Summary

The reasoning part treated reasoning as a control problem around computation. The lever varies. Sometimes the prompt itself elicits more latent work; in other cases the system searches over chains, trees, programs, solver calls, or proof scripts. A verifier may select among candidates, or training may work to make the useful trace habitual. And the service can simply spend extra computation at inference time when a request appears hard.

The benefit is real but conditional. More computation can improve coverage and selection, yet it can also hide failure, inflate latency, and spend budget on tasks whose difficulty was never measured. The part therefore pushes reasoning claims into operational questions: where is the extra work paid for, who checks it, what trace is kept, and what rule stops the loop?

The durable takeaway is that reasoning systems are not defined by a mystical internal faculty. They are defined by budgets, search spaces, verifiers, traces, and stopping rules. The open problem is routing: when test-time compute keeps helping, when it saturates, and how a production service should distribute scarce reasoning budget across real workloads. Part V turns that routing problem into serving machinery, where latency, batching, cache residency, and price decide whether the extra thinking can be offered at all.