Decomposition Buys Budget at Best, Nothing Usually

One model that plans, solves the parts and assembles buys budget, and only budget: the gain lands on the problems where its single pass is cut off by the token cap and on no others; what it cannot solve whole it cannot solve in pieces. Three other models solving the parts cost 2–17× more in dollars at the same token cap and solve no more. The last swarm operator the earlier notes had not measured: split a problem into subtasks and solve them one by one, with the same model or with three others, at the same token budget as one whole attempt. Pre-registered on 97 problems chosen by how often each model already solved them in sixteen whole attempts. On the twenty problems DeepSeek v3.2 solves four times in sixteen or fewer, decomposition adds nothing on the fourteen numeric ones: pass@4 0.21 against 0.21, none of the seven never-solved problems solved in eight tries; on the six multiple-choice ones it 'solves' never-solved items at the 25% guessing rate. On GLM's 38 problems that fail because one long pass runs out of tokens, decomposition gains 34 points, above the model's own pass@16: a budget effect. DeepSeek loses 41 points on medium and easy problems because it does not shorten its steps. Handing subtasks to other models is never better than splitting within one outside GPQA, where the difference is inside the noise. In dollars a split attempt costs DeepSeek 3.5–9 whole draws and at equal spend the single model ties or wins everywhere. Cost $5.73.