Sequence positivity through numeric analytic continuation: uniqueness of the Canham model for biomembranes

We prove solution uniqueness for the genus one Canham variational problem arising in shape prediction of biomembranes. The proof builds on a result Yu and Chen that reduces to proving positivity sequence defined by linear recurrence relation with polynomial coefficients. combine rigorous numeric analytic continuation D-finite functions classic bounds from singularity analysis derive an effective index where asymptotic behaviour sequence, which is positive, dominates behaviour. Positivity finite number remaining terms then checked separately.Mathematics Subject Classifications: 05A16, 68Q40, 30B40Keywords: Analytic combinatorics, D-finite, P-recursive, positivity, model