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We discuss the convergence of level truncation in bosonic open string fieldtheory. As a test case we consider the calculation of the quartic tachyoncoupling $\gamma_4$. We determine the exact contribution from states up tolevel L=28 and discuss the $L\to\infty$ extrapolation by means of the BSTalgorithm. We determine in a self-consistent way both the coupling and theexponent $\omega$ of the leading correction to $\gamma_4$ at finite $L$ that weassume to be $\sim 1/L^\omega$. The results are $\gamma_4 = -1.7422006(9)$ and$|\omega-1|\lesssim 10^{-4}$.}Comment: 17 pages, 2 eps figure

Level truncation and the quartic tachyon coupling