A385657 in the news, Erdős unit distance conjecture

[Ed Pegg]

The Erdős unit distance conjecture involves the bounding 
behavior for maximally dense unit distance graphs.
https://oeis.org/A385657
https://mathworld.wolfram.com/MaximallyDenseUnit-DistanceGraph.html
  
Open AI has provided a counterexample.  Basically, algebraic constructions 
beat square grid constructions.
https://openai.com/index/model-disproves-discrete-geometry-conjecture/

My take on it 
https://community.wolfram.com/groups/-/m/t/3719376

To kinda see this in action, look at large extremal unit-distance graphs.
https://mathworld.wolfram.com/PartsGraphs.html 
https://mathworld.wolfram.com/HeuleGraphs.html

[José Hdz. Stgo.]

In my Weltanschauung, this exploit is way cooler:

https://arxiv.org/pdf/2605.20579 

¡Viva la Resistencia!

Best regards,

José Hernández Santiago.

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[Gareth McCaughan]

On 21/05/2026 23:14, 'José Hdz. Stgo.' via SeqFan wrote:

In my Weltanschauung, this exploit is way cooler:

https://arxiv.org/pdf/2605.20579 

Well, yes, it's a more precise result, but of course as always with human so-called mathematics it's merely derivative of the creative accomplishments of the AI model's earlier work. As we all know, human brains merely spot patterns and repeat them, and can never truly produce anything original.

:-)

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g