The authors present an experimental search for the electric-dipole moment (EDM) of the neutron at the Institut Laue-Langevin (ILL) in Grenoble. They used ultracold neutrons (UCNs) stored in a trap permeated by uniform electric and magnetic fields to measure any shift in the transition frequency of the neutrons as the electric field alternated between being parallel and antiparallel to the magnetic field. The experiment carefully studied systematic uncertainties, including geometric-phase-induced false EDMs, and employed two independent analysis approaches. The results, incorporating comprehensive systematic error analysis, yield an upper limit on the absolute value of the neutron EDM of \( |d_n| < 2.9 \times 10^{-26} \, \text{e cm} \) (90% confidence level). The study also discusses various systematic errors, such as geometric-phase effects, translational and rotational motion, light shift, magnetic field fluctuations, electric forces, leakage currents, and AC ripple.The authors present an experimental search for the electric-dipole moment (EDM) of the neutron at the Institut Laue-Langevin (ILL) in Grenoble. They used ultracold neutrons (UCNs) stored in a trap permeated by uniform electric and magnetic fields to measure any shift in the transition frequency of the neutrons as the electric field alternated between being parallel and antiparallel to the magnetic field. The experiment carefully studied systematic uncertainties, including geometric-phase-induced false EDMs, and employed two independent analysis approaches. The results, incorporating comprehensive systematic error analysis, yield an upper limit on the absolute value of the neutron EDM of \( |d_n| < 2.9 \times 10^{-26} \, \text{e cm} \) (90% confidence level). The study also discusses various systematic errors, such as geometric-phase effects, translational and rotational motion, light shift, magnetic field fluctuations, electric forces, leakage currents, and AC ripple.