Routing, restart, and conversion

This overview explains how a frozen router, budgeted restart, and prefix conversion address costly exact computations. Protecting a catastrophic tail can help even when the route still loses overall to the best fixed representation. Imagine a job with a three-unit prefix and five-unit suffix. A routing budget expires after the prefix. Some partial state exists, but the complete output has not been delivered. The next strategy determines whether that partial work can be used. A full restart discards the useful partial state and runs the whole job again. The total is the spent prefix plus the repeated prefix and suffix, giving eleven units. The initial work must remain in the complete-request ledger. If conversion costs two and preserves enough state to continue at the suffix, the total is ten. That is better than this restart schedule. It does not establish that conversion beats every strategy available from the beginning. C9 freezes a static decision tree. C10 starts one exact representation and restarts after a product budget. C11 converts the already-built prefix into a packed representation so that prefix need not be recomputed. Use a conceptual work trace with prefix P and remaining work Q. Restart pays for P in the first representation and then repeats it in the fallback. Conversion pays for P once, a conversion step, and Q. These accounting expressions describe the routes, not measured elapsed times. A conversion may still cost more than choosing the best fixed arm at the start. The retained C9-C11 routes preserved exact outputs yet lost to the best fixed arm on their declared splits. C10's protection of a catastrophic tail is still a useful scoped result. It does not turn a losing median or aggregate into a successful default policy. With conversion costing four, the converted route totals twelve and is worse than the eleven-unit restart. The benefit depends on the actual conversion cost and on how much completed work it preserves. A fixed strategy that simply completes the original job costs eight in this example. It beats both the cheaper conversion schedule and the restart. Improving one adaptive route relative to another does not prove that adaptation itself is profitable. These numbers explain accounting choices rather than recreating historical timings. The retained routing results must still be read under their exact job definitions, fixed controls, and aggregate and tail criteria. Separate tail protection from aggregate profitability. Charge restart or conversion work and compare against the best fixed exact arm.