Balanced Support Calibrations for Moser's Worm Problem: Exact Certificate and Bound of Triangular Cover

Moser's worm problem asks for a planar region of minimum area containing a congruent copy of every rectifiable planar arc of length one. We study the Bellman's lost-in-a-forest problem escape path for the isosceles triangle \[ T=\text{conv}\{(-c,0),(c,0),(0,s)\},\qquad s=\frac{766}{\sqrt{625565}