Generative AI has made it hard to establish whether a student produced a piece of assessed work. Building on the argument that validity matters more than cheating, this paper tests four propositions drawn from a strongly stated position: that redesign is more sustainable than detecting or banning AI; that asking students whether and how much AI they used yields low-value information; that unaided ability should be tested directly in controlled conditions; and that the same logic applies to peer review. The propositions are tested against two purposively sampled, coded corpora: 41 research and sector sources and 55 university and sector policy documents. Coding was by a single coder and the policy sample is UK-weighted, so counts describe the sample, not the sector. The propositions hold unevenly. Redesign over detection is well supported, but only as redesign plus assurance: 4 of 55 documents prohibit AI by default, though about 10 of the 55 are publisher or editorial policies that govern authors rather than student assessment; of the 23 that take a position on detection, 16 reject detectors and one requires them. Testing unaided ability is supported as one lane within a programme, not as a return to invigilation. The disclosure proposition is complicated: institutions treat disclosure as valuable, yet the limited evidence suggests many students do not complete required declarations. The peer-review extension is plausible but under-examined. The field is converging on graded permission scales and two-lane designs, and 31 of 55 documents define named categories of use. From these findings the paper builds a nine-step decision chain that extends outcome-first design logic: the role of AI is decided after the evidence an outcome requires. It also separates design moves that add temporary friction from those that provide assurance. A worked example and the full policy matrix are included.
We measure, without sampling error, the probability a language model assigns to each integer from 1 to N when asked for a random number. For a fixed prompt the model defines one probability vector, which we compute by summing over each integer's scored spellings rather than estimate by sampling, removing the noise that limits earlier studies [1, 4]. We evaluate 18 open-weight model lines at five ranges up to N = 100, under 29 decoding configurations, on two inference stacks; 15 of them have matched base and instruction-tuned checkpoints that both give usable answers. Instruction tuning makes the distribution less uniform in all 15 pairs. It installs one heuristic, round-number avoidance, and sharpens another, endpoint avoidance. Base checkpoints do not avoid round numbers once the endpoints are removed from those sets; tuned checkpoints avoid them, multiples of 10 almost completely. Base checkpoints return the endpoints 1 and N at 0.30 to 0.60 of the interior rate; tuned checkpoints almost never return them. A preference for odd numbers is consistent across tuned checkpoints only at N = 100, where base checkpoints also show it weakly. Endpoint avoidance and the odd preference fit the account Kubovy and Psotka [6] proposed for human number choice; round-number avoidance is not part of that account, and the midpoint avoidance it predicts is essentially absent, with one slight exception at N = 100. Tuning does not install a new favourite integer shared across models: above N = 10 no modal integer is shared by more than 42 percent of tuned conditions, and P (17) rises in 10 of 15 pairs and falls in 5. The concentration is present in the model's own distribution: at temperature 1.0, nucleus truncation at top-p 0.95 adds a median of 0.035 to the total variation distance.