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Equation 1 · A History of Anthropic and the Claude Model Line

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C(model)≥τk  ⟹  deploy only if safeguards≥Sk,C(\text{model}) \ge \tau_k \;\Longrightarrow\; \text{deploy only if safeguards} \ge S_k,

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CC

Symbol C

the model’s evaluated capability on a specific threat class.

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τk\tau_k

Symbol tau_k

the threshold defining ASL level k.

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SkS_k

Symbol S_k

the security and deployment standard the policy requires once that threshold is crossed.

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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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The policy’s structure is what makes it useful to state formally, because its core mechanism is a conditional commitment rather than a fixed rule. Anthropic defines AI Safety Levels (ASL), each tied to a capability threshold on a specific class of risk — most concretely, the potential for a model to meaningfully assist in acquiring chemical, biological, radiological, or nuclear weapons capability, or to self-exfiltrate or resist correction. The policy’s operating logic, stripped to its structural claim, is a threshold trigger: C(model)≥τk  ⟹  deploy only if safeguards≥SkC(\text{model}) \ge \tau_k \;\Longrightarrow\; \text{deploy only if safeguards} \ge S_k. 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…
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The policy’s structure is what makes it useful to state formally, because its core mechanism is a conditional commitment rather than a fixed rule. Anthropic defines AI Safety Levels (ASL), each tied to a capability threshold on a specific class of risk — most concretely, the potential for a model to meaningfully assist in acquiring chemical, biological, radiological, or nuclear weapons capability, or to self-exfiltrate or resist correction. The policy’s operating logic, stripped to its structural claim, is a threshold trigger: C(model)≥τk  ⟹  deploy only if safeguards≥SkC(\text{model}) \ge \tau_k \;\Longrightarrow\; \text{deploy only if safeguards} \ge S_k. 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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