Kirti Joshi has been working on a set of preprints reformulating Mochizuki's Inter-universal Teichmüller Theory (IUT) - a brief intro: https://thehighergeometer.wordpress.com/2023/04/19/joshis-quest, outline by Joshi: https://www.math.arizona.edu/%7Ekirti/joshi-teich-quest.pdf, the preprints on arxiv.
This market will resolve YES if the programme leads to well accepted new results/mathematical approach. Some examples of what will resolve yes:
Proof of abc conjecture.
Proof of Mochizuki’s Corollary 3.12 (a problematic part of the claimed abc proof)
Notable critics of Mochizuki's ABC proof (e.g. Scholze and Stix) publicly claim that the programme has rehabilitated IUT as a useful piece of mathematics.
Non-trivial contributions to any notable open problem
A result will be attributed to the programme if a co-author on the result claims it is part of the programme and there are no strong reasons to believe otherwise.
"Accepted" here means that majority of the mathematical community will judge the results as trustworthy and proven beyond reasonable doubt - I will not require a complete capitulation by all critics or a computer-checked proof.
Since the resolution is partially subjective, I will not bet on this market.
1,000So there are some bangers that came out in March:
https://arxiv.org/abs/2401.13508
https://arxiv.org/abs/2403.10430
Edit: Some extra context at https://www.math.columbia.edu/~woit/wordpress/?p=13895