distinguishes the phase where the spike is impossible to recover from the easy phase where if you only had the matrix you recover the spike simply by spectral methods looking at the spectrum of the matrix then if the matrix was not there that is that delta 2 would be infinity 1 over delta 2 would be 0 then you only have the spiked tensor model which you know information theoretically is solvable at at some point uh highlighted with the red line here but even if the noise is smaller than that it's algorithmically hard and it's