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We investigate the development of the directed, $v_1$, and elliptic flow,$v_2$, in heavy ion collisions in mid-central Au+Au reactions at$E_\mathrm{lab}=1.23 A$ GeV. We demonstrate that the elliptic flow of hot anddense matter is initially positive ($v_2>0$) due to the early pressuregradient. This positive $v_2$ transfers its momentum to the spectators, whichleads to the creation of the directed flow $v_1$. In turn, the spectatorshadowing of the in-plane expansion leads to a preferred decoupling of hadronsin the out-of-plane direction and results in a negative $v_2$ for theobservable final state hadrons. We propose a measurement of $v_1-v_2$ flowcorrelations and of the elliptic flow of dileptons as methods to pin down thisevolution pattern. The elliptic flow of the dileptons allows then to determinethe early-state EoS more precisely, because it avoids the strong modificationsof the momentum distribution due to shadowing seen in the protons. This opensthe unique opportunity for the HADES and CBM collaborations to measure theEquation-of-State directly at 2-3 times nuclear saturation density.

Decoding the flow evolution in Au+Au reactions at $1.23 A$ GeV using hadron flow correlations and dileptons