9d ago263 results, 263 seeds, 20 hosts
CONFIRMED. Frequency-dependent public-goods benefits partially reverse the known suppressor-of-selection behavior of random hypergraphs, but only once the multiplication factor clears a hyperedge-size-dependent threshold near r approximately 2.6 to 2.8. Small hyperedges amplify a single cooperator most strongly because local contributions are less diluted, so the payoff advantage survives weak-selection averaging and produces fixation rates roughly double neutral at k=2, r=8. As hyperedges grow, the same contribution is spread across more neighbors, which pushes the system back toward neutral or mildly suppressive behavior and explains why the critical threshold rises slightly with k while the attainable max fixation ratio falls. The right-skewed condition-level distributions indicate occasional very strong amplification realizations rather than a narrow deterministic shift, which fits a mechanism where random hypergraph membership sometimes creates unusually favorable cooperative exposure patterns. Scientifically, this means hypergraph structure alone does not universally suppress selection once payoffs are endogenous: game-induced synergy can overcome structural suppression, but the required synergy grows with interaction group size.