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We prove that the general mean-field type networks at low load behave inaccordance with the Poisson Hypothesis. That means that the networkequilibrates in time independent of its size. This is a "high-temperature"counterpart of our earlier result, where we have shown that at high load therelaxation time can diverge with the size of the network ("low-temperature").In other words, the phase transitions in the networks can happen at high load,but cannot take place at low load.

Absence of Breakdown of the Poisson Hypothesis I. Closed Networks at Low Load