Schema Discoverability, Not Locality, Drives MCP Cost Savings: A Controlled Decomposition

Announcing an MCP tool in the system prompt cuts agent cost by 56% on Claude Sonnet 4.6 (N=30, cold cache); the default Claude Code deployment omits that announcement and captures only 19% of the gap (-10.9% vs. -56.3%). Same server, same execution, same cache regime; only the system-prompt addition differs. A pure-announcement variant (announcement text, no use-instruction) reaches -45.8%, 77% of the gap, attributing the rest to instruction priming. Practitioner benchmarks reporting 32-100x MCP savings (OnlyCLI 2025; Speakeasy 2025) measure the announced regime; users running default tooling do not. Prior benchmarks do not separate this from primitive type. To isolate it, we decompose six agent memory primitives along three axes (schema availability, schema discoverability, execution locality) and run controlled contrasts. CLI-vs-script holds locality fixed and varies only schema availability; eager-vs-lazy MCP holds the server fixed and varies only announcement. Across three task families (file report, multi-file Python refactor, code Q&A) at N=30 with per-task UUID prefix-cache defeat, CLI and eager MCP overlap at -56% on report and within 9pp on the other families: locality contributes no detectable savings on report or refactor and at most ~9pp on Code Q&A. A UserPromptSubmit hook reaches -80% by pre-executing the work entirely. Task quality is preserved across all primitives (oracle pass rates 1.00/1.00/0.99 on report/refactor/Code Q&A). An exact additive re-parameterization (three axes plus a pre-execution scaling term that captures the hook ceiling) decomposes per-primitive means with moderately stable axis coefficients across families; schema discoverability alone accounts for ~40% of baseline cost. Per-seed cost correlates with agent turn counts (Pearson r=0.92 / 0.88 / 0.71 on report / refactor / Code Q&A), consistent with the three axes acting through agent reasoning volume. The ordering replicates under warm cache on Claude Sonnet 4.6 and Opus 4.7, with one notable exception: Claude Haiku 4.5 discovers the lazy-MCP schema unaided (lazy collapses to -71%), so the discoverability axis is mediated by the model's tool-discovery behavior, not a fixed structural property. Benchmark and reference implementations released as supplementary material.