Merging and disconnecting resonance tongues in a pulsing excitable microlaser with delayed optical feedback

The paper reports and documents the phenomena (connecting resonance tongues, creation of extrema of the rotation number at a saddle transition, and two local scenarios of tongue reorganization) with strong numerical evidence and clear heuristic arguments, but the key claims are explicitly presented as conjectural and are not proved (e.g., the necessity of torus break‑up from connecting tongues and the genericity of the disconnecting/disappearing scenarios) . The candidate model supplies a normal‑form–based proof sketch under generic RFDE assumptions, but leaves crucial steps unproven (e.g., the existence and global connection of S‑boundaries from p:q to p:(p+q) cannot follow from a purely local Neimark–Sacker normal form), and it slightly misstates the geometry of the connections (it claims ‘along the same T branch’ whereas the paper observes connections across the two T branches near the Hopf–Hopf point) . Both therefore fall short of a complete, rigorous proof; the paper is careful to label parts as conjectural, while the model claims more than it securely justifies.