Two certificates about Hat tiling

[brad klee]

Hi Seqfans, 

First draft pretty-print certificates are now available for the Hat tiling 

sequences I mentioned earlier: 

>  https://github.com/bradleyklee/Artifacts/tree/main/09-Apex-and-chill

>  >   https://github.com/bradleyklee/Artifacts/blob/main/09-Apex-and-chill/apex_and_chill.pdf

> https://github.com/bradleyklee/Artifacts/tree/main/10-golden-hex

>   >  https://github.com/bradleyklee/Artifacts/blob/main/10-golden-hex/Mountain_and_Valley.pdf

There is also code there. I asked for it to be concise as possible, 

tried to run it once, and it seemed to work. 

The "Apex and Chill" certificate was not a joy to produce over 100 or 

200 iterations, but it turns out looking good. 

I'm going to let these sit for a while longer unless someone can reproduce  

our experiments thus saving Harm.On.ica from solitary confinement. 

My #2 choice after Chat GPT presently would be Google Gemini, and I 

will also accept a Claude reproduction as part of adversarial network. 

Friendly competition about present or higher apex records is still welcome, 

even and especially from human research programmers, but please, no poaching! 

Your friendly sherpa, 

--Brad