Nadler–Tanaka's point-generation conjecture for Lagrangian cobordisms

Set $M=\Lambda=pt$, consider $\Lag_{pt}(pt)$, and let

$$\cE=\operatorname{End}_{\Lag_{pt}(pt)}(pt)$$

be the endomorphism $E_1$-algebra spectrum. An object is a generator if its morphisms to every shift detect the zero object, and $\cE\operatorname{Perf}$ denotes the stable $\infty$-category of perfect $\cE$-modules.

Nadler–Tanaka's point-generation conjecture. The object $pt\in\Lag_{pt}(pt)$ is a generator, every object of $\Lag_{pt}(pt)$ is a finite colimit of objects $pt[k]$ for $k\in\mathbb Z$, and the Yoneda functor induces an equivalence

$$\Lag_{pt}(pt)\simeq \cE\operatorname{Perf}.$$

If true, this reduces the study of $\Lag_{pt}(pt)$ to the endomorphism algebra of its point object. The source gives no resolution of the conjecture.