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This certainly sounds like a very big claim so I've been trying to read the preprint to find out about all the fine prints. Below is my attempt to summarize their basic argument based on my first pass at the preprint. I simplify it a bit which may leave some room for ambiguity.

There are 4 players.

**Wigner (W), his assistant (A), his friend 1 (F1) and friend 2 (F2)**. I can think of them all as robots that do quantum experiments, record the outcomes in some physical states, and process that information to make predictions. No consciousness is required, and in particular, I don't have to assume that macroscopic conscious human beings can be put into a superposition.

**Step 1**F1 observes one of two possible outcomes from measuring the state $$ \sqrt{\frac{1}{3}} |H\rangle + \sqrt{\frac{2}{3}} |T\rangle $$ in the "Head" ## |H\rangle ## or "Tail" ## |T\rangle ## basis. F1 then coherently prepares a spin down state ## |\downarrow \rangle ## if she observes Head or ## |\rightarrow \rangle = \sqrt{\frac{1}{2}} = |\uparrow \rangle + |\downarrow \rangle ## if she observes Tail, resulting in the entangled state $$ | \psi \rangle = \sqrt{\frac{1}{3}} ( | H \rangle | \downarrow \rangle + | T \rangle | \downarrow \rangle + | T \rangle | \uparrow \rangle ). $$ She sends the spin state to F2.

**Step 2**F2 measures the spin in the Z basis (up or down).

**Step 3**A projectively measures F1 (the whole laboratory) and declares success if he gets the outcome $$ \sqrt{\frac{1}{2}} (| H \rangle - | T \rangle ) $$ or failure if he gets the orthogonal outcome.

**Step 4**W projectively measures F2 and declares success if he gets the outcome $$ \sqrt{\frac{1}{2}} (| \downarrow \rangle - | \uparrow \rangle ) $$ or failure if he gets the orthogonal outcome.

The preprint analyzes the situation where

**both A and W succeed**. This is possible because of the nonzero overlap of the projection operator $$ \frac{1}{2} (| H \rangle - | T \rangle ) \otimes (| \downarrow \rangle - | \uparrow \rangle ) $$ and the state $$ |\psi \rangle = \sqrt{\frac{1}{3}} [ ( | H \rangle + | T \rangle ) | \downarrow \rangle + | T \rangle | \uparrow \rangle ] . $$ It is the rightmost term that contributes to the nonzero overlap. Given that both A and W succeed, A infers that the spin must be in the up state, which means that F1 observed the outcome Tail. But if the result comes out tail then Wigner must fail! because projecting the state ## |\psi \rangle ## onto $$ \sqrt{\frac{1}{2}} |T \rangle ( | \uparrow \rangle + | \downarrow \rangle ) $$ means that Wigner will never succeed.

**Q.E.D.**

The step that seems problematic to me is the retrodiction that the spin has a definite (up) value. This seems to be reminiscent of Aharonov and Vaidman's Three-Box Paradox.