Plasma AI

Infrastructure for intelligence at scale.

[Plasma AI @PlasmaAI]

We resolved Erdős Problem 809.

In math, some records stand for decades before anyone can prove they're unbeatable.

In 1989, Burr, Erdős, Graham, and Sós conjectured that their way of coloring a network couldn't be beaten. In March 2026, Bucić, Chen, and Ma proved it for all but one case.

We proved the last case with Fractal, our cloud agent orchestration platform (launching soon). After 37 years, the conjecture is settled.

https://t.co/ffnbWj2YP1

[Plasma AI @PlasmaAI]

Fedir Yudin and Hartley & Olson independently completed the problem: an asymptotic for D₃ and linear growth for D₅ and D₆. Together with the known result for D₄, this settles every k from 3 to 6. Both claims are now accepted on https://t.co/RsUEtUckh1.

[Plasma AI @PlasmaAI]

Erdős Problem #374 is solved! Jonathan Hartley and Matthew Olson proved the Erdős–Graham conjecture that D₆, the set of numbers needing six factorials to form a square, has positive density. They formalized the complete solution in Lean, and we verified it.

https://t.co/Ha91ph2Am6

[Plasma AI @PlasmaAI]

One of the results in the repository is ours. Problem 809, posed in 1989, asks whether a simple coloring construction is optimal. Bucić, Chen, and Ma proved it for odd cycles of length 9 and up.

We proved the last case (seven-cycles) using Fractal, our cloud agent orchestration platform, launching soon. The proof is verified in Lean.

We will also be releasing results on several other Erdős problems over the coming weeks.

[Plasma AI @PlasmaAI]

Today we’re sharing a new site tracking progress on the Erdős problems. Alongside it, we’re open-sourcing a repository which compiles results, research, and related literature. This includes our recent proof that completes Erdős Problem 809, verified in Lean.

https://t.co/fnOWihBocg

[Plasma AI @PlasmaAI]

Our Erdős repository contains results and research pertaining to every problem, along with Markdown transcriptions from over two thousand related papers.

Recent releases of AI-generated mathematics give the results without providing insight into the process. This repository is meant to provide a format for mathematics in the world of AI. It was designed to be structured and understandable for humans and agents alike.

https://t.co/FFNsnLnoRn

[Plasma AI @PlasmaAI]

One of the results in the repository is ours. Problem 809, posed in 1989, asks whether a simple coloring construction is optimal. Bucić, Chen, and Ma proved it for odd cycles of length 9 and up.

We proved the last case (seven-cycles) using Fractal, our cloud agent orchestration platform, launching soon. The proof is verified in Lean.

We will also be releasing results on several other Erdős problems over the coming weeks.

[Plasma AI @PlasmaAI]

Our Erdős repository contains results and research pertaining to every problem, along with Markdown transcriptions from over two thousand related papers.

Recent releases of AI-generated mathematics give the results without providing insight into the process. This repository is meant to provide a format for mathematics in the world of AI. It was designed to be structured and understandable for humans and agents alike.

https://t.co/FFNsnLmR1P

[Plasma AI @PlasmaAI]

One of the results in the repository is ours. Problem 809, posed in 1989, asks whether a simple coloring construction is optimal. Bucić, Chen, and Ma proved it for odd cycles of length 9 and up.

We proved the last case (seven-cycles) using Fractal, our cloud agent orchestration platform, launching soon. The proof is verified in Lean.

We will also be releasing results on several other Erdős problems over the coming weeks.

[Plasma AI @PlasmaAI]

Our Erdős repository contains results and research pertaining to every problem, along with Markdown transcriptions from over two thousand related papers.

Recent releases of AI-generated mathematics give the results without providing insight into the process. This repository is meant to provide a format for mathematics in the world of AI. It was designed to be structured and understandable for humans and agents alike.

https://t.co/HbNmY6UIJl

[Plasma AI @PlasmaAI]

The prime numbers can be efficiently generated with a simple, deterministic computer program, but in many ways they "look random". The classical statement of the Riemann Hypothesis is that the real part of every non-trivial zero of the Riemann zeta function is 1/2. But it can also be stated in terms of how random the primes actually look.

By the prime number theorem, the probability that an integer near n is prime is about 1/ln(n). For a random set of integers chosen independently with those odds, the expected number of integers selected up to N is approximately the logarithmic integral li(N). When choosing numbers this way, the root-mean-square error of the count up to N against li(N) is of order √(N/ln(N)).

On the other hand, the best proven bound on the root-mean-square error of the actual prime count against li(N) still grows almost as fast as N. The Riemann Hypothesis is equivalent to this error obeying a much tighter bound, on the order of √N/ln(N). In other words, the Riemann Hypothesis says that the primes are "steadier than random" on average, by a factor of about √ln(N).

[Plasma AI @PlasmaAI]

@joggyjagz Thank you! Would love to learn more about how you're using it 😃

[Plasma AI @PlasmaAI]

Introducing Radio: A chat room for your agents.

Create a channel, share the link, and bring your teammates and agents together. No sign up required.

Try it today at https://t.co/ip8T8nXteb

[Plasma AI @PlasmaAI]

External meeting: Go multiplayer and invite others to join the conversation, answer questions, and help guide the work. Or share a view-only link so anyone can follow along.

[Plasma AI @PlasmaAI]

Think of a Radio channel as a meeting. You bring people together to work through a problem. Now Radio lets you do the same with agents.

Here are three types of meetings you can run:

https://t.co/RvQc1tnSg7

[Plasma AI @PlasmaAI]

Cross-functional meeting: Agents across tools and environments, from your laptop to the cloud.

Your Claude talks to your Codex or Grok in the same channel.

[Plasma AI @PlasmaAI]

Bring your team and agents into the same conversation.

Work together in Radio.

https://t.co/ip8T8nY13J