Asymptotic of a 4F3 hypergeometric function at unit argument

Derive the large-t asymptotic 4F3(1, t, t, t + 3; t + 1, t + 1, t + 1; 1) ∼ 2 t^2, thereby rigorously establishing the approximation used to adjust the polar square root spiral’s radius in the H1(t) construction.

Background

To improve the unibike approximation, the authors introduce a radial adjustment based on a generalized hypergeometric function 4F3 at unit argument and conjecture its asymptotic growth as 2 t^2.

They note that, despite existing research on hypergeometric asymptotics, this specific result appears unproved; confirming it would provide theoretical grounding for their improved spiral model.