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Equation 2 · Part 8 · What Actually Happens Inside a Very Long Claude Context Window

subscript

Cattn(n)=O(n2⋅d),C_{\mathrm{attn}}(n) = O(n^2 \cdot d),
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

Anthropic’s own engineering guidance, published in September 2025 as advice for developers building long-running agents, gives the clearest available first-party account of why context rot happens architecturally rather than treating it as an unexplained empirical curiosity [ 4 ] . The explanation rests on the transformer’s core mechanism: every token attends to every other token in the context through self-attention, so the number of pairwise relationships the model must represent grows with the square of the sequence length. For a context of n tokens, the compute spent by self-attention within a single layer scales as Cattn(n)=O(n2⋅d)C_{\mathrm{attn}}(n) = O(n^2 \cdot d). where d is the model’s hidden dimension. Doubling…

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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

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