The Ramanujan Machine continued fraction conjecture for $-\pi/4$

Consider the generalized continued fraction whose initial terms are

$$\cfrac{1}{-1 + \cfrac{1}{-4 + \cfrac{-2}{-7 + \cfrac{-9}{-10 + \cfrac{-20}{-13 + \dots}}}}}.$$

Ramanujan Machine conjecture. The continued fraction equals

$$-\frac{\pi}{4} = \cfrac{1}{-1 + \cfrac{1}{-4 + \cfrac{-2}{-7 + \cfrac{-9}{-10 + \cfrac{-20}{-13 + \dots}}}}}.$$

The identity was discovered algorithmically by the Ramanujan Machine and is presented here as a conjecture originating from that framework. The supplied text does not establish whether the conjecture has been resolved; the paper's stated aim is to provide a formal analytic proof via contiguous Gaussian hypergeometric functions and continued-fraction transformations.