Recently, advances in processor architecture have become the driving force for new programming models in the computing industry, as ever newer multicore processor designs with increasing number of cores are introduced on schedules regimented by marketing demands. As a result, collaborative parallel (rather than simply concurrent) implementations of important applications, programming languages, models, and even algorithms have been forced to adapt to these architectures to exploit the available raw performance. We believe that this optimization regime is flawed. In this paper, we present an alternate approach that, rather than starting with an existing hardware/software solution laced with hidden assumptions, defines the computational problems of interest and invites architects, researchers and programmers to implement novel hardware/software co-designed solutions. Our work builds on the previous ideas of computational dwarfs, motifs, and parallel patterns by selecting a representative set of essential problems for which we provide: An algorithmic description; scalable problem definition; illustrative reference implementations; verification schemes. This testbed will enable comparative research in areas such as parallel programming models, languages, auto-tuning, and hardware/software co-design. For simplicity, we focus initially on the computational problems of interest to the scientific computing community but proclaim the methodology (and perhaps a subset of the problems) as applicable to other communities. We intend to broaden the coverage of this problem space through stronger community involvement.