Though I demonstrated a hard upperbound on the D(10) dedekind in the link here (https://devrant.com/rants/8414096/...), a value of 1.067*(10^83), which agrees with and puts a bound on this guy's estimate (https://johndcook.com/blog/2023/...) of 3.253*10^82, I've done a little more work.

It's kind of convoluted, and involves sequences related to the following page (https://oeis.org/search/...) though I won't go into detail simply because the explaination is exhausting.

Despite the large upperbound, the dedekinds have some weirdness to them, and their growth is non-intuitive. After working through my results, I actually think D(10) will turn out to be much lower than both cook's estimate and my former upperbound, that it'll specifically be found among the values of..

1.239*(10^43)
2.8507*(10^46)
2.1106*(10^50)

If this turns out to be correct (some time before the year 2100, lol), I'll explain how I came to the conclusion then.

This morning I was exploring dedekind numbers and decided to take it a little further.

Wrote a bunch of code and came up with an upperbound estimator for the dedekinds.

It's in python, so forgive me for that.

The bound starts low (x1.95) for D(4) and grows steadily from there, but from what I see it remains an upperbound throughout.

Leading me to an upperbound on D(10) of:
106703049056023475437882601027988757820103040109525947138938025501994616738352763576.33010981

Basics of the code are in the pastebin link below. I also imported the decimal module and set 'd = Decimal', and then did 'getcontext().prec=256' so python wouldn't covert any variable values into exponents due to overflow.

https://pastebin.com/2gjeebRu

The upperbound on D(9) is just a little shy of D(9)*10,000
which isn't bad all things considered.