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

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

Equation 4 · Datacenters

AI Datacenter Interconnects in 2035: Scenarios, Signals, and Falsifiable Predictions

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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…

Meanings in this article

  • t0t_0: the time or time index used in this relationship.
  • TT: the assumed doubling period: [displayed formula].
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