Software engineering agents have advanced rapidly, but scaling their training remains constrained by the limited availability of high-quality executable tasks. Development histories contain valuable signals for constructing such tasks, yet they often require substantial reconstruction due to incomplete environments, missing tests, and inconsistent artifacts. We present SWE-Stream, a system for scaling executable SWE training data through progressive construction and elastic streaming execution. SWE-Stream progressively validates and refines task candidates, reusing existing artifacts when possible and applying targeted completion only when necessary. An elastic scheduler asynchronously coordinates construction stages under shared resource constraints, adapting execution budgets based on observed workload demands. Using development histories from 10,728 repositories across six programming languages, SWE-Stream constructs 80,874 validated tasks and collects 118,688 successful trajectories. Fine-tuning Qwen3-30B-A3B-Thinking-2507 on these trajectories achieves resolve rates of 69.0%, 49.3%, and 45.42% on SWE-bench Verified, Multilingual, and Pro, respectively. In a controlled comparison with approximately matched training budgets, SWE-Stream achieves a 45.6% resolve rate on SWE-bench Verified, outperforming three existing data sources. Moreover, its streaming construction strategy improves efficiency, delivering $1.45\times$ the accepted-task throughput of batch construction and accepting 13.2% more tasks than fixed-limit streaming.

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