Hexagon is a new preprint-style repository focused on research in mathematics and theoretical computer science. It launched in public beta around late September 2026 and is run by the Hexagon Mathematics Foundation, a Delaware nonprofit. It was created specifically in response to the impact of AI on math research, especially the rise of LLM-assisted or fully AI-generated results. Recall that arXiv is the long-established open-access preprint server founded in 1991 by Paul Ginsparg. It hosts millions of scholarly articles across physics, mathematics, computer science, quantitative biology, quantitative finance, statistics, electrical engineering & systems science, and economics. It became an independent nonprofit in 2026 after years of partnership with Cornell. Hexagon is a specialized, newer complement, not a replacement, that fills the gap for AI-generated or lightly human-understood mathematical results that arXiv will not host. The two can, and sometimes do, host overlapping suitable work. The founders of Hexagon have stated they spoke with arXiv leadership and designed Hexagon to serve what arXiv deliberately does not.
If something is not square away for arXiv, you may think about Hexagon 😉 My first deposit is hexagonmath.org:2610.00347v1, obtained by prompting ChatGPT‑6 Astra Pro about the idea of using Gaussians on fractals in order to give a meaning to the ghosts and shadows suggested by Alan Edelman years ago, motivated by the beta ensembles of random matrix theory. Roughly the idea is to construct some sort of Gaussians on $\mathbb{R}^\beta$ with a non-integer $\beta>0$, using fractals. The conclusion is “Thus a fractal cone realizes the exact radial-volume component of the idea, but not, by itself, the full ghosts-and-shadows calculus. A stronger construction must state which observables are jointly realized, which operations are defined, and which positivity and consistency identities they satisfy. No claim of a complete fractional-dimensional scalar algebra, or of novelty for the constructions collected here, is made."
Today a colleague asked me the following:
I noticed you posted hexagonal ghosts labeled “human understanding: no parts” and without any Lean formalization. What is your approach? Are you being modest, but actually understand a good portion of it and know the results are accurate? Do you trust ChatGPT informal assessments? Or do you figure it is okay to share texts with interesting ideas even without certainty about their accuracy?
Below is my answer to him:
I have moderate confidence in what people say on arXiv and in published articles, myself included, and a little more confidence in what the best artificial intelligence systems say. In fact, to borrow your phrase, I tell myself that we can share texts with interesting ideas even without certainty of their accuracy. Usually, for content that does not go through arXiv, I tend to use my personal website or my blog. Hexagon offers me a new channel, more rigid but undoubtedly more sustainable. This submission to Hexagon allows me to experiment with this new tool, in a direction orthogonal to arXiv, and on a topic that is a bit of a nod to the genre (ghosts, shadows, non-integer dimensions, etc.). I marked it as “no parts” because I only have what I consider a superficial and fragmented understanding, “superficially for most parts” would have been more accurate. I do not think I will find the time to truly digest the content intellectually on my own in the short term, so I prefer to share it with others. I find the issue addressed in the text interesting and fascinating, and I believe it is useful to explore and synthesize the fractal approach, despite its limitations. Regarding dissemination, my ideal since I began has been to maintain a spirit of sharing and to remain honest, regardless of the channel: arXiv, website, blog, etc. This can facilitate the dissemination of ideas. In about thirty years of academic life, I have seen multiple unpublished notes and posts of my own in the bibliographies of published papers, sometimes in the most prestigious journals. Finally, I think there is an art to coming up with the right idea or approach, or the right prompt, at the right moment, which has to do with intuition, and that intuition is one of the many drivers of progress. On the other hand, assessing the value of an idea or a text is a subjective and deeply human endeavor, whereas verifying its mathematical accuracy is something that can be objectified and automated... As you already know, I have also started to explore the subject of automatic proofs, reported on it in my blog, and uploaded the result to a dedicated repository (Palomar).