as it accumulates context about a task. The measured pattern runs the other way. METR’s time-horizon research tracks the length of task — measured in how long a skilled human would take — that a frontier model can complete autonomously with a given reliability, and finds current frontier models near 100% success on tasks taking a human under four minutes, collapsing to under 10% success on tasks taking more than about four hours, with Claude 3.7 Sonnet reported specifically among the models exhibiting this drop-off [ 13 ] . The organization’s headline trend — the task length completable at 50% reliability doubling roughly every seven…

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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.

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Sources cited in the surrounding passage

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