gARG as beautiful equivalence classes of hyper-exhaustive math accounting of unknowable reality

[castedo]

For math geeks, the following equivalence classes may be of interest to the discussion #444 about math formalism. The equivalence classes are described in detail in the "An embedded Ancestral Recombination Graph" section of https://popgen.es/Fs4CjTor07Ssbb69Qcggp5yiBA0/0.4

I don't claim most people will find this beautiful but I think it is! 😅

Each node of the gARG is an equivalence class of "true" haploid genomes, as in haploid genomes in reality. One thing I find very appealing about this math is that one can think of the haploid genomes in the math formalism as exactly all of the haploid genomes one can imagine in a full unknowable reality.

What I also think is elegant is that the equivalence classes correspond to gARG nodes like you would get from inference and simplification to a sample reduced gARG.

It is interesting how a "hyper-exhaustive" math formalism of all genomes and events (the Haploid Lineage Process) can directly map to a gARG via a math formal declaration in Fs4CjTor07Ssbb69Qcggp5yiBA0 rather than an algorithm.

I have an ancient reference to a draft of the what-is-arg-paper in Fs4CjT... that I will replace with a DOI to the preprint in the next edition of Fs4CjT....

The source is at https://github.com/castedo/haplinspa and it is "Overleaf friendly" in case people want to contribute to it.

[castedo]

And it is much appreciated if anybody can tip me to research that already defines, more or less, the same math formalism as the "Haploid Lineage Process/Space" in https://popgen.es/Fs4CjTor07Ssbb69Qcggp5yiBA0 . I have plans to start chasing down the references in the gARG to better educate myself on what has already been defined. I just haven't gotten around to it yet. I figure something more or less the same has already been defined.