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**Admission responses.** This endpoint answers four ways when the task has no usable machine. The three 409s are told apart by `detail.code`; a billing refusal is told apart by its HTTP status: - `machine_not_ready` (409, with `Retry-After`) — provisioning is in progress. Retry. - `task_run_busy` (409, with `Retry-After`) — the task holds an active run lease. Retry. - `task_terminal_no_machine` (409, **no** `Retry-After`) — nothing will ever provision this task. Do not retry. - 402 or 429 — the payer was refused by the credit gate. Do not retry; surface the billing error. What `detail` holds on a refusal is described below. `Retry-After` is present on the two retryable 409s and absent on the terminal one, so it is the quick check; `detail.code` is the precise one. Retrying a terminal answer will never succeed. On a credit refusal this endpoint returns the upstream entitlement body under `detail` — its `error` field carries the upstream code, for example `CREDITS_EXHAUSTED` — and the task is marked terminal.