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Equation 3 · Part 2 · Small and On-Device AI in 2035: Scenarios and Falsifiers

Symbol t

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]
tt

What this part means

t is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Its job in the formula

t is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

The passage around this formula

Whether on-device AI becomes the default computing substrate for everyday tasks — the thing a phone or a laptop does locally as a matter of course, with the cloud as the exception rather than the rule — is not a third axis; it is what the other two jointly produce, and testing that jointness is exactly what the room’s validation bench exists to do. Write P(t) for the share of everyday-task requests an on-device model can handle at rough parity with a cloud-frontier model — Axis A’s own proxy — and L(t) for the share of deployments where on-device personalization is reliable enough that a user or an operator trusts it without a cloud fallback — Axis B’s own proxy. A device that is fast but…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

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