Trope

I don't even want to imagine getting rid of expansions and stuff, but when I glance across my shelf, I'm pretty sure this is the one I feel the most happy and fuzzy about having.

OK this probably looks like a complicated explanation, but in the end it's actually fairly straightforward.
 
 
So basically we're talking about the two times in the film the Patronus charm successfully saves Sirius from the Dementors; the first time when Harry observes a mysterious figure doing it then passes out, and the second time when Harry realizes it was his future self he saw and successfully pulls it off himself.
 
The cue for the first scene is 6M5AN First Frozen Lake.  This cue is presented as recorded on the LLL CD as Disc 2 track 1 "The Dementors Converge (Film Version)"
 
The cue for the second scene is 7M4 Watching The Past.  This cue is presented as recorded on the LLL CD as  Disc 2 track 21 "Watching The Past (Alternate)"
 
The interesting thing about these two cues is of course that neither cue uses Window To The Past theme for the big Patronus moment; Each cue's climax is a similar passages of aggressive choir, rising strings, and horn triplets, but no thematic material.
 
At some point, someone decided that it made sense to use the Window To The Past theme for successful usage of the Patronus Charm.  I have no idea if this was before or after 4M14N The Dementor was recorded or not (the only version of 4M14 recorded that we know of), but we know from a sheet music leak that the original version of 4M14 Dueling The Dementor didn't use the Window To The Past theme either.
 
Anyway, for these two frozen lake moments, Williams didn't record a revision or insert synced to anything specific onscreen, a wild recording was made containing the past theme on horns with a calm choir backing.  I don't know what Williams' title was for this cue, but this is the cue Mike referred to in the liners as the "pre-recorded version of the Patronus music".  For the rest of this post I'll just called it "the Patronus Insert"
 
Cuaron decided for the film itself to keep First Frozen Lake as it was, but then use the Patronus Insert the second time around during Watching The Past when Harry realizes his potential and successfully performs the spell, saving the thematic statement for when the hero saves the day, and paralleling when it playing during the first time her performed it when training with Lupin.

The choices Williams then made for the OST album are then what really muddied the waters.  Here we get a version of First Frozen Lake where the climax is replaced by the horn recording from the Patronus Insert along with some hodgepodge of other edited elements, and he named the track "The Dementors Converge".  We don't know whether the Patronus Insert appears here because at one point Cuaron was going to use it at both spots in the film, or if this is just something Williams did for the album on his own. 
 
Watching The Past is also included on the OST - with the climax replaced by the Patronus Insert like Cuaron did in the film - as the first cue inside a track he titled "Finale". 
 
Finally, he included just the choir element of the Patronus Insert on the OST as well, in a track he titled "The Patronus Light".
 
The main program of the LLL album follows what the film does, and features First Frozen Lake as it was recorded (which had to be titled "The Dementors Converge (Film Version)" because of Williams' OST decisions), and Watching The Past with the Patronus Insert in place of the original climax was included inside a track called "Buckbeak Saves The Day / Watching The Past" (which also includes the ticking clock overlay over part of the cue).
 
Then the non-film-versions of First Frozen Lake and Watching The Past were included in the bonus track section, along with "The Patronus Light"
 
 
 
So, to sum up
 
What was recorded
6M5AN First Frozen Lake 7M4 Watching The Past "The Patronus Insert"; The Window To The Past Theme on horns with a choir backing, with the horn and choir elements recorded separately What the film does
6M5AN First Frozen Lake plays as recorded 7M4 Watching The Past has the climax replaced by the Patronus Insert What Williams did for the OST album
Track# 15 "The Patronus Light" is a presentation of JUST the choir element of the Patronus Insert Track #19 "The Dementors Converge" is 6M5AN First Frozen Lake, except the climax has been had been replaced by the horn statement of the WTTP theme from Patronus Insert mixed into other things {including apparently some material from 7M4's original climax} from 1:45-2:33 or so Track #20 "Finale" is 7M4 Watching The Past with the climax replaced by the Patronus Insert at around 1:13, which is crossfaded into 7M6 Sirius' Final Scene What the LLL main program does
Disc 2 track 1 "The Dementors Converge (Film Version)" is 6M5AN First Frozen Lake as recorded, premiering clean what we heard in the film Disc 2 track 4 "Buckbeak Saves The Day / Watching The Past" is 7M3 Buckbeak Saves The Day followed by 7M4 Watching The Past, which has its climax replaced by the Patronus Insert, like in the film (and also, the tick-tock element appears at various points throughout the whole track) What the LLL bonus tracks are
Disc 2 track 21 "Watching The Past (Alternate)" is 7M4 Watching The Past as originally recorded, premiering the original unused and never-before-heard climax and its unique denouement Disc 2 track 23 "The Patronus Light" is OST track #15 directly from the album master Disc 2 track 25 "The Dementors Converge" is OST Track #19 directly from the album master  
I hope that makes sense to everyone and answers all the questions!

Almost 2 years since the set came out and we're still making discoveries!
 
The Dementors Converge
After re-listening to Watching the Past (Alternate), I thought the ending was really similar to The Dementors Converge (the track from the OST) except that there is no horn playing the past theme.
The waveforms also look almost identical between both tracks (except of course during the horn sections):

 
So after lining up both tracks as perfectly as possible (very hard in this case because there seems to be a ~0.001% speed difference), I tried to invert one to see if I could isolate the horns, and here is what I got:
 

Even though it's not perfectly isolated, this clip clearly proves that the section from Watching the Past (Alternate) (1:13 to 2:00) comes from the same recording as The Dementors Converge (1:46 to 2:31). The horn was just an overlay, used for the OST track.
 
So I came back to the liner notes and found that The Dementors Converge is described as a "pre-recorded version of the Patronus music that was utilized for the original album", whereas the alternate to Watching the Past is said to contain an "initial version of the Patronus music". No mention about the fact these two cues actually share the same material!
 
The Patronus Light
Another thing I found is that The Patronus Light, while described in the liner notes as "the discrete choral component of that pre-recording [here referring to The Dementors Converge]" is actually used in the film score as an overlay in Watching the Past !
 
Again, after lining up both tracks to be sure it was used, I found out that The Patronus Light seems to be used as an additional choir section for Watching the Past. The cue is shortened and doesn't appear as heard in the album but I can confirm the take we have on the original album (and also on the LLL CD7) was used in Watching the Past.
 
Here is my attempt at removing that overlay from Watching the Past (notice how different the choir sounds like, especially in the beginning):
 

 
It also seems like Mike used the ending of The Patronus Light to present the clean ending for Watching the Past on the LLL set (Mike had to use the OST master for this cue, not the 192k high resolution source that he mainly used for HP3).
 
Did you know all that @Jay?

That one is in close second place! Followed by A.I. 

Pretty random question, but why is track 18 on Azkaban Disc 2 called "Window to the Past", and not "A Window to the Past" like on the OST? 
 
I've been revisiting this box set and have concluded that it is the best expansion I've ever purchased. If I had to get rid of every expansion I've ever bought and only keep one, this would be it. This music is so damn good, all 8 hours of it. 

Here you go @Josh500. This is the score as edited in the film, to picture. 
 

 
Now, just because I enjoy this, here are the most noticeable differences (that are not super specific edits):
Right away, the opening is different, removing the Ticking clock and Chimes until around 0:11 2:09-2:38 retains the ticking clock in the film. This section has no ticking on the LLL set or the OST. 3:55-4:03 plays the Flutes a second time. It's not looped, but overlayed over the top of the cue the second time. 4:52-5:00 retains the ticking clock in the film. This section has no ticking on the LLL set. This section is also slowed down, you can hear the tempo change in the ticking. 5:17 onward the film does not feature ticking. This section is present on the LLL set and the OST. 8:49-End is slowed down quite a bit from what is on the LLL set. It plays at 117% it's original length.  
There are plenty of other edits, loops, tempo changes, etc. of course, but the above are the very clear differences. I also just want to say, this was a pain in the ass to replicate and it's still not quite perfect. Damn editors. Lol.

One of my favourite OST assemblies from Azkaban is Secrets of the Castle. It was so strange not hearing the second half (Rainy Nights) come in after the Great Hall Ceiling cue in this set! The two cues just feel right together!

Nice straw man's argument. Come on mate, you're far better than that. Leave the whole 'putting words in other people's mouths' routine to the usual suspect (the one most people have on ignore).
 
 
I agree with your sentiment but disagree with the context. The artist in question was paid to write this music for a film we paid to see. A film we've paid to own. A score we've paid to hear performed live by an orchestra. A soundtrack we've paid to listen to. And now an expanded soundtrack we've paid for as well.
 
The music in question was previously unreleased and unavailable for purchase, for no insignificant length of time either (nearly two decades for the first score, two thirds of my life!)
 
Studios have ignored our community for years simply because we're a niche market. You can't turn around and complain when people acquire unreleased materials if you're refusing to sell them (especially when the same people are more than happy to pay for them, as evidenced by this very release!)

Williams’ original intentions for Lupin’s Transformation are honestly baffling to me. I find it much more musically interesting than what’s in the film, but it’s severely out of step with the horror and suspense of that scene. I’d love to know what he was thinking because it really, truly does not work for that scene.  It’s so out of step that I’d just assumed it was an unused opening to Chasing Scabbers when listening to it on the album for many years. 

Official lyrics to Pettigrew’s Theme:
 
Pet-er Pet-er Pet-er Pet-Ti-Grew
(repeat infinitely)

I think that is huge miss and it always shocked me that they left that off the soundtrack. It is used to staggering effect twice in the movies and is a very popular and memorable cue. And Willams left it off the OST!
 
I think the Gyrfindor winning the house cup also contains of the best statements of the friendship theme. Reunion of Friends essentially rehashes that but the original Gryfindor wins the cup in PS was the first with a warm horn led statement that conveyed the majesty of the theme. I think that theme is otherwise only memorably stated at the end of Quidditch when Harry catches the Snitch and then HWW which is a concert suite.

Listened to the first two discs today—I wholeheartedly agree. I would also add “Through the Doors” as another essential addition.

I think "Harry Gets His Wand", "Hagrid’s Flashback", "Fighting the Troll", and "The Dark Forest" are ESSENTIAL editions to the score.

Pretty random question, but why is track 18 on Azkaban Disc 2 called "Window to the Past", and not "A Window to the Past" like on the OST? 
 
I've been revisiting this box set and have concluded that it is the best expansion I've ever purchased. If I had to get rid of every expansion I've ever bought and only keep one, this would be it. This music is so damn good, all 8 hours of it. 

There's 3 things you can hear in the film that are not on the set. 
 
3 very minor, very short things.
 
 
1st up is "Shawm", a source music cue you can hear from 0:00-1:06 in this video (the score cue it overlaps with, heard from 0:44-end of the video, IS on the set)
 
 
 
Next up is a very short drum & tambourine passage that I can't find on youtube, but it plays after the Buckbeak scene and before the ghost knights bust through the stained glass window
 
And finally is a difference performance of the "Sir Cadogan" cue, where it was played at a slower tempo and there was drum and tambourine playing along with it.  You can hear it from 0:00-0:19 of this video
 
 
 
And then there is one piece of music that appeared in DVD bonus features but not the OST, LLL, or the film itself:  The original version of "Marge Points The Finger", which got replaced by a revision in the film, and that revision is what's on the LLL set. 
 
The original version is heard from 1:20-1:28 of this video
 
 
 
 
That's literally it in terms what what we know was recorded.
 
 
 
As for what might have been recorded, but we have no evidence of?  Well, there are at least SEVENTEEN things found in the sheet music  that we don't have recordings of.
 
You can see them all listed out in my google doc, at the bottom of the "Complete Cue List" tab
 
https://docs.google.com/spreadsheets/d/1R7JM5QmRNh6PbgqeBH_lbj2C3WLbzxz9px3Z7GKLaAk/
 
You will also find links in that section to videos in which mockups of those exclusive sheet music passages are synced to film footage

Another inspiration by Williams was this, i made it back on conservatory studies in Prague https://www.youtube.com/watch?v=231kHSV1u1o

I love coming to threads where members (mostly the same ones) continually post obscure quotes, references and in-jokes! They make for excellent engagement among other members, and add a lot of value to this wonderful resource of a site.

Well.
 
If this keeps him away from Jurassic Park, Star Wars, Star Trek, whatever, that's fine with me!

I love coming to threads where members (mostly the same ones) continually post obscure quotes, references and in-jokes! They make for excellent engagement among other members, and add a lot of value to this wonderful resource of a site.

It was...fun. Oh my.
 
 

It's not being complained about at the US Supreme Court or UN General Assembly. It's being discussed on a John Williams fan site. Settle down.
 
By the way, I do agree that we are doomed as a species. Just for other reasons.

Anyone getting this that doesn't want the map? I can offer good money. See, this is what we have been denied since the Walt Disney Company gained access to these properties. Sony always gave us nice bonuses like digital wallpapers and stickers. 

It's not being complained about at the US Supreme Court or UN General Assembly. It's being discussed on a John Williams fan site. Settle down.
 
By the way, I do agree that we are doomed as a species. Just for other reasons.

It's not being complained about at the US Supreme Court or UN General Assembly. It's being discussed on a John Williams fan site. Settle down.
 
By the way, I do agree that we are doomed as a species. Just for other reasons.

It's not being complained about at the US Supreme Court or UN General Assembly. It's being discussed on a John Williams fan site. Settle down.
 
By the way, I do agree that we are doomed as a species. Just for other reasons.