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[blue]

(NP59)r5c39 = (5)r4c7 - (5=2)r3c7 - (2)r3c3 = (QNP59)r5c239[AUR59:r35c13] => r5c1 <> 5,9

I'm curious why you don't also call the 1st "naked pair" a QNP.
I know that JC Van Hay is fond of calling them naked pairs, too.
I've never quite liked it, but I've always understood it.
After the recent conversations about "quantum" patterns, I finally found some comfort in the fact that at least I could think of them as being a "quantum" naked pairs.

I should probably explain why I never quite like calling them naked pairs.
It's that to me, in this case, if you want to call it a naked pair ... then the chain should start like: NP<59>r5c39 = (4|6)r5c9 - (...)
[ Note: I do understand that it would usually be difficult to do anything with "(4|6)r5c9" together as a single node in a chain. See my "BTW:" remark below, though. ]

On the other hand, if you want to use the 5r5c9 = 5r4c7 link, then it seems like when 5r4c7 is false, what you really have, is a hidden box single for 5 in r5c9, that couples with the bi-value cell (5|9)r5c3, to give something that, together, "acts as a naked pair", and/but (to my mind) certainly is not an "actual naked pair". It's a perfect occasion, it would seem ... to be using the term "quantum naked pair".

BTW: Reading my line from above ... [ "... if you want to call it a naked pair, then ..." ] ... I suppose you could conform with that idea, by having the chain start like: NP<59>r5c39 = (4|6)r5c9 - 5r5c9 = 5r4c7 - (...).

That seems like overkill, though, maybe ... I don't quite know.
I'm sure I've seen something similar in other people's solutions.
I think I always had a bit of distaste for it, after trying to enter it into XSudo, and seeing that (in this case) the "cell truth" for r5c9, from the naked pair ... should "cancel out" along with the "cell link" for "(4|6)r5c9 - 5r5c9" ... to leave just the 5B6 "box truth" and the 5r5 "row link" involved with 5r5c9.

Final note: I'm just thinking out loud here ... not advocating for anything, and not trying to condemn anything.

Cheers,
Blue.

[ronk]

(NP59)r5c39 = (5)r4c7 - (5=2)r3c7 - (2)r3c3 = (QNP59)r5c239[AUR59:r35c13] => r5c1 <> 5,9

I'm curious why you don't also call the 1st "naked pair" a QNP.
I know that JC Van Hay is fond of calling them naked pairs, too.
I've never quite liked it, but I've always understood it.
After the recent conversations about "quantum" patterns, I finally found some comfort in the fact that at least I could think of them as being a "quantum" naked pairs.

A quantum is not required in this deduction. I don't see a strange or questionable naked pair either.

(4|7=np59)r5c13 - (5)r5c9 = (5)r4c7 - (5)r3c7 = (hp59)r3c13 -UR- (59=4|7)r5c31 ==> r5c1 <> 59

[blue]

A quantum is not required in this deduction. I don't see a strange or questionable naked pair either.

(4|7=np59)r5c13 - (5)r5c9 = (5)r4c7 - (5)r3c7 = (hp59)r3c13 -UR- (59=4|7)r5c31 ==> r5c1 <> 59

Nice and clean. I like it

[sultan vinegar]

I'm curious why you don't also call the 1st "naked pair" a QNP.
I know that JC Van Hay is fond of calling them naked pairs, too.
I've never quite liked it, but I've always understood it.
After the recent conversations about "quantum" patterns, I finally found some comfort in the fact that at least I could think of them as being a "quantum" naked pairs.

The simple answer for not using QNP is that it is two candidates in two cells; a QNP needs two candidates in three (or more maybe? cells), as stated in the updated definition in my quantum guide.

I should probably explain why I never quite like calling them naked pairs.
It's that to me, in this case, if you want to call it a naked pair ... then the chain should start like: NP<59>r5c39 = (4|6)r5c9 - (...)
[ Note: I do understand that it would usually be difficult to do anything with "(4|6)r5c9" together as a single node in a chain. See my "BTW:" remark below, though. ]

I didn't quite like writing NP either, but I figured it clearly isn't a HP so that's why I went with NP.

On the other hand, if you want to use the 5r5c9 = 5r4c7 link, then it seems like when 5r4c7 is false, what you really have, is a hidden box single for 5 in r5c9, that couples with the bi-value cell (5|9)r5c3, to give something that, together, "acts as a naked pair", and/but (to my mind) certainly is not an "actual naked pair". It's a perfect occasion, it would seem ... to be using the term "quantum naked pair".

BTW: Reading my line from above ... [ "... if you want to call it a naked pair, then ..." ] ... I suppose you could conform with that idea, by having the chain start like: NP<59>r5c39 = (4|6)r5c9 - 5r5c9 = 5r4c7 - (...).

That seems like overkill, though, maybe ... I don't quite know.
I'm sure I've seen something similar in other people's solutions.
I think I always had a bit of distaste for it, after trying to enter it into XSudo, and seeing that (in this case) the "cell truth" for r5c9, from the naked pair ... should "cancel out" along with the "cell link" for "(4|6)r5c9 - 5r5c9" ... to leave just the 5B6 "box truth" and the 5r5 "row link" involved with 5r5c9.

Can we sum up all that with the fact that regardless of how you dress up the subsequent inferences in the chain, a NP is two cell truths covered by two 'house' links, and a HP is two 'house' truths covered by two cell links? What we have here is one cell and one house truth covered by two cell links. So maybe Steve K's 'Hybrid Pair' (YP) is more appropriate than NP? But in your words, that seems like overkill though, and I promised DPB that I would stop over-egging the pudding! BTW, I think that (YP) or (YT) etc. only exist in chains (i.e almost-patterns); they don't exist as stand alone structures without being de-generate.

A quantum is not required in this deduction. I don't see a strange or questionable naked pair either.
(4|7=np59)r5c13 - (5)r5c9 = (5)r4c7 - (5)r3c7 = (hp59)r3c13 -UR- (59=4|7)r5c31 ==> r5c1 <> 59

I agree that a QNP is not required. I only posted that chain to wind DPB up following his recent quantum rants! The fact that much simpler eliminations exist seems to have hit a particularly sensitive nerve with him - as intended

As for the questionable naked pair, I think that there is a trade-off here: your elimination has no questionable naked pair, but it does have a cannibal elimination; mine does have a questionable naked pair, but no cannibal elimination. The other way to go would be to use the (YP59)r5c39 notation for 'Hybrid Pair', which results in no questionable naked pair and no cannibal elimination but at the obvious expense of adding a new definition with questionable benefit.

[ronk]

I don't see a strange or questionable naked pair either.

As for the questionable naked pair, I think that there is a trade-off here: your elimination has no questionable naked pair, but it does have a cannibal elimination; mine does have a questionable naked pair, but no cannibal elimination. The other way to go would be to use the (YP59)r5c39 notation for 'Hybrid Pair', which results in no questionable naked pair and no cannibal elimination but at the obvious expense of adding a new definition with questionable benefit.

When the native truth set includes a UR (or AUR) and the exclusion set includes any UR digit within the UR, the logic set is cannibalistic by definition.