Week 4: The race as a loop

Turn a legal tyre strategy into a finishing time by making every lap, stop and physical-set age transition explicit

15 March 2027

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A strategy becomes a result only after we say what happens on every lap. “Stop on lap 12” leaves too much hidden: which physical set is fitted, how old it is, when the stop loss enters the clock, and whether the proposed sequence was legal before the car moved.

This week we write those facts as state — the complete record needed to advance the race by one lap — and make one transition at a time. A stint is a run of laps on one physical tyre set. Tyre age counts the laps already completed on that set, so a fresh set starts at zero and a refitted set resumes its previous age. A stop after lap 12 means lap 12 still belongs to the first stint, the 22.0-second synthetic pit loss is added once, and lap 13 starts on the next set.

The boundary is severe on purpose: one car, a dry and uninterrupted 30-lap race, fixed parameters, no traffic and no random draw. The evaluator therefore returns the same finishing time — total elapsed time at the end of the race — and the same lap trace whenever its inputs are unchanged. It does not return a finishing position. There is nobody else to finish ahead of.

The deck builds the loop from a five-lap fixture whose every row closes by hand. It then runs SlopU’s legal M2 → H1 strategy, shows why stopping after lap 12 gives 2804.500 seconds, and exposes a tie with the reverse order. That tie is evidence about what the model has omitted. Week 5 adds other cars and makes track position matter.

In the lab you implement the validator and transition, reproduce the supplied trace, sweep the stop lap and reject an illegal input before it runs. The lab supplies Week 3’s legal sequences and 22.0-second estimate; you do not measure or enumerate them again.

Assignment 1’s model-fitness criterion asks whether a recommendation answers the question it claims to answer, obeys the regulations and names what it omits. This is that obligation with one car and nowhere for an omission to hide.