NAS-Bench-201-VStar: exact optimal value function over the cell-construction MDP

Exact optimal value function V*(s) over all 19,531 states of the NAS-Bench-201 cell-construction Markov decision process, for CIFAR-10, CIFAR-100 and ImageNet16-120, together with the mean-over-completions potential and an exact criticality profile. Ng, Harada and Russell (1999) proved that potential-based reward shaping preserves the optimal policy and that the optimal potential is V*. The second half of that result is almost never used, because in practically no domain is V* computable: a proposed potential can only be compared against other potentials, never against its theoretical optimum. NAS-Bench-201 is an unusual case — the search space is exhaustively evaluated, transitions are deterministic, the horizon is fixed at six steps and the reward is terminal — so V* follows from backward induction over a tree of 19,531 nodes in seconds of CPU. This artifact publishes that computation. It also publishes the criticality profile with the permutation null required to read it. A profile aggregated by episode position is biased toward the final steps by tree averaging alone, so the raw profile is not evidence of structure: the null puts 88-95% of criticality on the last three steps, MORE than the 78-88% observed. Read against the null (residual = share / null), the three edges leaving the input node score 3-5x and do not overlap with the other three on any dataset, while the final step falls below chance. This inverts the naive reading, and an earlier uncorrected version of this claim is retracted in the documentation rather than removed. Two limits are stated up front: the law is global and fails locally (the share of a single step ranges from 6.7% to 99.1% across the 25 depth-2 subtrees), and the profile is descriptive rather than a control lever. Root V* values are 91.6067% / 73.4933% / 46.7333%, reproducing the published global optima, which is an independent check on the backward induction. Built from the authoritative NATS-Bench API and NOT from NAS-Bench-Suite-Zero's val_accuracy field, which disagrees by up to 0.60 pp with a sign flip. Ships with checksums and a verification script that runs 53 structural checks.