If I were diagramming it, I think I’d still label “accidentally” as an adverb, but would note that the corresponding verb has been omitted. It’s the written equivalent of hearing “Oh my, there’s a gigantic <RADIO STATIC> blocking the road.” The unknown word blocked by the radio static is still the noun, we just don’t know what it is.
Proper verbing would be "accidented", I believe (and I love English for how you can just verb or noun anything - it's like Lisp of natural languages!), but I guess "accidentally" can be chalked up to artistic license.
That's verbing a noun, but I don't think that's what is going on here. I think the title is trying to verb an adverb.
If the "correct" sentence is "I accidentally created a scheme", then I think it would be "accidentallied". In excising the verb, shouldn't one carry its tense over to the adverb?
If the "correct" sentence is "I created an accidental scheme", then it would be "acidentalled".
But verbing the adjective doesn't have the same rhythm as verbing the adverb, in this case. And rhythm is the most important rule of English. The indefinite article needs to fall on a low note, and the adverb form is flexible enough to end on a high note to give a lilting affirmation, whereas the adjective form is not.
English has zero-derivation of verbs [that is, the form of the derived verb is identical to the form of the word from which the verb was derived], and this construction is highly productive; many people have remarked on it. But there's nothing similar for nouns in English, so I don't see why you're listing nouns as parallel to verbs.
The meme expression "I accidentally [missing verb] [something]" does not obey the rules of English, as you can easily tell by the responses saying "you accidentally did what?"
If you really meant that parenthetical, you might be interested in Chinese, where academics sometimes get into arguments over what part of speech a given example of a word should be considered to belong to. There is very little inflection, which makes the confusion possible.
I'm speaking more about language culture, as it's used. My native language, Polish, allows for convenient derivation, but it's not a natural thing to do, and if you try, people will look at you funny. In English, it feels very natural and people will understand you when you do it.
> My native language, Polish, allows for convenient derivation, but it's not a natural thing to do, and if you try, people will look at you funny.
Cultural differences do crop up. The Romans mostly believed that if you wanted to talk about philosophy, you had to do it in Greek; there is a speech preserved from Cicero in which he complains about this belief and gives several examples of how it's possible to say the same things in Latin by using parallel derivational mechanisms. Construction of new words from roots was common in Greek and unusual in Latin.
Does he regularly a scheme? Or did he do it in the past? Both!