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The shortcut fails when quantum fluctuations of that energy are large, and its precise range of validity is unknown.","posed_since":"","precise":"Semiclassical gravity sets $G_{ab} = (8\\pi G/c^4) \\langle T_{ab}\\rangle_{\\omega}$ for a Hadamard state $\\omega$. Determine conditions on $\\omega$ and the spacetime (for example bounds on the fluctuation $\\langle T_{ab} T_{cd}\\rangle - \\langle T_{ab}\\rangle\\langle T_{cd}\\rangle$ relative to $\\langle T_{ab}\\rangle^2$, smeared over curvature-scale regions) under which solutions approximate the full quantum theory to leading order in $\\hbar$, and give a well-posed initial value formulation that excludes higher-derivative runaway solutions. An answer is a theorem or a large-$N$ derivation with stated error bounds.","problem_ref":null,"references":"","settled_by":"A proof, in a large-N or other controlled limit, that solutions of the semiclassical equations track expectation values of a quantum theory of metric and matter with explicit error bounds.","status_note":"Large-N arguments and order-reduction schemes exist; no general error bound is known as of 2026.","title":"When is the semiclassical Einstein equation a controlled 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