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Equation 4 · Part 6 · AI Datacenter Interconnects in 2035: Scenarios, Signals, and Falsifiable Predictions

=

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

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

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 number is offered to be doubted, not believed. The assumption it encodes — that the doubling period keeps compressing on a fixed clock rather than lengthening as channel loss and signal-to-noise margin close…

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the surrounding passage

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