HID highlighting hysteresis patterns for X-ray (blue) and gamma-ray (magenta) domains for the flat trend case shown in Fig. 8 (centre) with additional LIV effects, namely τ = +400 s TeV⁻¹ (top pannel) and τ = −400 s TeV⁻¹ (bottom pannel), showing that LIV effects can significantly modify the hysteresis pattern and even cause a change in loop orientation in the gamma-ray domain. While the X-ray hysteresis pattern is left unchanged relative to the case at τ = 0 in Fig. 8, a rotation pattern appears in the gamma-ray pattern (either clockwise or anticlockwise depending on the sign of τ).