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α=2\alpha = 2

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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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α=2\alpha = 2

Equation 53 · Crossed Fields

Every Crystal Has Its Own Speed of Light

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

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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