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Equation 51 · Part 5 · Every Crystal Has Its Own Speed of Light

subscript

vLR=12eJmax⁡v_{\mathrm{LR}} = 12eJ_{\max}
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

The first verdict is a genuine win for the theory. Every exponent measured is super-linear — ζ\zeta > 1 at seven of the eight points — exactly where the long-range bound says a finite-velocity linear cone is not guaranteed and faster-than-linear growth is required instead, and the propagation outright violates the nearest-neighbour bound vLRv_{\mathrm{LR}} = 12eJmax⁡J_{\max} once α\alpha drops below 1 [ 4 ] . Read against a naive short-range picture, the ion chain is unambiguously non-local. The second verdict tempers the first: the three competing long-range thresholds theory offers — a worst-case bound, a typical-state bound, and a free-particle bound — all sit above α\alpha = 2 , while Richerme’s…

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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 surrounding passage

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