When is one data-ordering scheme better than another? This release shows that the answer depends on the mathematical quantity being compared. Its first paper gives an exact computer-assisted classification of the Recht–Ré matrix inequality through five factors, plus balanced six-factor families. Its second paper follows one rational counterexample into repeated optimisation dynamics. There, reshuffling can have a worse mean iterate but a better expected squared error. Fresh reshuffling beats with-replacement sampling in the certified invariant Gram channel at every positive epoch count. Reusing one permutation, called single shuffle, agrees with fresh reshuffling after one epoch but is strictly better at every later epoch at the endpoint, with exact phase transitions away from it. Averaging independent runs introduces a separate bias–variance crossover at one hundred and forty-five over seven. These are exact, family-specific and metric-specific statements, not a universal ranking of optimisation algorithms. The public archive includes both papers, exact rational certificates, separate internal verifiers, mutation controls, manifests, checksums and a clean-extraction replay receipt. Those checks establish artifact identity and producer-side internal replay. They do not establish independent reproduction, formal verification, specialist acceptance, peer review, novelty priority or real-world performance.