= Solution
\b[Five independent isolating <orbit> labels describe a regular closed, nonstationary <orbit> in three-dimensional space:] its <phase space> closure is one-dimensional. Five is the maximum at a nonzero flow vector, since every conserved differential annihilates that vector in the six-dimensional tangent space. A global <superintegrable Hamiltonian system> example is the <Kepler orbit>, where <specific orbital energy>, <angular momentum> and the <Laplace-Runge-Lenz vector> have two vector/scalar relations leaving five independent invariants. A circular or radial <orbit> requires a separate treatment of any rank-degenerate formula for these invariants. Five integrals do not force an escaping trajectory to be periodic: unbound <Kepler orbits> also have the conserved apsidal vector. The closure criterion concerns recurrent bound motion.
Closure of one resonant <orbit> need not imply five smooth independent integrals on an open neighborhood of all nearby <orbits>. The orbit-wise count and global superintegrability must be distinguished; the distinction matters in part (b).
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