2 problems

Costate proportionality conjecture. The costate variables satisfy

Let $X$ be an $N$-dimensional Hilbert space, let $S:=\{x\in X\colon\|x\|=1\}$ be the unit sphere, and let $L:=\{x=\lambda a+\alpha b\colon\lambda\in\mathbb{R}\}$, where $a,b$ are o…