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2:01 PM
(and by sard's theorem you can omit the points where $\nabla f=0$ on the right)
 
Isn't every system thermodynamic in the fact that you could assign entropy to any physical system?
wait
does von neumann entropy count here
prolly
 
if $g_i$ are the generators of $G$, then we say that $G$ is generated by $g_i$, and $\mathfrak{g}$ is "..." by $g_i$
"..."=spanned?
 
@AccidentalFourierTransform yup
 
@Secret all exact path integrals are in Grosche's handbook of path integrals
 
2:14 PM
uh, dumb question
 
@ACuriousMind Also, people who use $-$ for set difference are irredeemably wrong and should be expelled from science.
God gave you $\setminus$ for a reason.
 
@Yashas, second one is enthalpy
 
Enthalpy = U + PV
 
Setminus is bad though
Too slanted
 
dH = dU + d(PV) = dU + PdV + VdP
 
2:15 PM
@EmilioPisanty I'm an ardent follower of $-$ - you just started a holy war!
 
I prefer set substraction to be slightly askew -
 
@ACuriousMind =P
 
I prefer $-$ to \ because \ is easily confused with $/$
 
Are scalars literally just one dimensional vectors? I just had memories of kiddo school and covering vectors and scalars, and it seems abhorrently wrong. I can't think of anything distinguishing them plus they're bijective
 
$A-B$ is reserved for $\{a-b: a\in A,\ b\in B\}$
 
2:16 PM
@Yashas, entropy
 
@Secret to the extent that $A$ is easily confused with $\forall$, yes
 
O so there's a difference, I see
 
for reversible reactions, entropy is defined as dS = dq/T
 
Scalars form a vector space yes
Since they obey all axioms of a vector space
 
Entropy can also be defined as the number of ways of arranging the system
S = k log W
 
2:17 PM
@Secret It's not \, it's $\setminus$
normally on more of a 45° slant
 
Scalar fields are defined by a vector bondle
The line bundle
With fiber R or C
 
@ACuriousMind If I'm reading that definition correctly, homotopy equivalence requires a homeomorphism
 
@EmilioPisanty No - every homeomorphism is an equivalence, but there are far more such equivalences than homeomorphism. Basically, homotopy equivalent spaces should be thought of as spaces that can be continuously deformed into each other by shrinking or expanding parts (even expanding a point into some n-dimensional ball, or vice versa!)
 
@Yashas, ideal gas
 
@AlbertEinstein Check kinetic theory of gases for the assumptions
 
2:21 PM
@ACuriousMind hmmmm
oh, ok
you only require that $f\circ g$ be homotopical to the identity
maybe link to a description that makes that clear?
and yes, explaining why it's homotopy that matters wouldn't be amiss there
Also, this might could be shortened.
 
@EmilioPisanty Changed it, but not really shortened it :P I'll think about how to explain the relevance of homotopy better - it's really just because it was more convenient to argue on the $S^2$ than on the punctured $\mathbb{R}^3$, but I see how one might be confused about why that's allowed
 
How to do this question:
An eye specialist prescribes spectacles having combination of convex length of focal length 40 cm in contact with concave lens of focal length 25 cm coaxially. The power of this lens combination in dioptres is _____ ?
My Solution:
Add the two powers after calculating them using P = 1/f
Is this method correct?
 
O great, I think I don't understand bell inequality, I need to re-study it again
Too many physics people tell me today that it is not the correlated outcomes of the observables get transported between the subsystems (which has no information), but it is which pair of outcomes that will pop out after the measurement (which also has no information)
now combined this with:
Your marble experiment does not violate Bell's Theorem (or any other theorem of classical probability) and is therefore quite entirely irrelevant to the issue here. The wave function does not count as a hidden variable because it cannot *determinstically predict the outcomes of all measurements. In your marble experiment, we can easily explain the result by invoking some determinstic (though mysterious) force. — WillO Apr 29 at 15:47
so back to the drawing board I go
I wonder if entanglement is really something that violates my "A interact with B" mindset, which might explain why I keep making mistakes on it
 
Bell's inequality isn't really even a physics thing
It's related to probability theory
 
2:37 PM
uh
Entanglement isnt long range interaction though is it?
 
Well, its (bell inequality) violation is, and that is what I am trying to understand what has happened there. I have heard the magic square example as an elaboration, but it still feel really magical to me, like, exactly when is that correlation establish, and why is that not classical (other than showing that some number is larger than $2$)
 
It's just two, spatially separated particles being described by a non-seperable wavefunction isn't it?
 
That's how it is said, but then that will imply the correlation is already there the moment you start makeing the wavefuncton of the two subsystems inseparable (at least that's what I thought)
 
But "interaction"
doesn't that imply there's something mediating it
 
and logically, the next step on that thought process will then be every possible pairs of outcomes (and their superpositions) become correlated, thus this deduction will then cause me to think of it is still randomly selecting one of the pairs from this sample space of noncommutative probabilities
this will then cause me to conclude that the measurement is not very mysterious since the correlation is already established throughout the wavefunction when some interaction that entangle the particles make their wavefunction inseparable
But
WillO (and later on many of my physics friends) said this is the wrong way to understand what happens in entanglement
 
2:42 PM
You talk about "correlation" as if it is something that "exists". But "correlation" just means that certain outcomes are, well, correlated. I don't get what you're talking about.
 
honestly
i'd just take the same approach to the collapse of an entangled state as I would a normal single particle wavefunction
just with a few extra conditions like the angular momentum needing to balance out if it's a pair made by a photon with 0 angular momentum or something
 
Well, the way I think about e.g. the singlet state is that since neither subsystems can be represented as a state vector, but must be an ensemble represented by the reduced density matrix, and that I knew that measuring any spin along any of the axes will always give anticorrelated results, this naturally cause me to have the conception that all possible pairs of spin in all directions are already anticorrelated once the two particles become entangled and the wavefunction becomes inseparable
and thus the measurement only end up picking randomly one of the correlated pairs and becomes the ou
so you still have the result that the outcomes don't exists until you measure it, but the correlations are already encoded in the wavefunction
 
Im confused though
 
@Secret The whole point of (the standard interpretation of) quantum mechanics is that the "pairs of spin in all directions" don't exist prior to measurement. It doesn't make sense to talk about their correlation before you have measured them.
Saying "the spins don't exist but their correlations do" is just playing meaningless word games, in my opinion. In the entangled state it is encoded that the spins, if measured, will be (anti-)correlated. Seeking for "where" or "when" this correlation comes about is not really a question whose meaning I can understand.
 
So basically when we say we entangle two particles, there is no way to know they are entangled (have inseparable wavefunction) until the correlation is established by measuring it?
 
2:53 PM
@Secret No, Bell-inequality violations are not a long-range interaction.
@Secret that is correct
 
@Secret You can never "know" what state a system is in without measuring it (the measurement can be crafty, as in state tomography, but it's still a measurement).
 
wait
 
Moreover, there is no way to know whether the preparation procedure produces entangled pairs without multiple, different measurements on an ensemble of systems.
 
@ACuriousMind so you can't know a system is entangled before measuring it, but how can you be certain that a system was entangled after you've measured one of them?
 
@Phase you can't.
 
2:55 PM
@Phase A single measurement rarely tells you anything about a state
 
oh for fucks sake
 
you need to take an ensemble of identically prepared states and measure them all
 
...and, in addition, you need correlated measurements for that to work
 
@ACuriousMind Ok... that's , a very new concept to me. In the past I knew that outcomes don't exists until we measure it, but I previously not aware that even the correlation itself don't exists until we measure it
 
local measurements confined to one of the subsystems are incapable of providing any information about entanglement.
 
2:56 PM
Ok so wait
 
@Secret correlation is a description of measurement outcomes
of course it doesn't exist until you measure
 
The standard answer for the FTL entanglement paradox is that the person measuring the particle can't be sure that it wasn't collapsed / interacted with before measurement, right?
 
user228700
Hey, @Johnr :-) YHM.
 
nevermind
I just realised why what I was about to say was dumb
 
Yeah, I always thought the wavefunction being inseparable already somehow contain those correlations that can manifest when a measurement take place, but it appears there is no way to know whether the wavefunction is even inseparable before measuring it
 
2:58 PM
@Kaumudi.H not arrived yet, but it can take a little while to escape the Indian subcontinent ...
 
user228700
:-)
 
@Secret that is ultimately interpretation-dependent. The wavefunction may well physically exist, but any information about it is inaccessible to you until and unless you measure.
 
@Kaumudi.H hey, how are you feeling?
 
user228700
@AccidentalFourierTransform Hey! :-) I feel much better. Thanks so much for asking!
 
2:59 PM
You're all a bunch of math-savvy topology folks right? Is there any physical / mathematical actual argument to support MWI or is it just a pure hypothesis?
 
To the extent that it does exist, though, for an entangled pair, it is a nonlocal quantity that nevertheless cannot be used for communication.
 
@Kaumudi.H got it, thanks. I'm with you on this one.
 
@Phase What do you mean by "physical argument to support MWI"?
 
user228700
Wokay, thanks! :-)
 
MWI is a terrible name, though
I just tend to call it "QM taken at face value".
 
3:01 PM
@EmilioPisanty Everett Interpretation then, and by physical argument I mean an experiment that can be explained usefully by it
 
@Phase I have never seen an actual argument that would support any interpretation, but then I'm starting to think I'm just a grumpy operationalist who doesn't care :P
 
@EmilioPisanty I am ok with that no communication point (given I have ran through no communicaton theorem at least thrice), but what acuriousmind said about the correlation is only established at the moment of measurement, and not within the wavefunction due to it being made inseperable by some interaction (even in interpretations where it physically exists) is what is new to me
 
@Phase oh, all of quantum mechanics.
An experiment that can only be explained usefully by MWI and not by other interpretations? No.
That's why we call them interpretations.
 
@EmilioPisanty how does the Everett interpretation explain weird things like youngs slits?
 
@Phase the same way QM does
 
3:02 PM
@Secret I think we have a language issue here: By definition, a "correlation" is a pattern in measurement outcomes. A pattern in X cannot meaningfully "exist" before X exists, can it?
 
ok lemme ask this:
What's the difference between Many-worlds when you only consider one universe, and immediately forget any ones that branch off, and Copenhagen?
 
@Secret What ACM just said. You can play word games and try to add meanings to the word "correlation" if you want to, but you're just fooling yourself that you've understood things.
@Phase How do you decide that a wavefunction component has "branched off"?
i.e. what objective criterion do you use?
 
@EmilioPisanty I thought the whole point about MWI is that each different outcome happens, but the universes diverge into their own, self contained ones to accomodate each outcome
 
@ACuriousMind I was thinking about something like: (Using an interpretation where the wavefunction is physical) In an inseparable wavefunction $\psi (a,b)$, the probability amplitudes for all a,b are already correlated in a way such that it result in the measurements to give the correlated outcomes as expected. That's what I mean by "correlations already exists") I am not sure what thoguht process I got wrong for thinking about the correlation exists at the level of probability amplitudes forany a,b
 
I don't know what a "correlation of probability amplitudes" is.
 
3:06 PM
@Phase yeah, well. Self-contained unless conditions bring them to indistinguishable states, in which case they can interfere destructively.
 
@EmilioPisanty Universes can interfere with each other? How do conservation laws work?
 
@Phase how does the second question relate to the first?
 
Oh boy
I got a letter from CERN!
I wonder what it is!
(It's the PDG booklet)
The 2016 booklet, the last paper one they will ever print
 
@Secret From a $\psi$-ontic perspective, that is a crude understanding but it can be mapped into something correct.
 
@EmilioPisanty Because wouldn't interacting universes change energies of the system?
Or do you just treat it like adding the two together
or something
 
3:09 PM
@Slereah Wow, they finally sent it to you?
 
Well, not everything
I ordered the booklet and the book
 
However, decreeing that a nonlocal $\psi$ has physical existence is pretty meaningless, because you can't say anything about it that's operationally meaningful until and unless you measure.
 
I wonder what's new in it
Probably the LHC results
And the PLANCK results
Last one I got was the 2006 booklet
 
@Phase yeah, particularly the 'or something' =P. It's probability amplitudes that add/substract, not energies.
 
Indeed there is now a mass for the Higgs!
$m = 125.09 \pm 0.24 \text{GeV}$
 
3:11 PM
If $\hat A$ is conserved in the evolution, only states with the same $A$ can interfere.
 
0
Q: Physycs Stackexchange rules?

Georgi Pavlov"If your motivation for asking the question is “I would like to participate in a discussion about ______”, then you should not be asking here. However, if your motivation is “I would like others to explain ______ to me”, then you are probably OK." And the website at the same time has a "homework...

 
@EmilioPisanty Is that where the vacuum ground state comes from?
 
@Phase I have no idea what you're talking about, sorry.
@Slereah you should get the first one and put them together
 
@EmilioPisanty A bit confused here, why a nonlocal physical $\psi$ has no operational meaning until a measurement took place?
 
@EmilioPisanty well it's the same book
So
 
user228700
3:12 PM
@JohnR: I've just had pizza in a sandwich, BTW!
 
@Secret because no $\psi$ has operational meaning until a measurement takes place.
 
@Kaumudi.H I used to eat all sorts of thinks in sandwiches. Meat pie sandwiches was my finest hour.
 
user228700
Meat pie sandwiches, hmm, I see :-|
 
@Slereah so it's not like the CRC handbook?
 
@EmilioPisanty Ah I see. I guess that's the concept I have been missing for all these years
 
3:14 PM
Look at this baby
 
user228700
Oh, what the heck, did u actually stuff pies in between two slices of bread?!
 
@Kaumudi.H Have you ever had a calzone? It's kind of a sandwich made from a pizza.
 
@EmilioPisanty you're talking about destructive interference, so I was wondering if that leads to a sort of quantum-noise, like the vacuum ground state
The virtual particles
 
@EmilioPisanty Well, the PDG book is like that
 
3:14 PM
in my uni library back home they had a first-edition reprint
 
The booklet is a tiny version of the book
 
it actually fits in your hand
 
I think the book itself is 1800 pages
 
they put it next to the 95th edition or so
 
But they haven't sent it yet
 
3:15 PM
@Kaumudi.H yes
 
I kinda want to buy the CRC but it costs a gold bullion
 
@Phase Sorry, as far as I can tell that's an incoherent jumble of concepts.
 
user228700
@JohnRennie Unfortunately, no, I haven't yet had calzones. But they're available in a store next door so maybe I will try it soon!
 
@Slereah it can't be more expensive than Prudnikov, though, can it?
 
user228700
@JohnRennie Whoa. I'm mystified and also literally LOL x'D
 
3:16 PM
@EmilioPisanty What is Prudnikov
 
Are we bragging about books?
 
@EmilioPisanty :/
 
Yes we are
Tell us about your fancy books, @0celouvskyopoulo7
 
@Kaumudi.H they were very nice, though the filling in the pie tends to dribble down your chin.
 
@yuggib probably wins
 
He has all of Bourbaki, Reed-Simon, and Hörmander
 
that's volume one, there's five
 
@EmilioPisanty I have the other book
The one by... Gradhkin?
I forget his name
 
because there's only two books ever?
@Slereah presumably you mean Gradshteyn and Ryzhik
 
that's the one
 
user228700
3:18 PM
@JohnRennie Nice! :-) BTW, I didn't put a slice of pizza in b/w slices of bread. I cheated you with that sentence because what I did was, I spread some pizza spread on the slices and put pieces of cucumber in b/w.
 
I'm not sure there are more than two books like that :p
 
@Kaumudi.H though I'm currently munching my way through a kg of apples in an attempt to eat a bit more healthily.
 
That there are two is already amazing
 
ultimately, though, there's things like this one
 
Well yeah but if we start looking at engineering books
 
3:19 PM
@Kaumudi.H if you like that you will love calzone!
 
A simple example: consider $\Psi(a,b)=\psi (a)\psi (b)$ vs anantisymmetric $\Phi(a,b)$. Picking any ordered pair (a,b) the former does not show any correlation to the function value, but for the later, since $\Phi (a,b)=-\Phi (b,a)$ by antisymmetry, the graph of $\Phi (a,b)$ has a symmetry under inversion about the line $a=b$ (where the amplitude must be zero because zero is the only number that is neither positive nor negative), while amplitudes at any (a,b) will always be the negative of (b,a) hence there's a correlation between any two points on the graph with that relationship
 
a fifteen-volume set, but still
 
Then that's another conversation
 
A calzone (/kælˈzoʊni/, US /kælˈzoʊneɪ/ or /kælˈzoʊn/, UK /kælˈtsoʊni/; Italian: [kalˈtsoːne], "stocking" or "trouser") is an Italian oven-baked folded pizza that originated in Naples. A typical calzone is made from salted bread dough, baked in an oven and stuffed with salami or ham, mozzarella, ricotta and Parmesan or pecorino cheese, as well as an egg. Different regional variations on a calzone can often include other ingredients that are normally associated with pizza toppings. == Regional variations == === In Italy === Sandwich-sized calzones are often sold at Italian lunch counters...
 
I know that some material physics books are 10.000 pages long and cost thousands of dollars
 
user228700
3:20 PM
@JohnRennie Oh, nice! :-) Man, I wish I could do things like that.
 
also
 
@Slereah A minor but very definite achievement in my career so far is no. 469 here
 
Compared to the 2006 particle handbook
This one is in color
Well, a little color
The graphs have colors
 
user228700
@JohnRennie Yeah, I liked it :-) Wokay, I'll try it and tell you!
 
@EmilioPisanty which integral did you do
Was it $\int 1 dx$
 
3:21 PM
@Slereah I caught a misprint
 
I hadn't realised that calzone means trousers. It brings a whole new meaning to the phrase eat my pants.
@Kaumudi.H eat apples?
 
It is cognates with french "caleçon", underwear
Let's check the GR section
 
@Slereah 2.477.9 and 2.477.10, according to my records
 
user228700
@JohnRennie Hadn't heard that phrase before :-/
 
"Big bang cosmology"
 
3:22 PM
@yashas , The amount of heat required will be minimium if it is heated through:

1. 1K

2. 1°C

3. 1°F

4. Same for all
 
@Kaumudi.H never watched The Simpsons?
 
user228700
@JohnRennie Well, yeah eat a bag of apples for lunch, I mean.
 
user228700
@JohnRennie Nope, not even one episode :-|
 
$$\Omega = 1.000 \pm 0.005$$
how will we ever know if we are globally flat
 
there was just no chance that was correct
 
3:25 PM
There is indeed the PLANCK results in the booklet
 
@Kaumudi.H apples aren't very nutritious. That's fine for me because it helps me recover from eating like a pig at the weekend, but for a teenager I think it's a road to malnutrition.
 
user228700
@JohnRennie But I certainly think that I could do with more meals consisting of fruit, rather than, you know, bread and spreads.
 
Apparently one accelerator is called the KEK
 
1kg of apples contains only 500 calories. You'd need to eat 4kg a day to stay alive.
 
aka the superKEKB
 
user228700
3:27 PM
@JohnRennie Hey, no one is proposing that I take up this "1 meal a day" habit like you! :-P
 
@JohnRennie wot
you don't need 2000 cal a day to stay alive
 
Some people eat 1200 and gain weight
 
why are people kissing the LHC's ass but nobody speaks of the KEK
It collides electrons and positrons at 7 GeV
Pretty nice
 
@Slereah I have all of Spivak, which is nice
 
user228700
3:29 PM
@0celouvskyopoulo7 WebMD doesn't agree...
 
I don't have all of Hörmander, but I probably should just buy the last one while it's on sale
 
@0celouvskyopoulo7 you can frame them
They make nice art
 
@0celouvskyopoulo7 AFT has an emoticon that nicely expresses my view of that statement.
 
user228700
@JohnRennie Huh?
 
@JohnRennie Don't let your balls sway in the wind. A sheep might come by and kick them.
@Slereah I don't have all of Weinberg, but I do have Weinberg's GR book which is rare
oh, @JohnRennie
 
3:32 PM
@Kaumudi.H it's, erm, something that AFT got banned for posting. I'm not sure I dare repost it here :-)
 
best thermo book
 
user228700
@JohnRennie Accidental Fourier Transform! Ah, I was wondering what the heck you were talking about.
 
user228700
Hang on, whoa whoa, he got banned for posting it?! Wow, OK...
 
This is relevant:
2 hours ago, by ACuriousMind
I swear, if this is a setup for some ASCII testicles again...
 
user228700
Yes yes, I saw that before x'D
 
3:34 PM
I should put that on my quotes page for my thesis
 
Perhaps this picture would fit better
 
@Kaumudi.H well, not a ban, it was the automatic 30 minute suspension when one of your posts gets flagged.
 
user228700
Ah, OK.
 
God I want Pizza
@JohnRennie are you unimpressed by that book?
 
@0celouvskyopoulo7 I read about the index theorem but largely failed to understand it, so its potential applications to thermodynamics don't leave me hot and slippery.
 
3:36 PM
@JohnRennie The thermo was a joke, but it's that book I wanted
the one from the UK
the heat equation has largely nothing to do with heat
unlike the wave equation that really does have to do with waves
 
Ah, you've got it then. Cool :-)
£200 well spent I'm sure!
 
@JohnRennie My lease was 200 less than expected so it worked out
@JohnRennie that's questionable
I wonder if I'll have time to read it
I should be reading right now, but meh
 
@0celouvskyopoulo7 If you're made homeless at least you'll have something to read :-)
 
Apparently our local scientology center was shut down!
 
where will you go to get audited now
 
3:42 PM
[Philosophy random] My conception of exists = anything that can be mapped into some kind of parameter space
this is because anything that look like space is somehow more tangible to me in that I can manipulate them mentally
 
does consciousness exist?
 
probably, but we don't know the exact types of parameters
we knew a few neuro circuitry but nothing is conclusive yet
 
rob
@0celouvskyopoulo7 "I like to think so," he said self-referentially
 
So in short, most knowledge look like space to me, and that is how I remember and learn things
Nothingness trivially exists under this weird conception because emptiness is obviously space look like
Exercise: Now you can understand why I tend to wrongly think the wavefunction is a kind of "stuff"
 
You need to drink more. The problem of consciousness is easily solved by the application of lots of alcohol.
2
 
3:48 PM
that's sick, John
alcohol is not good
 
Right, it's not good, it's great.
 
Add some sugar in it
 
it's bad for you
 
It will taste better
 
@Slereah yes, I always put two teaspoons of sugar in my champagne.
It's too sour otherwise.
 
3:49 PM
Well I meant more some fruit juice with vodka :p
 
@Slereah I really don't understand why people drink vodka.
 
Why does everyone insist on being an alcoholic?
 
It's mostly alcohol?
 
It must be very good
 
It has little flavour (apart from the speciality vodkas) and all it does is get you drunk.
 
3:51 PM
Well yes
That is all I ask of alcohol
I find wine and beer to be terrible tasting
 
You could drink a fine red wine or an excellent English beer and really enjoy getting plastered.
 
I couldn't
I tried
 
@JohnRennie or drink 5 shots of whiskey like a man
 
Instead people drink an expensive vaguely fruity mixer with vodka. Pointless.
 
All my friends told me that I didn't like beer because I haven't tasted a REAL beer, that is, the brand they like
It's always terrible
 
3:52 PM
Whiskey does not deserve to be drunk as shots.
 
@ACuriousMind well excuse me we can't all afford $50/bottle whiskey
 
Whiskey does not deserve to be drunk.
 
@Slereah It's not compulsory to like beer. Personally I love a good beer, and because it isn't as strong as wine I can drink a lot more of it.
 
ban @AccidentalFourierTransform
 
I also don't like wine
Or cognac
Or rum
I can tolerate sweet cider
 
3:53 PM
what kind of frenchman are you
 
we have a french that doesnt like wine, and an englishman that doesnt like tea
 
I don't even like cheese
 
I don't like whisky very much. I'd choose a brandy over whisky any day.
 
@AccidentalFourierTransform I'm an american who doesn't like football
 
@0celouvskyopoulo7 It's not the price - but I wouldn't drink "bad" whiskey in any form and I don't think drinking it as a shot does the "good" whiskey justice
 
3:54 PM
please tell me that 0celo7 doesnt like guns and ACM doesnt like refugees
 
Oh I love guns
Arm the students.
 
There's a French apple brandy that is excellent - the name escapes me at the moment, probably due to all those brain cells being killed by drinking.
 
Arm the teachers.
 
in Mathematics, 2 mins ago, by Eric Stucky
Secret, I'm about 98% sure you're rediscovering concrete categories.
and I don't even know what that is
 
duh Calvados of course.
 
3:55 PM
@Slereah what's a "germe de sous-variete" ?
 
Germ of a submanifold?
 
doesn't make much sense
 
you're going to trigger the ACM
 
3:57 PM
does he not like sitcoms
 
Dammit, I started saying Euclid like the Germans do ironically, but now I can't stop
 
Oiclid?
 

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