Does it state anywhere on the cover, or inside page that this is the first edition ..... ?
Good question. I did some reading on the subject:
"According to the definition of edition above, a book printed today, by the same publisher, and from the same type as when it was first published, is still the first edition of that book to a bibliographer. However, book
collectors generally use the term first edition to mean specifically the first print run of the first edition (aka "first edition, first impression"). Since World War II, books often include a number line (printer's key) that indicates the print run."
"Many book
collectors place maximum value on the earliest bound copies of a book—promotional advance copies, bound galleys, uncorrected proofs, and advance reading copies sent by publishers to book reviewers and booksellers."
https://en.wikipedia.org/wiki/Edition_(book)
As this is a sort of advance offering, I think that the definition we are working with is that of the 'first run'.
It would be problematic for me to write '1st Edition' on the cover for two reasons. First, it would be misleading in that it is one of many books. Second, It may need its own ISBN number, which is easier said than done. I will be printing through the distributor company, which means that any book that I have printed via them would also need to be offered for sale by them. Obviously, I want to limit the '1st Edition' to 100. Assuming things go to plan, the book will be offered for sale through a distributor sometime in the future, though those would obviously not be signed or be the '1st printing'.
I think the best approach is for me to print up to 100 copies for myself, which I will then number, sign, and ship. I can use a stamp, and possibly a sticker on the front saying something like 'Special First Edition - Numbered".