This seems like the next step, but the smallest counterexample in n=2 is degree greater than 100. (This is a paper of Moh. Wikipedia has details.)

Wasn't it proven true in general for n=2

(NGL I wanted to suggest someone to go for the JC using 5.6 after the CDC proof came out, but then on reflection felt I should neither waste people's time NOR contribute to the myth of AI :)

My prediction is that the bubble will burst in 2031 Q4, one year after the Riemann Hypothesis is expected to fall (according to Demis)

After 2031, I will suggest going for the JC for N=4 because they would (dis)prove the Dixmier conjecture for N=2 :)

https://xcancel.com/BrunsJulian1541/status/20790734625601334...

https://arxiv.org/abs/2410.06959