  Quantum bound-state energies are assumed generated by PT-symmetric
Hamiltonians H where P is, typically, parity. It is known that their spectrum
only remains real and observable (i.e., in the language of physics, the
PT-symmetry remains unbroken) inside a certain domain D of couplings. We show
that the boundary of this domain (i.e., certain stability and observability
horizon formed by the Kato's exceptional points) remains algebraic (i.e., we
determine it by closed formulae) for a certain toy-model family of
N-dimensional anharmonic-oscillator-related matrix Hamiltonians with dimensions
between N=2 and N=11.
