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 Sex differences in cognition are well documented, but their biological roots - especially network-level origins, remain elusive due to hormonal, environmental, and societal confounds. To isolate genetic effects, we used isogenic iPSC-derived neurons from a rare mosaic Klinefelter donor. Utilizing calcium imaging assays, we revealed a temporal divergence in maturation as XY networks show augmented connectivity patterns early on, while XX networks surpass them later on. Conversely, XY networks exhibit an increasing level of synchronization over time, while XX networks exhibit more connections. We demonstrate that such features alone accurately classify independent XX/XY networks, revealing a robust, generalizable signature.Simulating information flow revealed faster, broader spread in XY networks at later developmental stages, indicating differences in function. Modeling cognitive tasks, we found XY networks enable faster, more accurate focused problem-solving, while XX networks excel in parallel information processing. This suggests that chromosomal composition shapes cognition via inherent differences in network topology.To mechanistically unify the findings, we introduced a generative network model governed by a single parameter p (cooperativity), which controls how local synchrony is amplified into global connectivity. Varying p generated a family of networks spanning hypocooperative, optimal, and hypercooperative regimes, simultaneously moderating topology and link weights. Remarkably, empirical XX and XY networks map onto distinct regions of the cooperativity landscape, as XX networks cluster closer to an intermediate p-range, whereas XY networks exhibit higher effective cooperativity.Together, our results identify cooperativity as a unifying, quantitative biomarker linking chromosome composition to network topology and emergent cognitive function. This work reveals fundamental sex-based differences in cortical network organization and provides a principled framework for sex-aware neuroscience, with implications for personalized diagnostics and targeted interventions.