Precision asymptotics of string amplitudes

Recent work revealed a tension between the Gross-Mende analysis of the high-energy fixed-angle behavior of string amplitudes and the explicit numerical data. Motivated by this puzzle, we revisit the problem of classifying saddle-point geometries for the one-loop amplitude. We find an infinite family of complex saddles that dominate the high-energy regime. Using general constraints and matching to numerical data, we formulate a bootstrap problem that determines their multiplicities. This procedure yields a precise asymptotic expansion of the one-loop amplitude at high energies. The resulting oscillatory contributions lead to a much richer high-energy behavior than that predicted by the original Gross-Mende analysis.