What does this equation mean?

A fourth fact transfers, but only with a correction the paper computes rather than sets aside. A quasiparticle wavepacket moving at speed v inside the linear window carries an internal clock — a spinor phase, a zitterbewegung oscillation — that runs slow by the familiar factor $\gamma$ = (1 - $v^2$/$c_{\mathrm{eff}}^2$)^{-1/2} : 1.15 at v = 0.5\,$c_{\mathrm{eff}}$ , 2.29 at 0.9\,$c_{\mathrm{eff}}$ . That dilation is real and, in principle, measurable, but only inside a window whose edge the band’s own curvature sets. Writing the correction as a term proportional to (k/$\Lambda_{\mathrm{curv}}$)^2 , the fractional error in $\gamma$ stays under one percent as long as the wavepacket’s momentum sits below roughly a tenth of $\Lambda_{\mathrm{curv}}$ ; for graphene, where $\Lambda_{\mathrm{curv}}$ $\approx$ 1.5$\times$10^{9} inverse metres, the clean window covers momenta up to about 1.5$\times$10^{8} inverse metres. Dilation is graded structured rather than exact for exactly this reason: it holds inside a window with a computable edge, and the paper’s contribution is computing where that edge sits rather than asserting the effect and moving on.