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Equation 3 · Part 9 · Anthropic in 2035: Four Scenarios, Their Signals, and What Would Falsify Them

subscript

Safeguard(m)={ASL-2,R(m)<τ3ASL-3,τ3≤R(m)<τ4ASL-4,R(m)≥τ4\text{Safeguard}(m) = \begin{cases} \text{ASL-2}, & R(m) < \tau_3 \\ \text{ASL-3}, & \tau_3 \le R(m) < \tau_4 \\ \text{ASL-4}, & R(m) \ge \tau_4 \end{cases}
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

The threshold-triggered structure underneath all three versions is stable even as what triggers what has moved. Write R(m) for a model’s assessed risk on a given threat class and τ3\tau_3, τ4\tau_4 for the thresholds separating safety tiers: Safeguard(m)={ASL-2,R(m)<τ3ASL-3,τ3≤R(m)<τ4ASL-4,R(m)≥τ4\text{Safeguard}(m) = \begin{cases} \text{ASL-2}, & R(m) < \tau_3 \\ \text{ASL-3}, & \tau_3 \le R(m) < \tau_4 \\ \text{ASL-4}, & R(m) \ge \tau_4 \end{cases}. What changed between versions is not this shape but the codomain attached to crossing a threshold . Under the original policy, crossing the top implied a commitment to halt. From version 3.0 onward, the same crossing implies an obligation to publish a Risk Report and justify the decision publicly — a disclosure requirement, not a hard constraint. That distinction is the entire disagreement about whether the architecture is strengthening…

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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.

Open the illustrated subscripts: which member of a family? guide →

Sources cited in the article section

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