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Coronal mass ejections (CMEs) and eruptive flares (EFs) are the most energetic explosions in the solar system. Their underlying origin is the free energy that builds up slowly in the sheared magnetic field of a filament channel. We report the first end-to-end numerical simulation of a CME/EF, from zero-free-energy initial state through filament channel formation to violent eruption, driven solely by the magnetic-helicity condensation process. Helicity is the topological measure of linkages between magnetic flux systems, and is conserved in the corona, building up inexorably until it is ejected into interplanetary space. Numerous investigations have demonstrated that helicity injected by small-scale vortical motions, such as those observed in the photosphere, undergoes an inverse cascade from small scales to large, “condensing” at magnetic-polarity boundaries. Our new results verify that this process forms a filament channel within a compact bipolar region embedded in a background dipole field, and show for the first time that a fast CME eventually occurs via the magnetic-breakout mechanism. We further show that the trigger for explosive eruption is reconnection onset in the flare current sheet that develops above the polarity inversion line: this reconnection forms flare loops below the sheet and a CME flux rope above, and initiates high-speed outward flow of the CME. Our findings have important implications for magnetic self organization and explosive behavior in solar and other astrophysical plasmas, as well as for understanding and predicting explosive solar activity.