Discuss Findings

over all 1747 numeric sanitized payloads, the strongest resolved slowdown appears in the N=100 runs before the time cap saturates larger systems: for K=8, ratio=0.001 gives mean normalized consensus time 50.00000 [50.00000, 50.00000] with completion 0.00000 [0.00000, 0.00000], while ratio=1.0 drops to 41.47158 [41.38313, 41.56003] with completion 0.46470 [0.46089, 0.46851]; for K=4 the same comparison is 49.99960 [49.99883, 50.00038] versus 41.80114 [41.71250, 41.88977] and completion 0.00001 [-0.00001, 0.00004] versus 0.44877 [0.44493, 0.45261]; at fixed ratio=1.0, increasing community count from K=2 to K=8 shifts N=100 consensus time from 47.22268 [47.16673, 47.27864] to 41.47158 [41.38313, 41.56003] and raises within-budget completion from 0.16047 [0.15774, 0.16321] to 0.46470 [0.46089, 0.46851].

CONFIRMED Strong modularity creates a real consensus bottleneck and, in the resolved regime, drives the process all the way to the simulation budget ceiling. The mechanism is two-stage coarsening: opinions align quickly inside communities, then spend most of the runtime waiting for rare inter-community copying events. Because many larger-system conditions saturate the common 50N cutoff, the effect is visible most cleanly in completion fractions rather than raw times alone. The result therefore supports a bottleneck-controlled crossover, with modular structure suppressing within-budget consensus well before fully mixed behavior is recovered.