This conjecture is motivated by the accumulated evidence over the decades that the energy spectra of very simple non-integrable classically chaotic systems contain universal level fluctuations described by random matrix theory. Given random matrix theory’s successful application to nuclear spectra and these classical results, the question of whether there were analog results for quantum systems with chaotic systems as an appropriate limit seems reasonable. The conjecture basically means that the energy spectra for the semi-classical analogues of classical chaotic systems are structurally the same as those classical systems. This conjecture remains unproven, though it appears to hold for the case of classical chaotic billiards and their semi-classical counterparts. Since this is a conjecture about semi-classical systems, this means that the structure of the energy spectra of semi-classical systems is strictly dependent on chaos in the corresponding classical systems  not on any chaotic behavior in quantum or semi-classical systems.