The Ten Commandments of Knox or the Knox Decalogue are a series of ‘rules’ for mystery/detective fiction codified by Ronald Knox. During the Golden Age of Detective Fiction, mystery stories were considered ‘games’ where the audience would be presented a set of clues and the challenge was to figure it out before the author…or, more accurately, it was the challenge of the author to successfully and fairly mislead the audience. If the audience figured it out, they won and if they failed, the author won.
Thus the rules were established to help make the games fair for participants and to avoid the author from tricking the audience or making the game unfair.

Now that I’ve become immersed in Storytelling Theory, I find the Decalogue interesting. I was first introduced to it years ago, but was re-introduced to it most recently by Umineko no Naku Koro ni which misrepresents the Decalogue big-time.^A)
The reason I find it interesting is because it gets very close to what I figured out regarding the mechanics of storytelling. It’s scarily close but isn’t quite there, so most of the commandments are Context-Dependent Writing Rules. They are a decent guideline, but only if you already understand how storytelling works.

As a complete side-note, I’m wondering whether Golden Age authors were among the closest to get to storytelling theory? That may explain their success, since a very well-written story (mechanically) is more likely to be popular and profitable.

I’m going to lay out the Decalogue first before I analyze it. I’m getting these rules from Wikipedia, the evil, but I’ll double-check other sources much later.
The Ten Commandments are: ¹⁾

1. The criminal must be mentioned in the early part of the story, but must not be anyone whose thoughts the reader has been allowed to know.
2. All supernatural or preternatural agencies are ruled out as a matter of course.
3. Not more than one secret room or passage is allowable.
4. No hitherto undiscovered poisons may be used, nor any appliance which will need a long scientific explanation at the end.
5. No Chinaman must figure in the story.
6. No accident must ever help the detective, nor must he ever have an unaccountable intuition which proves to be right.
7. The detective himself must not commit the crime.
8. The detective is bound to declare any clues which he may discover.
9. The “sidekick” of the detective, the Watson, must not conceal from the reader any thoughts which pass through his mind: his intelligence must be slightly, but very slightly, below that of the average reader.
10. Twin brothers, and doubles generally, must not appear unless we have been duly prepared for them.

Though it should be noted that most of these can be summarized as “don’t do anything without adequate prior setup”.

Now it’s time for the analysis.

The intent of this rule is to prevent the writer from making the criminal a character that has never been seen thruout the story and is only revealed at the last minute.
Basically, the criminal has to have been adequately introduced to the audience. It’s easiest and best to do this at the start of the story.

However, this doesn’t mean that they have to physically appear in the story. Their presence can still be alluded to and felt thruout.

For example, the ‘culprit’ in Firewatch is someone we never see with our own eyes, but we know he’s there because he’s talked about.

The purpose of the latter point I don’t really understand, so I’ll have to think about it later.

This is sensible only if the supernatural agencies are not adequately explained.
If this is a story where (for example) telepathy is a known factor, then it can be.

Minority Report (is a bad film, but I digress) builds its mystery 100% on a supernatural element. It’s not inherently bad, so this is one of the worse rules.

I’ll quickly note that the version of this that I encountered first was the Umineko one where it is rendered as “It is forbidden for hidden passages to exist.”
That one is a lot more exclusionary and, consequently, bad than the actual commandment.

So…because the actual commandment is a bit different, my initial write-up is not applicable.

The only issue I take with this one is that it’s “not more than one”. I think secret rooms and passages are fine if they’re adequately set up beforehand. Though as practical advice, it’s probably fine.

Because I don’t want that previous write-up to go to waste, here’s an expandable section where I go over it. I think that it’s still useful, just that it’s not a response to the commandment.

I think the key point is the “explanation at the end”. As long as something is adequately established, it should be fine to.

A Chinaman must figured in the story.

This gets into the problem of coincidence in stories.
I think this one is also unambiguously good without further context. In a mystery, the audience must be given the reasoning behind the mystery – and the reasoning must be reachable with the evidence presented.

This is sensible in general, but I think it’s fine as long as the detective isn’t acting incoherent.

What this means is that he can’t be uncovered as the culprit while he was actively working to uncover them. This implies that the detective isn’t the culprit because he himself is not aware of it.
Though that would be an interesting premise for a mystery.

This one is also unambiguously good, since the audience needs to know the same clues as the detective. This rule is violated by, for example, Death in Paradise.

This is one of the more context-sensitive commandments…I think?
This one only applies if the ‘Watson’ is the POV character or narrator. Not if the POV character is a detective.

It should be noted that Umineko no Naku Koro ni renders this in a form that is difficult to understand, almost incomprehensible.

This one is unambiguously good and says exactly what is required in order for it to be fine: establishment.

Violated by Glass Onion: A Knives Out Story.