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Equation 2 · Part 1 · What Actually Happens Inside a Very Long Claude Context Window

Symbol C_attn

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

What this part means

CaC_attn is part of the quantity the equation computes from the expression on the right.

Its job in the formula

CaC_attn is part of the quantity the equation computes from the expression on the right.

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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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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