Equation 1 · Part 3 · AI Memory Systems and the Bandwidth Wall in 2035: Scenarios, Signals, and Falsifiable Predictions

Symbol B_0

B(t) \approx B_0 \cdot 2^{(t - t_0)/\tau},

B_0

What this part means

the bandwidth at reference year $t_0$ .

Its job in the formula

$B_0$ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Full expressionSymbol B_0Article meaning

Where the article explains it

where $B_0$ is the bandwidth at reference year $t_0$ and $\tau$ is the doubling time implied by the data.

The passage around this formula

With two verified anchor points — HBM3 in 2022 at roughly 0.82 terabytes per second per stack, HBM4 in 2025 at up to 2.0 terabytes per second per stack [ 1 , 2 ] — it is possible to build an explicit, falsifiable trajectory rather than a vague “bandwidth will keep rising.” Model the growth as a simple exponential in calendar time, $B(t) \approx B_0 \cdot 2^{(t - t_0)/\tau}$ . where $B_0$ is the bandwidth at reference year $t_0$ and $\tau$ is the doubling time implied by the data. Solving for $\tau$ from the two JEDEC anchor points gives

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A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the article section

[13] AI and Memory Wall ↗

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