Falsification of the Tropical Mixed Volume Hypothesis: Dimension-Dependent Phase Transitions and Parameter Redundancy in Neural Network Generalization

  The hypothesis that tropical mixed volume (MV) predicts neural network generalization (H-P1) was generated by the Explore mode of a multi‑model orchestration system (eVoiceClaw V3). This note reports its experimental test across input dimensions d = 32–64 and on CIFAR-10. The results definitively refute a universal monotonic relationship. MV correlates negatively with test error at d=32 (underfitting), strongly positively at d=38 (overfitting), and collapses to near zero at d=40 (an anomaly). Moreover, MV is statistically indistinguishable from simple parameter count (ρ differences <0.05). This negative result demonstrates that tropical MV provides no unique predictive value beyond parameter counting, and its utility is dimension‑dependent with a singular anomaly at d=40.