A No-Go Theorem for Unbounded Cognitive Integration --- Why Stable Cognition Cannot Exist Under Near-Total Functional Accessibility

It is widely assumed across neuroscience, cognitive science, and artificial intelligence that increasing functional integration within a cognitive system monotonically improves performance, coherence, or intelligence. Despite its prevalence, this assumption has rarely been subjected to formal impossibility analysis. In this work, we present a constraint-based computational study examining whether abstract cognitive systems admit arbitrarily high global integration while remaining stable and self-consistent. Using an implementation-independent dynamical framework that enforces finite energy dissipation, information-flow conservation, noise propagation, causal coherence, and self-model consistency, we progressively increase functional integration from weakly coupled regimes to near-global accessibility. We find that beyond a critical integration threshold, stable cognition becomes impossible. The system undergoes a sharp phase transition marked by runaway causal loop density, interference-dominated dynamics, and collapse of coherent self-modeling. No admissible cognitive attractor exists beyond this boundary, regardless of initialization or evolution history. This result constitutes a no-go theorem for unbounded cognitive integration. It demonstrates that maximal accessibility is not merely unnecessary but fundamentally incompatible with stable cognition under minimal physical and informational constraints. The findings imply that modularity, selective access, and attentional bottlenecks are not implementation artifacts or evolutionary accidents, but necessary conditions for cognitive stability across all possible substrates.