← Back to article

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

What does this equation mean?

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}

Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.

This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

Read it piece by piece

mm

Symbol m

m is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Understand this part →

RR

Symbol R

R is one of the signed contributions combined to compute the quantity on the left.

Understand this part →

τ3\tau_3

Symbol tau_3

tau3u_3 is one of the signed contributions combined to compute the quantity on the left.

Understand this part →

τ4\tau_4

Symbol tau_4

tau4u_4 is one of the signed contributions combined to compute the quantity on the left.

Understand this part →

=

=

The expressions on both sides represent the same quantity under the stated assumptions.

Understand this part →

See an illustrated explanation →
subtraction

subtraction

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

Understand this part →

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.

Understand this part →

How to interpret it

Read it with the definitions, units, and assumptions supplied by the article.

What the article says around this equation

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…
Read the full surrounding passage
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 or weakening. Axis B is not whether Anthropic “has” a scaling policy — it already does, on every version — but what obligation attaches to the top of the function, and whether that obligation is Anthropic’s alone or shared.

Read the equation in its article →

Sources cited in the article section

These citations give research context. Read each source to check which claims it supports.

Return to Anthropic in 2035: Four Scenarios, Their Signals, and What Would Falsify Them

See this formula across 1 published context →

Browse the mathematical compendium →