= Solution
<Phase space> combines all independent <canonical coordinates> and <momenta>. Its <Hamiltonian> <velocity> has divergence $\sum_i[\partial_{q_i}H_{p_i}-\partial_{p_i}H_{q_i}]=0$ by equality of mixed <Derivative>[derivatives]. Thus an infinitesimal material phase volume has zero fractional rate of change. This is <Liouville's theorem>, valid also for explicitly time-dependent <Hamiltonian>[Hamiltonians]. It preserves fine-grained volume, not necessarily the area of any projected coordinate pair.
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