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Equation 1 · Part 9 · AI Memory Systems and the Bandwidth Wall in 2035: Scenarios, Signals, and Falsifiable Predictions

subscript

B(t)≈B0⋅2(t−t0)/τ,B(t) \approx B_0 \cdot 2^{(t - t_0)/\tau},
subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

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)≈B0⋅2(t−t0)/τB(t) \approx B_0 \cdot 2^{(t - t_0)/\tau}. where B0B_0 is the bandwidth at reference year t0t_0 and τ\tau is the doubling time implied by the data. Solving for τ\tau from the two JEDEC anchor points gives

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Learn the underlying idea

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

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