Are Rovelli and Vidotto wrong about fermions?

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Carlo Rovelli will publicly admit that the claim is problematic.

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Francesca Vidotto will publicly admit that the claim is problematic.

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Ding Jia (question creator) will publicly admit that his own criticism is problematic.

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The claim will be modified or removed in a new edition of the textbook.

In their influential textbook "Covariant loop quantum gravity" physicists Rovelli and Vidotto claim that: "The formulation of the gravitational field as a pseudo-Riemannian metric cannot be fundamentally correct, because it does not allow coupling to fermions, and fermions exist in the world. For this, we need the tetrad formulation."

I think this claim is wrong, for reasons summarized in this youtube video: https://youtu.be/k-ECHbFKPic

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