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Equation 3 · Part 6 · OpenAI and Claude on Formal Reasoning: What the Benchmarks Show, and Where They Mislead

subscript

pk=1−(1−p)k,p_k = 1 - (1-p)^k,
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

Consider what the o1 numbers alone expose about how these gains are produced. If a single attempt at a problem succeeds with probability p , and k attempts were independent, the probability that at least one succeeds is pk=1−(1−p)kp_k = 1 - (1-p)^k. a curve that climbs fast and then saturates. It is tempting to read o1’s jump from 74% (one sample) to 83% (64-sample consensus) to 93% (1,000-sample rerank) as roughly this shape. It is not, for two reasons that matter for how the number should be read. First, repeated attempts by one model on one problem are correlated — the same misconception that causes one failure tends to recur — so the realised gain from added samples falls well below what…

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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.