This paper establishes analytical stability boundaries for robot-mediated human-human (dyadic) interaction systems, subject to haptic communication under network-induced time delays. Bypassing conservative approximations, we employ a frequency-domain zero-crossing methodology to extract explicit stability limits based on the robotic hardware dynamics and coupling stiffness. To demonstrate the scalability of this mathematical framework, we extend the analysis from an elastic coupling to a highly complex, asymmetric virtual proxy topology. The theoretical analysis reveals how interaction stiffness non-linearly constrains the system's stability margin, heightening its vulnerability to delay. Furthermore, we validate these theoretical boundaries through experimental trials, highlighting the correlation between analytical stability margins and empirical motor performance. The proposed framework provides rigorous design guidelines for stable remote dyadic systems and suggests the prerequisites for effective delay-compensation strategies.

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