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In any hadron synchrotron, the half-integer resonance is among the strongest effects limiting the achievable maximum beam intensity. The heavy-ion superconducting synchrotron SIS100, currently under construction at GSI, should provide intense beams for the future FAIR experiments. Using SIS100 as an example, this paper develops a quantitative framework for characterizing the half-integer stop band for realistic, Gaussian-like distributed bunched beams. This study identifies the tune areas affected by the gradient-error-induced half-integer resonance for varying space charge strengths. A key insight of our analysis is that, for bunched beams a relatively small gradient error can result in a large half-integer stop band width. The achievable maximum bunch intensity, often referred to as space charge limit, is thus reduced significantly. This contrasts the findings in existing studies in literature based on more simplified beam distributions. The reason for discrepancy is identified in the increasing stop band width for Gaussian distributions when space charge becomes stronger, which appears on longer time scales as relevant for synchrotrons. The role of synchrotron motion in providing continuous emittance growth across the bunch is scrutinized. To minimize the half-integer stop band for a bunched beam, and hence increase the space charge limit, lattice corrections are applied: Including space charge in the optimization procedure recovers results equivalent to conventional lattice correction. Therefore, we find that conventional correction tools are well suited to increase the gradient-error-induced space charge limit of synchrotrons.