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The Brief Advanced Computerized Neuropsychological Battery (BACNB) was developed as a compact protocol to investigate, in a fully in silico environment, the functional geometry produced by four classical tasks: the Sustained Attention to Response Task, Stop-Signal Task, Flanker Task, and Digit Span. The study does not establish clinical norms or diagnostic validity. Its aim is to test whether synthetic agents completing all four tasks produce a coherent, reproducible, and theoretically interpretable state structure. We simulated 200,000 agents, each with continuous latent microparameters and observable metrics extracted from the four tasks. Measures were standardized into an oriented functional scale so that higher values represented greater cost under the task ecology, without implying biological inferiority. Variable clustering yielded 8 emergent cognitive parameters; agent clustering yielded 4 phenotypic-functional attractors. The main result is the BACNB Cognitive State Space: each agent is described by a compositional vector of relative approximation to attractors P1-P4. Because the weights sum to 1.00, the system has three degrees of freedom and can be visualized as a tetrahedron. The external comparison with Inhibitory Control, Working Memory, and Cognitive Flexibility showed partial convergence but did not literally reconstruct the Miyake model. The proposed interpretation shifts the battery from a taxonomy of deficits to a contextual cognitive kinematics in which functional cost depends on the relation among organism, task, and environment. This framing treats simulation as theoretical instrumentation for generating falsifiable hypotheses and clarifying which assumptions require empirical tests.