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An answer is a theorem with stated assumptions, or a model counterexample with controlled $T_c$ above the bound.","problem_ref":null,"references":"","settled_by":"A proof within a controlled model of electrons coupled to phonons (for example Holstein at all couplings via exact numerics) or an explicit counterexample.","status_note":"Bounds proposed in 2018 and 2025 are heuristic or order-of-magnitude, placing the ceiling at about $10^{2}$ to $10^{3}\\,\\mathrm{K}$.","title":"Is there a rigorous upper bound on phonon-mediated 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