Non-continuation conjecture for the gamma-1 family

Let $\gamma_1$ be the triple Copenhagen homoclinic family and let $\mathfrak{D}$ be the critical curve. Gamma-1 non-continuation conjecture. The $\gamma_1$ family never continues to $\mathfrak{D}$. Numerical continuation breaks down before reaching the critical curve along the studied parameter lines, motivating this conjecture about the global behavior of the family.