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The passage around this formula

The first verdict is a genuine win for the theory. Every exponent measured is super-linear — $\zeta$ > 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 $v_{\mathrm{LR}}$ = 12e$J_{\max}$ once $\alpha$ 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 $\alpha$ = 2 , while Richerme’s…

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