Coverage↔connectivity frontier · 32×32 / 10 agents · 6 penalties × 4 seeds (24 runs)

Coverage↔connectivity frontier — turning one dial 0 → 4

What it tests: a single knob — the weight on the SOFT connectivity penalty — swept across six settings (0.0 · 0.25 · 0.5 · 1.0 · 2.0 · 4.0), four seeds each, everything else held fixed. As the dial rises the team is paid more to keep the comm graph together and less to spread out, so this traces the coverage-vs-connectivity trade-off curve directly: how much coverage you give up per unit of connectivity bought.

Key finding Measured live from the rendered tiles below. A clean monotone interpolation: as the dial rises 0 → 4, coverage slides down while connectivity climbs. In the training logs, strict connectivity (λ₂ > 0.5) climbs ≈ 7 → 30% — but saturates around 30% at 32²/10 no matter how hard you push. That ceiling is the connectivity wall, quantified. The live table below shows the same trade-off measured on the rollouts (coverage + giant-component connectivity).
Per penalty (ascending) — mean of 4 seeds · rollout coverage + giant-component connectivity (mean over the 100-step re-roll)
Soft penaltyCoverageGiant-component connectivityseeds
computing from the rendered rollouts…

The run list is grouped by penalty, ascending — step down the groups to watch the swarm pull tighter and cover less. Both columns are computed live from the rendered rollouts (strict λ₂ > 0.5 in the prose comes from the training logs); the giant-component figure is the mean fraction of agents in the largest connected component over the rollout.

t = 0