Aaand this is the most badass thing I have ever written. This lemma (2nd page) was totally from scratch. #math #prime #markovsnakegraphs #primenumbers I am very, VERY happy with this lemma!!! It makes Markov Snake Graphs really relevant to prime numbers!

Now I have a really dangerous approximation. I'm building a false #Markovsnakegraph on a pitched #ChristoffelLatticePath, one that is the stacking of two true #Markovsnakegraphs, and app the number of #perfectmatchings as the product of the two respective #MarkovNumbers times (1+(L2D/N)/(4+L2D/N)).

Ah. That's how you do the #combinatorics without #clusteralgebra to show that the #markovsnakegraphs (themselves constructed iteratively according to strict rules, in this approach) always have #perfectmatching counts equal to #MarkovNumbers.