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Equation 3 · Part 1 · Small and On-Device AI in 2035: Scenarios and Falsifiers

Symbol D

D(t)=1 ⁣[P(t)≥p∗]⋅1 ⁣[L(t)≥ℓ∗]D(t) = \mathbb{1}\!\left[P(t) \ge p^{*}\right] \cdot \mathbb{1}\!\left[L(t) \ge \ell^{*}\right]
DD

What this part means

D is part of the quantity the equation computes from the expression on the right.

Its job in the formula

D is part of the quantity the equation computes from the expression on the right.

The passage around this formula

…that personalizes beautifully but cannot match cloud capability on hard tasks still routes those tasks out. Becoming the default substrate needs both conditions at once, not an average of them: D(t)=1 ⁣[P(t)≥p∗]⋅1 ⁣[L(t)≥ℓ∗]D(t) = \mathbb{1}\!\left[P(t) \ge p^{*}\right] \cdot \mathbb{1}\!\left[L(t) \ge \ell^{*}\right]. D(t) stays at zero however high either term climbs alone. Axis A determines whether P(t) can plausibly clear p∗p^{*} within this article’s horizon; Axis B determines whether L(t) can. Neither can be inferred from the other, which is why they are kept as two axes rather than folded into one.

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A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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