gukoff

Interesting, thank you for sharing.

Yes, and the standalone formal proof and independent review will follow.

By the way, I'd like to note that it will likely be a formalization of not the last result in that conversation, but of one of the initial proofs that relied on the Langford sequences and theorems of their existence.

Apologies for the confusion - the playground had a typo (7 instead of 8) which is fixed now. Now it works as you would expect, and zeroed potentials correspond to a zeroed hexagon.

The "wide ring" gadget is an interesting idea. I think it will be linear pyramids and not gaussian. A set of these gadgets can also form a basis, and in such a different basis the potential fields may look very different - almost flat, perhaps?..

Thank you, I'm glad you found it readable on mobile!

Thanks a lot for the detailed perspective!

The potential fields are a curious phenomenon. I feel like - and I haven't verified this in any way yet - the smoothness is dictated by the fact that all values are within a not-so-broad range. Then as you "peel" the hexagon from the outer layer using those 6-rings, building the potential field, each next layer inwards shouldn't changed too much.

I had also explored a case of n->inf where the sums turn into integrals, and consecutiveness turns into the uniform distribution. Then it's not so hard to find a solution. It's not in the article, because it turned out to be a dead end for solving the discrete case, and I didn't want to make the article too heavy - but if I remember correctly, there I also observed the smoothness.

You're absolutely right, technically the title should have said "every order other than 2" or "every order larger than 2". The case for 2 is impossible, because it immediately forces equal numbers on the outer layer.

How do you run these models on AMD GPUs?

Timestamps are conversation metadata and don't need to be fed to the LLM and require tokens.

Draw.io already allows creating editable PNGs and SVGs: it embeds the diagram definition in the image metadata. You can then import this image like you would import any other .drawio diagram

The VSCode integration is the cherry on top. All files with the correct extension (such as xxx.drawio.png) will automatically open for edit in the draw.io UI embedded in the IDE.

I use this feature often to build on top of the previously made diagrams.

> Prof Penadés' said the tool had in fact done more than successfully replicating his research.

> "It's not just that the top hypothesis they provide was the right one," he said.

> "It's that they provide another four, and all of them made sense.

> "And for one of them, we never thought about it, and we're now working on that."

The Google's co-scientist still seems to make a useful assistant.

That's very impressive - how do you do this? I also see an IDE screen with the debugger in your other article about telegram - presumably also HTML/CSS

Thank you, this is very interesting