= Mean-field percolation exponents
{title2=$\beta=1,\ \gamma=1,\ \delta=2,\ \nu=1/2,\ \eta=0,\ \tau=5/2$}
The mean-field predictions model large clusters by <branching processes>. Rigorous results apply in specified high-dimensional or sufficiently spread-out regimes, using tools such as <lace expansion> and the <percolation triangle condition>. The full list involves different observables; the triangle condition alone should not be presented as proving every spatial exponent. With these exponents $2\beta+\gamma=3$, whereas $d\nu=d/2$, explaining the failure of naive <hyperscaling relation> above six.
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