Microscopic benchmark study of triaxiality in low-lying states of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow/><mml:mn>76</mml:mn></mml:msup><mml:mi>Kr</mml:mi></mml:math>

We report on a seven-dimensional generator coordinate calculation in the two deformation parameters $\ensuremath{\beta}$ and $\ensuremath{\gamma}$ together with projection on three-dimensional angular momentum and two particle numbers for the low-lying states in ${}^{76}\mathrm{Kr}$. These calculations are based on covariant density functional theory. Excellent agreement is found with the data for the spectrum and the electric multipole transition strengths. This answers the important question of dynamic correlations and triaxiality in a fully microscopic way. We find that triaxial configurations dominate both the ground state and the quasi $\ensuremath{\gamma}$ band. This yields a different picture from the simple interpretation in terms of ``coexistence of a prolate ground state with an oblate low-lying excited state,'' which is based on the measured sign of spectroscopic quadrupole moments. This study also provides for the first time a benchmark for the collective Hamiltonian in five dimensions. Moreover, we point out that the staggering phase of the $\ensuremath{\gamma}$ band is not a safe signature for rigid triaxiality of the low-energy structure.