Determine the finite contact correction in the top-zipped phase

Determine the precise asymptotic value of the lower-pair contact statistic m_b(a,b) in the top-zipped phase of the three-osculating-walk star model, beyond the established estimate m_b(a,b)=O(1).

Background

In the top-zipped phase, the upper two walks have a macroscopic number of contacts, while the lower-pair contact number remains bounded. The authors expect an expansion of the form m_b(a,b)=const+o(1), but their computer algebra calculations could not extract the constant term from the quartic generating function. This leaves the precise finite contact contribution unresolved.