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A collider needs both, and no scheme yet works for positrons in experiment.","posed_since":"","precise":"In the nonlinear blowout regime, plasma electrons are expelled and the ion column focuses electrons but defocuses positrons. Find a wake configuration (hollow channel, finite-radius plasma, electron filament, magnetized wake, quasi-linear wake) that simultaneously gives gradient above $1e7\\,\\mathrm{eV}/\\mathrm{cm}$, energy-transfer efficiency above 30 percent, rms energy spread below 1 percent and collider-level emittance preservation. An answer is a demonstrated configuration or a proof that the requirements are incompatible.","problem_ref":null,"references":"","settled_by":"An experiment accelerating a positron bunch meeting all four metrics simultaneously.","status_note":"Several schemes meet subsets of the requirements in simulation (2023-2026, e.g. magnetized wakes, arXiv:2608.30455); none meets all in experiment.","title":"Collider-quality positron acceleration in 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