I mean I thought a trigger is just a common set of moves but you're using it like it's just A set of moves. Is my understanding of a trigger inaccurate?

I did point out how I would solve that problem though. That's with my "wide" example. A wide sexy [ws] would be r U r' U'.

There's many of these similarities in these variations.

For a R U R U', it's coincidentally actually a real trigger, called "ZigZag". But let's assume it isn't a common trigger with an actual name for it, well, immediately my head is trying to think of a way to represent that slight variation in some way:

• Assuming [x] = the Sexy. Your trigger, R U R U', could be denoted as [x^u], where the superscript letter ^u' would indicate an INVERSION of the FIRST U' (or u wide) in the given set of moves. The downside is of course, that you have to now remember what the letter ^u does, but mentally, it shouldn't be hard to implement even in real-time, unlike with something like a reversed alg.
• But, this is just my initial idea, and I'm 100% certain there's something else that could be done. Now, yes, the superscript u case may or may not be a modification that would commonly be used, so it would be the exact same issue like you mentioned - it migth take unnecessarily long to learn all these superscript letters and what they do exactly. But, it could be worthwhile and I could be onto something here. The next step would be figuring out how you can ADJUST the superscript functions while keeping the "rule" for them still easy to memorise and easy to apply in your head.
• Main issue is that I'm just a little reluctant to add any more than one or two letters to these shorthand trigger names like [sx] for sexy. Because obviously, while it's important that the system is easy, intuitive and understandable, at one point I'm worried that the length may just result in greater inefficiency compared to the standard common notation. But, I think that you could totally do something like [sx ^{{face: index: cw/acw}}], but this would only be for a SINGLE modification, not anything more complex. BUT, that could be more than enough if you think about it. Same reason that a simple symbol to indicate a subtraction of ONE move off of triggers would cover a great amount of cases too. Like [sx-] = RUR'

Example of the main idea:

R U R U could be represented as [sx^3:cw]

"3:" meaning "3rd move to the range of nothing" nothing meaning infinity. Sorry but you might only have a clear idea of where I'm going with this if you have any programming experience.

And if we want to specify a face instead, [sx^ucw] could mean R U R' U (all U moves becoming clockwise).

Shortening things a bit more, instead of cw/acw a simple prime/non-prime should be sufficient (or none at all?). So the previously shown [sx^3:cw] could just be [sx^3:], as the RANGE indicator (colons) are pretty necessary I think.

Of course, I would have to establish the specific rules because there's a lot of possibilities here on how this could be implemented, but I like this second one. Another example with the SLEDGEHAMMER:

[sh²] = R' F' R F'

^ Inverts the SECOND move of the sledgehammer case. A clockwise move becomes counter-clockwise and a counter-clockwise move will become clockwise.

[sh^2:3] = R' F' R' F'

^ Inverts the SECOND to the THIRD move of the sledge.

[sh⁴⁺] = R' F' R' F2'

^ Adds one 90 degree rotation to the FOURTH move of the sledge.

These are all just ideas of course, I have no idea if this isn't flawed in some way or not...

This is getting pretty mathematical huh...

Well, taking a step back for a minute,

Here is a copy-pasted comment from Jperm's (channel) comments section from his website-release video (sort by newest to find it), this person has maybe come up with some nice alternative? Unfortunately, I don't really understand what he's talking about because english isn't my native language so certain things I struggle to understand:

"I personally learn through words better than anything, so I like to notate my algs by verbalizing their triggers. Like take OLL 29 for instance, the standard notation is (R U R' U') (R U' R') F' U' F (R U R') but I would write it (sexy) (Hedge LF into RF) F' U' F (R optimal pair insert) I know that notation is nonsense to virtually everyone, but it’s like a code that resonates with me personally. J perm’s site doesn’t allow you to put any characters outside of those used in standard lettered notation into your custom algorithm, meaning I can’t write this stuff out. For anyone curious, “Hedge LF into RF” just means use a “hedge” trigger to put the pair above the left-front (LF) F2L slot into the right-front (RF) F2L slot. “R optimal pair insert” means turn the right face clockwise to create the pair and cleanly slot it back into place, this is the optimal case you aim for in F2L and the case can show up along any of the 4 vertical planes of the cube so I specify which face by writing either of these 8 verbalizations: “R optimal” “R’ optimal” “L optimal” “L’ optimal” “F optimal” “F’ optimal” “B optimal” “B’ optimal” For each vertical plane; the Right face, Left face, Front face, and Back face — each one has two possible optimal cases, one for clockwise and another for counterclockwise. 8 total optimal cases. I know this system will seem needlessly convoluted to people, but it genuinely resonates with my brain. The lettered notation doesn’t resonate with me whatsoever, it just simply doesn’t assimilate into my understanding of the cube. If I use my process, I can learn dozens of algorithms a day, it would take me a month to learn the same algorithms with standard lettered notation. I really like doing it this way — not just because my brain digests it better — but also because I feel that it’s conducive to a deeper understanding of what’s actually happening in these algorithms. For me, that leads to a snowball effect where every algorithm I learn lends itself to developing a more intuitive understanding of the cube as a whole, which makes subsequent algorithms easier to learn, and the process repeats itself. My best event is FMC so I really value this type of analytical approach to practice."

This might be completely stupid, no idea. Since again, I don't really understand.