We demonstrate that the energy scaling limits observed in dense neuromorphic architectures arise from a single combinatorial mechanism: the pairwise tracking of correlations within bounded-memory neurons. Using a custom simulation engine calibrated against published Intel Loihi 2 performance data, we show that Informational Residue scales as R = αC² , where C is the relational complexity of the network. A negative-control experiment — capping the interaction window W — suppresses the quadratic exponent toward linearity (p ≈ 1.07 at W = 5), establishing pairwise correlation counting as the causal driver. These results locate the “Efficiency Cliff” in the Closure Postulate: bounded memory forces periodic reset operations whose cost grows superlinearly, linking datacenter thermal loads to the thermodynamic cost of collapsed informational trajectories. ** Full companion PYTHON code and pre-computed results are included as supplementary material. **