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Equation 1 · Part 2 · Small and On-Device AI in 2035: Scenarios and Falsifiers

Symbol t

P(t)P(t)
tt

What this part means

t is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

t is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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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