Conflicting Supervision Moves Commitment, Not Capability

Post-training corpora routinely contain the same problem written under several equally correct conventions, and practitioners ask whether the order in which such data is presented matters. The published record is divided: large ordering effects and none at all are both reported, and the disagreement is usually attributed to task or scale. We show it is attributable instead to the learning-rate schedule — something every run fixes and no run reports as a variable. We prove a bound in which the arrangement and the learning-rate schedule enter an ordering effect as separate multiplied factors — the arrangement only through the period of its alternation, the schedule only through how much weight the endpoint can place on any one moment of the run — so the schedule is not a background condition for the question but the averaging operator that decides it. Tested on ten orderings of one conflicted corpus, run twice under families differing in lr_scheduler_type and nothing else, the interior spans 11.63 contrast floors at a constant rate and is monotone in how blocked the arrangement is, while under the single cosine every published arm uses the same ten arms occupy two distinguishable states where their own resolution would allow about ten; three mechanisms we had preregistered were falsified. What the path writes is not capability but commitment: across twelve arms accuracy summed over both conventions is constant to within 9.7% while the allocation share runs 0.04 to 0.87, so a 12.29 sigma arrangement effect is exactly zero under a convention-agnostic score. An ordering result is therefore uninterpretable without the schedule it was measured under, and marking the convention in the prompt collapses the effect and recovers 87.5% of the union ceiling.