= Solution
An <isolating integral> is a single-valued <integral of motion> $I(\mathbf x,\mathbf v)$ whose fixed value confines an orbit to a lower-dimensional level set of <phase space>. Along the flow, $dI/dt=0$; for an autonomous <Hamiltonian>, this means $\{I,H\}=0$. Several <isolating integrals> are independent when their gradients are linearly independent on the regular region considered. Counting them requires a specified domain: merely local orbit labels in a flow box do not establish global single-valued integrals. The following cases concern regular globally meaningful orbit constraints.
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