Two months ago, Louis de Branges has released a seemingly new version of a paper (running 97 pages) on his approach to the Riemann Hypothesis. New ingredients seem to involve Fourier analysis on the adelic skew plane (section 4 page 72, defined using quaternions with adic coefficients), with the part on RH being section 6 page 95. There’s also an updated short description of his line of thought.
As discussed on MO, and on wikipedia, his previous attempts from the 90s had been found to contain a gap by Conrey and Li in 1998, while his 2004 paper, which received some attention at the time, got revised repeatedly up to 2009 without ever being published.
In 2006, Lagarias had looked at de Branges’ 90s approach, and reformulated RH in terms of the existence of certain de Branges spaces, outlining 3 possible approaches to construct them.
No idea if de Branges’ new paper is correct or not, hopefully someone knowledgeable will have a look at it, or least at the 2 pages of section 6 to see if it makes sense…