There is no spec for Markdown other than his buggy Perl implementation. He also didn't exactly appreciate the fact that other people tried to standardize "his" language.
I'm not even sure Markdown in general can rightfully be called an invention (in the same sense as JSON is not considered such by its "inventor"). It's just one of several plain-text formatting conventions that happened to become popular (though, again, not really his exact implementation).
In fact, because of the limited scope Gruber's original Markdown addressed and the redundancies he implemented (such as the different "bullets" for unordered lists) are biting implementers now that the format is used for other things than originally envisioned (by making extensions difficulty or unintuitive).