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Equation 4 · Part 5 · AI Datacenter Interconnects in 2035: Scenarios, Signals, and Falsifiable Predictions

Symbol T

R(t)=R0⋅2(t−t0)/TR(t) = R_0 \cdot 2^{(t - t_0)/T}
TT

What this part means

the assumed doubling period: [displayed formula].

Its job in the formula

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

Where the article explains it

Writing per-lane rate as a function of time, with R0R_0 the most recent standardised rate at time t0t_0 and T the assumed doubling period: R(t)=R0⋅2(t−t0)/TR(t) = R_0 \cdot 2^{(t - t_0)/T}.

The passage around this formula

Analysis. A naive extrapolation makes the compressing cadence explicit rather than hiding it. Writing per-lane rate as a function of time, with R0R_0 the most recent standardised rate at time t0t_0 and T the assumed doubling period: R(t)=R0⋅2(t−t0)/TR(t) = R_0 \cdot 2^{(t - t_0)/T}. Anchoring at R0R_0 = 200 Gb/s per lane, t0t_0 = 2026 , and holding the most recently observed four-year doubling period fixed gives R(2035) = 200 ⋅\cdot 2^{9/4} ≈\approx 950 Gb/s per lane by 2035 — essentially a 1 Tb/s single electrical lane. That…

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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 surrounding passage

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