We don't know what the "effective dimensionality" of the network of credit relations in the economy is, and it might even depend on other factors.

What we do know is that for any dimension there is a p_c, that is, that regardless of the structure of the financial system, for sufficiently high densities (how high depends on the details of the financial system) of "ponzi-financing economic units" the probability that there is a system-wide cluster of such units linked together by credit relations approaches 1. And then the probability of systemic crises is high since all that needs to happen is for one of the ponzi units in the cluster to go belly up.

That's all. I don't expect that estimating p_c is possible given plausibly available information.

But there's more. The system will naturally tend towards a p_c density of ponzi units, because at lower densities we have Minsky's natural tendency towards increasing leverage in stable times, and at higher densities crises quickly decompose existing clusters by, through bankruptcy, eliminating ponzi sites.

So after a fairly long period of financial stability one can be pretty confident the economy will be in the critical phase of the percolation system.

Economics is politics by other means