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Equation 3 · A History of Anthropic and the Claude Model Line

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τk\tau_k

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the threshold defining ASL level k. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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τk\tau_k

Symbol tau_k

the threshold defining ASL level k.

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subscript

subscript

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.

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where C(model\text{model}) is the model’s evaluated capability on a specific threat class, τk\tau_k is the threshold defining ASL level k , and SkS_k is the security and deployment standard the policy requires once that threshold is crossed. This is worth writing out because a threshold-triggered commitment is only meaningful if it is sometimes not satisfied by default — otherwise it is a description of business as usual, not a constraint. Whether the policy binds in practice is therefore an empirical question about later events, addressed below.

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