Long-horizon tasks remain uncommon in large language model (LLM) evaluation, and for a reason: when each step depends on the last, per-step accuracy that looks excellent in isolation decays catastrophically, as errors cascade and the end-to-end failure probability grows sharply with length. Existing agentic benchmarks report end-to-end success but confound this state-tracking difficulty with instruction interpretation, give no control group that isolates it, and are vulnerable to shortcuts such as a hallucinated final answer, so they cannot say why a long run fails. Whether an LLM can carry exact intermediate state across many tool calls at all is itself not well established. We test this cleanly by having the model compute a cryptographic hash, MD5, step by step: a sequence of $196$ dependent tool calls over $64$ rounds while it carries four $32$-bit words $(a,b,c,d)$ in its own context from one call to the next. Interpretation is trivial and, because we implement MD5 from scratch (RFC~1321), we align every call to the ground-truth trace and check the digest to the bit, so any failure is pure bookkeeping. gpt-oss-120b, a mixture-of-experts model with only $\sim$5.5B active parameters per token, at temperature $0$ with a short fixed prompt, carries the full state across all $196$ calls and returns the correct digest on a majority of completed runs. In the strongest setting we replace every primitive tool with a second LLM, so a driver and a worker compute the whole hash from scratch with no exact-arithmetic oracle in the loop. Two ingredients decide success and neither changes the weights: keeping the model's own reasoning in its context each turn, and voting over a thinking-enabled worker to remove its modular-arithmetic slips. We localize the residual failures by origin, separating state-carrying from arithmetic and from serving.

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