Discuss Findings

sigma_c/May prediction = random 1.05863 [1.05819, 1.05907], modular 1.11282 [1.11234, 1.11331], nested 1.03467 [1.03415, 1.03519], predator-prey 0.66458 [0.66310, 0.66606]; modular-random = +0.05419 [0.05356, 0.05483], nested-random = -0.02396 [-0.02465, -0.02326], predator-prey-random = -0.39405 [-0.39563, -0.39248].

CONFIRMED. The stability threshold depends strongly on interaction structure rather than following a single random-matrix baseline. Relative to the random case at 1.05863, modular networks shift upward to 1.11282, nested networks shift downward to 1.03467, and predator-prey structure drops much further to 0.66458. Those gaps are large and well resolved, with modular-random +0.05419, nested-random -0.02396, and predator-prey-random -0.39405. This shows that May's criterion needs structure-dependent corrections, with modularity stabilizing and nested or antagonistic organization destabilizing the system earlier.