Equation 3 · Anthropic in 2035: Four Scenarios, Their Signals, and What Would Falsify Them
What does this equation mean?
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.
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Symbol m
m is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.
Symbol R
R is one of the signed contributions combined to compute the quantity on the left.
Symbol tau_3
ta is one of the signed contributions combined to compute the quantity on the left.
Symbol tau_4
ta is one of the signed contributions combined to compute the quantity on the left.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →subtraction
Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.
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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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 , for the thresholds separating safety tiers: . 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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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 , for the thresholds separating safety tiers: . 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.
Sources cited in the article section
- [2] Responsible Scaling Policy v3 ↗
- [1] Anthropic's Responsible Scaling Policy ↗
- [3] "Anthropic's RSP v3.0: How it Works, What's Changed, and Some Reflections" ↗
- [12] "System Card: Claude Opus 5" ↗
- [13] Introducing Claude Sonnet 5 ↗
These citations give research context. Read each source to check which claims it supports.
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