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The dilemma that neurotheorists face is that (1) detailed biophysical models that can be constrained by direct measurements, while being of great importance, offer no immediate insights into cognitive processes in the brain, and (2) high-level abstract cognitive models, on the other hand, while relevant for understanding behavior, are largely detached from neuronal processes and typically have many free, experimentally unconstrained parameters that have to be tuned to a particular data set and, hence, cannot be readily generalized to other experimental paradigms. In this contribution, we propose a set of "first principles" for neurally inspired cognitive modeling of memory retrieval that has no biologically unconstrained parameters and can be analyzed mathematically both at neuronal and cognitive levels. We apply this framework to the classical cognitive paradigm of free recall. We show that the resulting model accounts well for puzzling behavioral data on human participants and makes predictions that could potentially be tested with neurophysiological recording techniques.