= Solution
A <continuum limit of a quantum field theory> sends the <ultraviolet cutoff> $\Lambda_0$ to infinity while holding chosen physical masses and amplitudes fixed. In cutoff units this requires a diverging <correlation length>, so the bare couplings must be tuned onto the <critical surface> of an ultraviolet <renormalization-group fixed point>. Each <relevant direction of a fixed point> requires one coordinate fixed by measurement; predictivity requires only finitely many such directions, and irrelevant microscopic details disappear.
Several behaviors are possible. In an <asymptotically free> theory the trajectory approaches a <Gaussian fixed point> in the ultraviolet and interactions vanish logarithmically. In an <asymptotically safe quantum field theory> it approaches a non-Gaussian fixed point with finitely many relevant directions. A theory with a <Landau pole> may possess only a <trivial quantum field theory> as its continuum limit; retaining a nonzero interaction then requires a finite cutoff. Finally, if no ultraviolet-complete trajectory exists, the model remains an <effective field theory> valid only below a physical cutoff.
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