Visibility of heteroclinic networks

The paper’s claims match known dynamics and its own definitions: (i) the Guckenheimer–Holmes (GH) cycle is asymptotically visible when ρ123>1 and only Lyapunov-visible at resonance ρ123=1, where trajectories approach nearby periodic orbits rather than the cycle itself, so quasi-visibility fails ; (ii) the Kirk–Silber (KS) network is never visible as a whole, for any parameters, because trajectories asymptote to at most one subcycle and do not repeatedly visit the entire network . The candidate solution incorrectly asserts quasi-visibility (hence A-visibility) at ρ123=1 by forcing a prefactor K ε^κ<1 via shrinking sections; this contradicts the paper’s resonance picture with an infinite family of periodic orbits near the GH cycle (distance to the cycle does not tend to zero) . The KS analysis in the candidate is directionally consistent with the paper’s conclusion but is not needed to overturn the main discrepancy at GH resonance.