This does get confusing with say...

"A/An herb."

Because different dialects pronounce herb differently, sometimes the 'h' is pronounced, sometimes not.

I know you specified American English, but even within American English, you can find areas that differ on this, and I'm sure there are other words where this kind of thing crops up.

Also, I guess this may be worth mentioning as well:

Though this no longer seems to be as common as it was 10-20 years ago...

"An hero."

Sometimes, either an unintentional misuse of this a/an rule will be ironically copied, and more widely used, essentially to either mock the original usage/user...

... or the a/an rule can be intentionally misused, as a way of infantilizing yourself, trying to come off as cutesy/ditzy, or maybe play up your own awkardness or inexperience, something like that.

The rule I've always used is that if the first letter of the word immediately following it is a vowel, it's "an" and if it isn't use "a".

For example, "an apple" or "a potato". If there is an adjective, go by that first letter, for example "a large apple" or "an average potato".

Native English speaker here. This is incorrect, the "n" is added for phonetic help "a elephant" involves an awkward break between the two words, so enter "n" to help mouth muscles work around that.

This is the same reason for weird artifacts like: "a unicorn" because unicorn starts with. "Yoo" sound and so mouths don't need the help of the "n" to break up the awkwardness.

Also seconds language but I’ve learned it depends on how the first letter of the following word is spoken. If the following word has a vocal sound (even if the first letter is technically a consonant), it’s 'an', which it thusly would also be here.

I don't think that's accurate, but I'd be happy to see a source proving me wrong. I looked briefly, but wasn't able to find a paper dealing with that alternation specifically (though I didn't look very long, and there may very well be one).

Also, I'm pretty sure that for the dialects that do use "strong the", they also use "strong a" in exactly the same environments, which to my mind makes it a non-issue.

Either way, there are plenty of other ways to get a word-final unstressed schwa followed by a word-initial stressed vowel, and we never see an "n" repair in any of those other situations either - the important point is that this is a process centered entirely around a single lexical item, and it doesn't make sense for a process affecting a single lexical item in a common environment to be "easing pronunciation".

Good questions - hopefully the explanation here helps clarify my position.

To ease pronunciation, we take the older form (containing the consonant at the end) when a vowel follows and the reduced form (without the consonant) when a consonant follows.

We don't, though. This is clear from the fact that "the" occurs in exactly the same phonetic environment (including the lack of stress), with exactly the same vowel, and it doesn't show the same behavior. This data tells us that there's no articulatory reason for this alternation. There is no phonotactic constraint active in English that speakers are getting around with this behavior - the process is specific to a single morpheme.

There are tons of other ways we could make this exact same sequence of unstressed schwa followed by another stressed vowel as well, and in exactly none of them do we ever see an "n" inserted to repair the hiatus the way we do with /r/ in many dialects (which one could analyze as an example of "easing pronunciation", depending on one's assumptions, though I probably wouldn't with all of the deserved stigma around the ill-defined idea of "easing pronunciation"). This is telling us that this alternation has nothing to do with "ease of pronunciation", since speakers clearly don't need their pronunciation eased in this environment.

As for "strong the" specifically, we see a parallel form in "strong a", which can also be argued to end with a yod, and which seems to alternate under the same conditions as "strong the" in most dialects, whatever those conditions are. For this reason, I don't really think "strong the" is very relevant to the discussion.

When the sound change originally took place, of course, it could be argued that it was for "ease of articulation" purposes since the change was regular, but post facto explanations for sound change are always a bit dicey.

So, if you want to argue that the original source of the alternation was "ease of pronunciation", well, sure, maybe, but it's pretty clear from Modern English data that the "a/an" alternation has nothing to do with ease of articulation at all.

It's a dichotomy because something either eases pronunciation, or it doesn't, and in this case, the data makes it clear that it doesn't. It may feel "easier" to speakers because it sounds wrong to them without it, but that's due to morphophonology, not phonotactics, and it's why we rely on tests like the above instead of speaker intuition whenever possible.

How about this: let's take the f/v morphophonemic alternation in leaf/leaves, knife/knives, etc.

There's a decent argument to be made that this medial voicing change in Old English was originally to "ease pronunciation", but once this alternation became morphophonemic, the "ease of articulation" argument falls apart pretty quickly.

I don't think any serious linguist would assert that it's 'life/lives' in Modern English due to "ease of pronunciation" instead of "historical accident" when 'fife/fifes' and countless other later borrowings do not show the same alternation, and the 'a/an' alternation is this exact same sort of morphophonemic process.

Yes and no. Imprecisions is instability. Stable diffusion was named because the noise and the unstability were low enough you'd be able to kinda make sense of the result. However stability is far from being achieved.

The post is 100% fake but the lines are too straight, there are two fonts displayed at once and each time they are consistent. Thats what i mean by "too stable" for me.

Seems the pink paper has a backing on it to stiffen it. Left side seems to show the backing, which may be pink cardboard. Given the mounting location, I would expect it to be "floppy" like the "lined" paper without a stiffener.
All of my above to say, I think someone put a "lot" of effort into the pink sign.

The first scrap piece of paper they had laying around.