: How to tell readers that I know my story is factually incorrect? Sometimes, it so happens that I do some research for a story and find that a major plot point could never work in real life.

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This might not be quite what you are looking for, but it may give you an idea.
In one of Higashino's novels, Malice, it becomes clear that the first person narrator is lying to the Reader, who naturally wonders why? (He is also lying to the Police). Maybe you could find a way to use your impossibilities as a plot device. (Actually The Matrix does this).

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You can always take a middle way, by discussing the issue in the story.

So, your hero gets trashed but miraculously survives. Have a doctor discuss it.

"Seriously, Mr. Smith, I've never heard of anybody with your injuries living. I have no idea why you are not down in the morgue right now."

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Never let the truth get in the way of a good story.

(Mark Twain, allegedly)

If your licence (or licences) from the truth really troubles your conscience, leave your explanation/justification for a note at the end of the novel. This way you won't break the flow for the reader, and you'll leave your explanation for a time (at the end of the novel) when the reader is keener on suspending their suspension of disbelief. My two cents.

The writers of the TV series "Breaking Bad" (or was it "Better call Saul"?) drive another excellent point when they make a character say:

I once told a woman I was Kevin Costner, and it worked because I
believed it.

In other words: if you don't believe your own story, it's not going to work.

Another way of addressing the issue could be to be playfully unapologetic about it.

The novel The Baron in the Trees by Italian writer Italo Calvino is an excellent example of how unlikely situations can be delivered in a believable way without ever having to give explanations to the reader or making the reader feel cheated. The novel is the story of a kid that climbs up a tree after a fight with his noble family and decides to never climb down. He spends an entire life of adventures in the trees. The novel is set in Italy in the XVI century and it is dense of historically accurate references. Everything that happens, no matter how unlikely, is consistent with the time and place in which the events are set. One can tell that Calvino did not have to sit down and "do the research" to do so. He knew those time and places well enough to play with them comfortably in the first place. More importantly, he was immersed in the reality that he was weaving, he believed it, and in turn so does the reader (or perhaps I am just gullible).

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This happened to me earlier while I was writing fan fiction - given the informal nature of it, I simply let my character survive a wound that he shouldn't have survived

If this impossible thing is not critical to the story, you might be writing yourself out of a corner with magic. This can yank the reader out of their immersion, and demonstrates that nothing really has consequences in your stories. Change it to something plausible.

If the impossible thing is critical to the story, do it and quickly move on before the reader notices. Absolutely do not draw attention to it with a note. If it's in the middle of a tense situation the reader will probably be so immersed they won't notice until hours later, if ever.

For example, there's that awesome scene in Raiders of the Lost Ark where Indiana Jones escapes capture by climbing on board a German submarine and catches a ride across hundreds of miles of open ocean to a secret German U-Boat base. Wow!

Hold on... Did he hang on to the outside of the submarine for hundreds of miles and days on end? Did it never dive? Did he sneak inside? How do you sneak inside a submarine? If he did, how do you stay hidden inside a submarine?

Forget it, rule of cool applies. If you have the reader wrapped up enough and it's awesome enough, it won't even occur to them that it's implausible.

They filmed scenes of Indy hanging onto the periscope trying to sleep and wisely did not include them. This is the equivalent of your note. Trying to explain it just draws attention to how implausible it really is. Just move along quickly.

Or make sure the impossible thing goes along with the theme of the story.

For example, Greg Egan's Permutation City is hard sci-fi about computing and virtual reality... except for one bit where he decides...

"dust theory" works. There is no difference between physics and its mathematics. So long as their virtual reality can be computed it will continue to be computed no physical hardware required.

This is not the central plot of the story, but it's built up as an outside possibility over the course of the story. It's an extreme exploration of the theme the story: virtual reality is truly virtual and not tied down to physical limitations of time nor space.

Greg Egan has a FAQ about this (note: contains big spoilers to a very good book) where he admits he doesn't take it very seriously.

Which is all to say: if you're going to do something impossible, make sure it's either really cool, or has a thematic purpose. Best if it's both. If it's neither, it's lazy writing.

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One classic approach is to “hang a lampshade on it.” If he really shouldn’t have survived that, you can have a character in the story point out how lucky he is. It calls attention to the fact that the plot is implausible (although this is could be a clue that there’s really more going on). But at minimum, it tells the reader you’re aware of it.

John Bois’ online story “17776, or What Football Will Look Like In The Future” goes a step further. Someone who’s survived in a way that wouldn’t be possible in the real world suddenly breaks character in the middle of a conversation. The author makes a joke out if it, but still has his mouthpiece say that he’s breaking the Fourth Wall for the sake of your personal safety and well-being. “I can only do that because I am unkillable. [... Y]ou are extraordinarily killable. [... Y]ou'll be remembered as the person who died in some crappy cave because you read it in a story you read online about sentient 178th-century space probes who watch football all day, even though the most handsome character in the story completely interrupted everything to explicitly tell you not to.”

There are a few novels that use footnotes as a conceit. Mary Gentle’s The Book of Ash comes to mind. In Nabokov’s Pale Fires, the editor adding footnotes is a character of his own with an unreliable point of view, but the best example I can think of is actually a non-fiction book. Some editions of Edward Gibbon’s Decline and Fall of the Roman Empire, including the one on Project Gutenberg, have multiple dueling sets of footnotes, where Gibbon himself is often more witty and acerbic than in the main text, and the commentators are arguing with each other, particularly about Gibbon’s views on organized religion.

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One of the best examples I can think of--where the plot requires a counter-factual setting--is the beginning of Never Let Me Go. It simply states the assumptions the reader needs to accept:

"The breakthrough in medical science came in 1952. Doctors could now
cure the previously incurable. By 1967, life expectancy passed 100
years."

By stating the "facts" that the reader needs to accept, up front, it lets the reader know that an "alternate reality" as is the setting for your story.

If the idea of an "alternate reality" is too strong, I agree with the other answers that you don't necessarily need to draw attention to "the impossible." You just write as if it were possible and move on. There is precedent to this. For example, there is the writing style of "magic realism." According to its Wikipedia page, it has been defined as "what happens when a highly detailed, realistic setting is invaded by something too strange to believe."

Another example I can think of is Dream Boy, by Jim Grimsley. In the book, a youth is beaten to death. From the description of the aftermath, the book gives the strong impression that the boy is dead. Yet he wakes up and walks away from the scene. Grimsley leaves the story ambiguous whether the boy didn't really die, is a ghost, someone else's fantasy, or something else. According to this NPR reviewer, "Grimsley realizes literature is not bound to the laws of the physical world, and he makes the most of this."

In the theatre community, we often talk of the "suspension of disbelief button." Audience members—or readers—will often be willing to push this button, in the service of engaging with the story, if the story is well-told and otherwise believable. From a technique point of view, I think it helps if the situation around the "factually incorrect" event is left a little ambiguous, and that part of the story is relatively fast paced, so the reader isn't forced to dwell on the inconsistency.

In short, I think the answer to your question is in the question itself:

"I can either continue with my impossible (for a non-fantasy, non-scifi setting) idea, or scrap it completely."

Right. I'm submitting this answer to say that "continuing with the impossible" is a legitimate thing. It has an established precedent. The flip side of the coin is that some readers will be less willing than others to plays fast-and-loose with reality, even if it in the service of the story.

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A really good example of this is The Martian, where the key event for Watney being stranded on Mars is a violent storm which damages equipment, injures Watney and threatens the lander. Andy Weir was perfectly aware that Mars does not in fact have winds which would match the novel's events - whilst winds on Mars can be extremely fast, the thin atmosphere means they simply could not have sufficient force. However the plot required an event like this, so the event happened. Weir is unapologetic about this, because the important point is to tell the story.

The context in which this is done is relevant. In every other regard, Weir took pains to ensure the science and engineering were correct. Moreover the "windy Mars" environment keeps recurring throughout the book, presenting Watney with new challenges, but also showing that this is business as usual for Weir's "windy Mars" and not a freak event that comes out of nowhere.

So if you're going to rework some piece of the real world to fit your plot, the answer is pretty simple - just make sure that you've figured out all the consequences of that change and how it relates to the rest of the world, your characters, and/or their opponents. So long as the novel is internally consistent, your readers simply don't care.

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Every book is going to play around with reality to some degree, though some do it more than others.

Every case is different. Is this a story that would end up on a "I can't believe they survived!" style TV show?

In my own book, I've included one of my favorite songs. But the song didn't exist in that time period. It's in Aramaic and Aramaic and Hebrew weren't languages yet; people spoke Canaanite, the precursor language to both.

I am handwaving this away because it's a very old song and it's not inconceivable that a form of it existed even earlier. But I know that's a load of BS I'm telling myself so I can include it.

And...so...I'm including it anyway. Because it's my book and that's what I want to happen. I'm also including things that didn't happen historically, at least not in the United States. They're things that could have happened, but they didn't.

I have no idea if I'll have an afterword that talks about any of this, because that's more up to the publisher than anyone else. But I do have a blog. I can talk about all of these pressing issues as much as I want. And if gasp some readers do not care as much as I do about linguistics and liturgical history as I do, they can just skip that post.

In your situation, let your character survive and move on. If you need to, tweak the details just slightly as others have recommended, so survival is possible, even if improbable. As long as it's not too extreme (no one survives their head being cut off), readers can chalk it up to some amazing stroke of luck. You don't need to explain medical probability to the reader, just make it believable.

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Sometimes writers make mistakes. Sometimes they didn't know something. Sometimes they chose to ignore a fact because it got in the way of their story. This is so common, TV tropes has a whole family of tropes related to the phenomenon. Of particular interest to you would be Artistic License - Medicine with all its subtropes, and Critical Research Failure.

If you choose to write something, you don't add a footnote saying "actually, this is total bull". Imagine if Dan Brown added an addendum to all his books, explaining that all his "facts" are entirely made up, wrong, and incompatible with reality. He wouldn't be nearly as famous, would he?

If you're uncomfortable with writing something that is painfully wrong, rewrite it. Correct it. Make your work something that gives you pride rather than mild shame. If you don't really care, then you don't really care.

As a reader, a mistake I notice throws me out of the story, always. It breaks my suspension of disbelief, because I know "that couldn't have happened". Depending on the mistake, sometimes I can forgive it, gloss over it, move on. The author is, after all, just human, sometimes they make mistakes, no big deal. Or it could be that they made the choice deliberately, because it works so great for the plot. Sometimes that too can be forgiven.
Other times, the author should really have known better, should have done their research. Sometimes a mistake is so bad, I feel the author is showing blatant disrespect towards their audience. Then I will put the book down and never pick up anything by that author again.

But if you straight up add a footnote and tell me that the things you wrote can't actually work, what you're saying is "I couldn't be bothered with making it right, I do not respect you, the reader, enough to write something that works. Rewriting the work after I found a mistake was more work than I was willing to put into this, so here, take this half-baked product." I'm sure you can see how I wouldn't forgive that.

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"I simply let my character survive a wound that he shouldn't have survived"

Real people do this all the time, one of my favourites was a guy in Alaska who accidentally severed his own jugular vein with a chainsaw and then proceeded to walk 20 odd miles to the nearest town for help. He should have been unconscious almost instantly and died a few moments later. Sometimes people just get ridiculously lucky; to maintain realism and immersion for your audience people should comment on how lucky the survivor is, possibly until they're sick of hearing it. This means only saying it once in the direct narrative and having the character immediately tell that person they've had it with everyone reminding them of how dead they should be.

Now without knowing exactly what you're proposing to do this time around it's hard to say how you might go about justifying the outcome you want but luck and odd happenstance can get you a long way to the apparently impossible.

You can write a foreword that says, among other things "anything that's wrong with this story is deliberate and/or my fault" but within the narrative don't say anything about inconsistencies, it destroys the readers' experience.

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I simply let my character survive a wound that he shouldn't have survived, and then left a note at the bottom about what would have really happened.

As a reader, this would break my immersion and ruin the story, everything after that is BS, I know it, the author knows it, and did it anyway.

Change the plot point.

Change the injury to something crippling (for the moment) but survivable.

Make it so the injury isn't what the character thought it was.

Make the character recognize the gravity of the injury and do something about it, to make it non-fatal.

Invent another character to prevent the hero from dying, even if you have to write 10,000 words.

Or, as a last resort, just don't tell us. This is fiction, an entertainment, so take the liberty without apologizing for it. If 10% of readers call BS on it, you still entertained 90% of them. Stop worrying about "justification" or your "integrity" or "honesty".

Yes, I'd like my fiction to be plausible; and I would probably choose to rewrite, but I don't expect deep plausibility in fiction that will withstand any level of research. IRL I am a scientist, but I do not expect readers to take my fiction as literal truth, I don't expect my fiction to withstand close scientific scrutiny. You just need some surface plausibility, or as we call it in science, "hand-waving" justifications a reader can accept without much thought, and read on.

Don't let your ego get in the way of writing an entertaining story.

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Many authors do include that kind of information outside of the story itself. Typically it goes in a foreword or afterword, which are essays the author finds useful to include with the story that can contain almost anything, including the acknowledgements section (usually separate). These are directed to the reader, often in a conversational tone. I imagine that if an author were to give a live reading of their story, they'd have the opportunity to speak about it to the audience. These sections have the same purpose and effect.

I've encountered explanatory and historical notes more often in the Afterword simply because to discuss plot points and details is to risk spoiling something for the reader, or because the reader wouldn't understand the context without having first read the story. The exception I've seen is when this is a later edition, and the author is reintroducing or reframing the work in some retrospective way.

As F1Krazy suggested, many readers cut to the chase and only read the story, so you would have to accept that not everyone would get that explanation.

I think if your story doesn't make sense or isn't self-contained and you must convey that information to them somehow, it would be better to include it as part of the work itself. You could do substantial reworking to incorporate it into the story, but barring that you have another alternative: I've seen authors slip this in as a prologue that isn't in the narrative voice of the rest of the work, such as offering a faux dictionary definition or quote, or a quick backstory. It feels contrived but ensures that the reader has that information going in.

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I've read a few books that had an "afterword" section at the end, where the author would address the reader directly to talk about the work. I know Anthony Horowitz did this with the Alex Rider series; one book had him list his top 10 favourite deaths across the whole series, and I think another had him discuss his decision to have Scorpia end with

Alex getting shot by a sniper.

So you could always add an afterword at the end of your own novel, and in there, you could explain how you knew that X was unrealistic or incorrect, but you put it in anyway for artistic license. This relies on your readers actually reading the afterword and not just closing the book the minute they finish the actual narrative, but it's the best way I can think of.

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