Planning-then-executing loses to direct execution at 12,000 tokens, and the gap closes as the budget doubles

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arXiv 2609.20449 (submitted 2026-09-17) runs controlled workflow experiments on externally verified software-engineering tasks in two matched resource panels. Direct execution scores 59.6 percent at both 12,000 and 24,000 logical-token ceilings, while information-constrained planning rises from 36.2 to 51.2 percent, narrowing the planning disadvantage by 15.0 points (95% task-cluster bootstrap interval 4.2 to 25.8). In a read-only planning campaign, letting the planner see the task issue is worth about 16 points at 12,000 tokens. The practical read: splitting an agent into planner and executor only pays once each stage has room to think.