Token Reduction Is Not Cost Reduction

arXiv:2607.12161v1 Announce Type: new Abstract: Context-reduction layers for API-based coding agents, including command-output compressors, retrieval rankers, and payload-optimizing proxies, are usually evaluated by how much text they remove. We ask instead: when does reducing retrieved context or tool output lower the actual billed cost of a coding agent without reducing task success or lengthening its trajectory? Our primary evidence is a pre-specified, hash-frozen, paired campaign of 2,908 provider-billed Claude Code runs, of which 2,848 were analyzed, covering 103 tasks, seven repositories, and three models. The campaign compared a baseline with two generations of hook-based compression and an API-boundary proxy, within a broader measured program of roughly 5,500 billed executions. Three findings emerge. First, prompt-cache traffic dominated cost composition. Cache creation and reads accounted for about 87% of reconstructed four-component cost, or about 80% of the actual bill, with an 8.7% dollar-weighted residual that retained telemetry could not attribute. On Haiku 4.5, this residual scaled with thinking effort. Second, tool-output reduction did not reliably predict billed-cost reduction. An arm that removed 38% of estimated raw tool-output tokens had 6.8% higher paired cost (95% CI: +2.8% to +11.3%), while per-task reduction was only weakly associated with cost change (Pearson r = 0.15, CI crossing zero). Third, compression can harm task completion by removing action-critical evidence. In a small single-shot study on SWE-bench-derived Go tasks, compression reduced patch application from 27/40 to 15/40 by corrupting verbatim edit anchors, and the compressed grounded arm produced fewer solves at higher observed cost per solve. We propose a layered evidence standard centered on success-adjusted billed cost rather than token reduction alone.