Verified solutions and certificates for three open scheduling benchmark instances (nurse rostering MER and MER-A; medical student scheduling I40_12_1)

This deposit records three results on public combinatorial optimisation benchmarks, each accompanied by the solution file itself and the complete, unedited transcript of the checks run on it. Nurse rostering, instance MER (Employee Scheduling Benchmark Data Sets, University of Nottingham, XML schema 3.0): a roster of penalty 7080, improving the previous best known solution of 7081. The instance is now bracketed in [7079, 7080]. Nurse rostering, instance MER-A (same benchmark, XML schema 2.4): a roster of penalty 7320, improving the previous best known solution of 8779 by 16.6 per cent, together with the first lower bounds ever published for that instance: 5240 for the instance, and 7070 over the rosters expressible in the benchmark's own solution format, which brackets it in [7070, 7320]. Medical student scheduling, instance I40_12_1 of Dataset 2 (Zanazzo, Ceschia, Dovier and Schaerf, Journal of Scheduling 28(2):233-246, 2025, DOI 10.1007/s10951-024-00806-z): a proof that the optimum is exactly 4127, closing the instance. The previous best upper bound was 4237 (CPLEX, one hour). This is the first instance of Dataset 2 to be closed, and the deposited optimal schedule was found independently of the authors' published one. For each result the deposit contains the solution in the benchmark's own format, the full output of an independent checker, a second implementation of the same constraint semantics for cross-checking, SHA-256 digests of every file, and a record of solver versions, operating system, hardware and running times. Every checker is first calibrated against published ground truth: 5 of 5 closed instances for result 1, 41 of 41 published solutions for result 2, and 129 of 129 published solutions for result 3. Result 3 is additionally verifiable end to end with the original authors' own MiniZinc model and a public solver. This is a data and certificate deposit, not a paper. It records what was achieved and how it can be checked, and does not describe how the solutions were found. Benchmark instances and datasets are not redistributed here; they belong to their maintainers and authors.