We propose a hybrid equation of state ($\mathrm{VDF}+\mathrm{MIT}$ EoS) to describe the hadron-quark phase transition in dense nuclear matter. By coupling this EoS with the a multiphase transport-hadron cascade transport model and comparing to recent experimental data on proton and $\mathrm{\Lambda }$ directed flow $v_1$, we constrain the transition to likely occur near $5{\rho }_0–6{\rho }_0$, ruling out transitions below $3{\rho }_0$. Furthermore, we introduce the energy derivative of the midrapidity $v_1$ slope, $d(d{v}_1/dy)/d(\sqrt{s_{NN}})$, as a weakly model-dependent observable. Its zero crossing provides a direct signature of the phase transition critical point, offering a new tool for mapping the quantum chromodynamics phase diagram in future experiments.

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• Collective flow
• Nuclear matter in neutron stars
• Relativistic heavy-ion collisions