So quickly before we get into the actual video, I just want to make something as clear as possible for you guys, that I did not include every single detail about Help Wanted in this video. Simply because there's been so much that has been revealed over the past few weeks that it's been actually pretty hard to keep up with all of it and include it all in this video. So for that reason, not everything is included. I just thought I'd bring up some important clips and important details about the game to help solidify this, I guess, like mini FNAF theory, I guess you can call it. But I don't know, maybe I'll do a part two to this. But for now, this is it. It's already got a few good points in there that I think can really help the case. But yeah, just not everything is included. Super sorry about that. I just didn't want to make it over complicated for me or for you guys watching. So yeah, super sorry about that. I just wanted to make it quick and simple. Anyways, enjoy the video. Oh, people of the internet, my name is Johnny and welcome back to another FNAF VR Help Wanted discussion video where today I'm going to be asking a very simple question. But as you're going to find out, has a very complex answer. And that is, is Five Nights at Freddy's VR Help Wanted Five Nights at Freddy's 7? Or I guess in other words, is Five Nights at Freddy's VR Help Wanted Canon? Now, this again has a very complex answer so I didn't want to waste any time. And let's get into the facts. Now, before we can start accusing the canonicity of Help Wanted, we first need to figure out what Canon means in the real world and then convert that definition to something that roughly aligns with what it could mean in the FNAF universe. Now, according to the two seconds it took for me to Google what Canon means, the definition of Canon is a general rule, law, or principle by which something is judged. So putting that into FNAF terms, Canon means a game, minigame, cutscene, etc. that is dubbed relevant to the lower timeline or story by Scott Cawthon or the community. Or at least something along that lines, I don't really know, I'm bad at this, okay? In total, Scott has released eight games not including Help Wanted and they are FNAF One, Two, Three, Four, FNAF World, Sister Location, Freddy Fazbear's Pizzeria Simulator, and Ultimate Custom Night. Out of those eight, six of them are considered Canon, those being FNAF One through Four, Sister Location, and Pizza Sim. FNAF World isn't Canon because, well, isn't it obvious? It's FNAF World. And while yes, Ultimate Custom Night does have lore in it to help strengthen the timeline and story of FNAF as a franchise, it is not Canon because every single animatronic in Custom Night cannot be in the same place altogether. It just, it can't happen. Even with our latest and what is considered to be the best timeline of FNAF made by MatPat a few months ago, none of those characters will ever be in the same location all at the same time. And even if you disagree with that last statement about Custom Night, just think about this. Jack O'Chica is one of the characters in the game and Scott himself confirmed back during the days of FNAF Four that she is, in fact, not Canon. Now, of course, this isn't a perfect explanation about what Canon means in the FNAF universe, but as long as we're finding something similar to that, I think we've got a pretty good case. But to kick things off, let's take a look at the main gameplay features of Help Wanted. Now, over the past few weeks, there have been many, many teasers and videos alluding to what we do in Help Wanted, which those are going to be very, very helpful to answering our question. Looking through most of the videos and teasers, we can find out basically exactly what we're going to be doing throughout the game. We can figure out that we will be repairing at the very least the FNAF One animatronics of Freddy, Bonnie, Chica, and Foxy, surviving either one or multiple nights in different locations throughout the franchise, and finding secret plushies and action figures that we can then use at the prize corner to unlock some sort of secret mini-games or something along those lines. Now, right off the bat, there was a huge problem with what we've just said. Traveling from location to location literally cannot be done in just one game without some sort of passage of time. So it seems like Help Wanted in that case may be on the lines of some sort of ultimate custom night game, where the gameplay itself can't be canon because, like I said, all the characters in location simply cannot be happening all at the same time. But the game will also have some lower bits secretly put aside for people to uncover and connect pieces to the lore in the story with the rest of the game. Just based off of this information alone, it seems like Ultimate Custom Night and Help Wanted may be in the same sort of category with the gameplay itself not being canon due to all the characters and locations happening at the same time, but that they also have lower bits put aside for people to find and connect with the rest of the timeline. And just the other day, actually, Steal World Studios confirmed that the game is going to have different difficulty levels where if you beat the normal difficulty, you can then unlock something that they call the Nightmare Difficulty. And if you beat that, then they say that there was going to be secret lower bits for the community to put together to fit with the rest of the timeline. And looking at some of the different trailers that have been released, we can also find out that we will be surviving in the FNAF 2, 3, and 4 locations. We also know that we will be surviving in the sister location because Scott himself said over on Reddit in one of his posts that we will be reenacting the Night 3 minigame where the character is walking through Funtime Auditorium, fending themselves off from Funtime Foxy. And well, yeah, Scott and Steal World have confirmed that there are going to be new and exciting levels added to the game. It seems like a bit of a stretch to have the majority of the game be a remake of the old ones if it is canon. And even the FNAF wiki itself that features some upcoming books, movies, and games says that the FNAF VR experience will not be canon. So, guess we just gotta trust them on that. Like I said at the start of this video, there have been so many teasers, trailers, news articles about Help Wanted and its features, its secrets, that it's been really really hard to keep up with at all. And so for that reason, I haven't included everything in this video. But I am going to leave you with one last piece of evidence that, at least in my opinion, basically confirms that Help Wanted is not going to be canon to the rest of the franchise. On the teaser that is currently on ScottGames.com, you can see a few characters that are going to be in Help Wanted. Freddy, Baby, Plus Trap, the original game from FNAF 1. It seems like there's going to be a lot of characters in this game. Right in between Freddy and Funtime Foxy, you can see Nightmarion. Nothing that out of the ordinary, it's just another character that's going to be in the game. Something that sets Nightmarion aside from every single character in that teaser is that Nightmarion itself is not canon. You see, all the way back during FNAF 4's lifespan, on the day of Halloween, or at least near the day of Halloween, Scott released an update for the game called the Halloween Edition. This updated the game to include more animatronics that were previously in FNAF, such as Mangle, the Puppet, Balloon Boy. They were now all characters in FNAF 4. With the addition of taking on their roles as a Nightmare animatronics, Scott also gave us a bit of information about their backstory. He also confirmed whether or not they were canon to the rest of the franchise. Nightmare Mangle wasn't canon. Surprisingly, Nightmare Balloon Boy was, however, the topic for today's discussion, Nightmarion. Scott confirmed that Nightmarion is in fact not canon. So including them in a game that is argumentally canon or not seems a bit non-canon to me. But anyways, that was just my thinking on whether or not Five Nights at Freddy's VR helped wanted it's going to be canon to the rest of the franchise or not. Feel free to leave what you guys think in the comments below and do your own research and again leave them in the comments. Maybe we can get something started. But anyways, thank you everyone for watching and I'll see you all on the flip side. Goodbye.


Governor Mark Dayton has vetoed a bill that would have aligned Minnesota state tax code with federal changes past last year. The Democratic governor rejected the bill passed by the GOP-controlled legislature with about 20 grade school students standing behind him at a St. Paul's school. Dayton said the bill did not include the money for schools he requested and was tilted toward the wealthy and corporations. I'm vetoing the bill because they have not met the condition I set, which is to include the emergency school aid, and also because it's a bill that's skewed toward the rich. Even in the individual, they make a big deal about the individual. A family of four, making $65,000 a year is about the median family income. They get $92 a year in tax breaks. A family making $250,000 you get three times that amount. People making $250,000 a year get 12 times more tax cut than people making $20,000 a year. They got it upside down. This gives tax relief to people who most need it and lets the rich and the super rich and the big corporations do fine on their own. Our bill actually gave tax relief to low and middle income Minnesotans in the process of tax conformity. This was as reasonable a bill as you could have found. It actually was a slight increase on taxes for businesses. That's what federal tax conformity did here in Minnesota, it increased taxes on businesses. We left some of those increases in place and actually gave the tax relief to low and middle income Minnesotans. What the governor did today was veto a bill that would have put money in low and middle income Minnesotans' pockets. And I am incredibly disappointed that the governor has decided to play politics with this bill instead of giving Minnesotans some certainty in allowing them to file their taxes more easily next year. Minnesota needs to adjust its tax code to account for federal changes that took place last December. Doubt and other lawmakers say that if the governor does not sign a tax conformity bill filing taxes next April will be extremely complicated for Minnesotans. If you enjoyed this segment of Lakeland News, please consider making a tax-deductible contribution to Lakeland PBS.


OK, let me do it then. Good enough for me. So it's not really going to be any kind of complete proof. But let me write down the theorem again. So you have this is a scalar manifold. And this is a holomorphic line bundle. And it comes with a metric e to the minus phi. And the scalar manifold has a metric with scalar form omega. And then you assume that dd bar phi plus the Ricci curvature is greater than or equal to some theta, which is greater than or equal to 0. Then for all alpha d bar closed, l valued such that the integral over x with a finite l2 norm, there exists u. It's a some section of l such that d bar u equals alpha, and the l2 norm of this section is less than or equal to, again, I did this. You use this non-negative form theta. Yeah, so theta is a 1, 1 form. And this is the, so you think of it as a metric. And you compute the norm with respect to that. So if it's degenerate, then you have to, it's an algebraic expression. You have to make sure that this is finite. Think of it as strictly positive for this purpose. So 0, 1 form.  Right, but then how does this inverse exist? It doesn't exist, but I mean the formula for an inverse is a formal formula. You can write it down, and for this to be finite, alpha has to be in some direction 0. So just think of it as strictly positive. It makes you, it's a good point. I didn't want to worry about it too much. OK, so as I said, it's just going to be a quick sketch. So this d bar operator maps sections of L to 0, 1 forms with values in L, and 0, 1 forms with values in L to 0, 2 forms with values in L, and so on. So you can compute an adjoint for this thing. So it's going to map a 0, 1 form to a function. And the way you do that is you take a smooth section with compact support, and you define the adjoint. This is the formal adjoint by this formula. So this is a norm for sections. This is a norm for 0, 1 forms. And then you form this Laplacian d bar d bar star with respect to the data that's defining the L to norms here, omega. Yeah, yes. And so you make this Laplacian associated to the d bar operator. So what you're going to want to try to do is solve the equation. This is another 0, 1 form, say v equals alpha. OK, so you want to somehow argue that this guy is invertible. So there's a little trick to try to estimate it. So you can think of alpha in two ways. First, you can think of it as a 0, 1 form with values in the holomorphic line bundle L. And so that has a d bar operator, and that's where our operator comes from. But you can also think of it as a section of t star 0, 1, x, tensor L. And then you may want to try to apply a d bar operator to this guy, but you can't, because this is not a holomorphic vector bundle. So you want to turn it into a holomorphic vector bundle, which you can do by using the metric. So by using the metric, any 0, 1 form will turn into a 1, 0 vector field. In the metric omega, you get sections of this guy, and then you have a d bar operator associated to. It's not a section. It's a d bar operator associated to sections. And if you conjugate that operator, you get an operator that's called nabla bar. And so you can try to compute a Laplacian for this operator. But now this operator maps sections of this vector bundle, which are not seen as differential forms, into 0, 1 forms, tensored with this thing. So they're like 0, 1 forms squared. They're not 0, 2 forms. But anyway, so you can also compute an adjoint for this guy with the appropriate inner product for such sections. But remember that now this is a section. So when you form the Laplacian, you don't have this term. So then you have another Laplacian, nabla bar star, nabla bar. And the magic is that formally, these two operators, they differ by a 0th order operator. So this is an identity, I think, first written down by Kodaira. But it comes from a technique sort of worked out by Bachner. I've done more carefully here. Amazing thing is that this is, in this case, exactly dd bar plus the Ricci of omega. OK, so now what you've got is a, well, this operator, this Laplacian is always, any Laplacian is always non-negative. So if you write d bar, d bar star plus d bar star, d bar, say it to some form beta, take inner product with beta, that's equal to the norm d bar star beta squared plus norm d bar star d bar beta squared. These are different norms for different spaces, but they all come from the same data. And so what you get here is that this is equal to nabla bar beta squared plus some operator that comes from the action on these forms from the curvature. So you have to appropriately raise indices to turn it into an operator that acts on forms. But I'll just write it L of, well, maybe it's L is fine. It's a multiplier. So you can now forget about this term. And let me just write L for short. And if you know that this quantity is non-negative, then you get an estimate here. If you have it in terms of this thing, then you get this kind of an estimate. At this point, if you want to proceed rigorously, you have to invoke a little bit of precise functional analysis. But morally, it's already clear what's going on. So this operator L gives a kind of lower bound for this smallest eigenvalue of the Laplacian. So if it's positive, then you can invert the Laplacian. So that's morally what's going on, even though there are all sorts of issues of regularity, but we just assume that those work out in the end. And so now that means that if you've got any 0, 1 form, you can solve the equation Laplacian v equals that 0, 1 form. But that's still not Hormander's theorem. Actually, the way you do this is you use this norm to define a Hilbert space. This inequality tells you that it is positive. And then you just use the Reiss representation theorem. And it tells you that the solution v will have a norm, this particular norm, less than or, this inequality says that the inclusion of this Hilbert space in L2 is bounded. And then when you invert it, the norm of this solution will be less than or equal to the norm of this alpha in L2.  And the norm d bar star v squared plus d bar v squared is less than or equal to that integral. It should be theta. So this is really, I didn't really do it a lot of justice, but this is really linear algebra of some sort. So OK. But this still doesn't give us the theorem that we're looking for, except that if alpha happens to be d bar closed, then you can apply d bar to this whole thing. And this term will go away because you have d bar squared. So you find that d bar, d bar star, d bar v is equal to 0. And so then in particular, the inner product with d bar v is also equal to 0. But that's just the norm of d bar star d bar v squared. So that's 0. So this term here is gone. Or if you prefer, you can write this as d bar star d bar v v. That's also 0. And now you move the d bar to the other side. And so this d bar v is equal to 0. And so what you've now got is you're solving this equation. And if you let this be u, then the estimate is right there. So that's basically the existence part without any irregularity. OK. Maybe you regret asking me to perform Anders's theorem now, but I hope not. OK. So now I want to move on to the statement of Barenson's theorem. I have to set things up a little bit. So the first thing I need is a family of metrics for my holomorphic line bundle, l to x. So I'm going to usually write this family as e to the minus vt and t is something in some domain omega and cm. So the rigorous way that I need to define this, which will be slightly useful in a moment, is you look at x cross omega. And then you have a projection map to x. And then this x has a line bundle. And so you can pull back this line bundle. And what you're asking for is a metric of this thing. But then every fiber here, of the form x cross t, is the same as this original thing. And the line bundle is naturally isomorphic. So when I write this, I mean I identify the metric I've got for here with its restriction to a fiber. I need that because I want to define the l to norm that I'm about to define in such a way that the base doesn't depend on t. Integrating over a space that doesn't depend on t. So here is the Hilbert space. So the notation is going to be, is this too low to see? Risk it. It's OK. So anyway, it's high at this point. So if I've got one of these metrics, this is going to be the set of all sections, which are holomorphic. And then I have the l to norm I've been using there. f squared e to the minus vt. And I've got some fixed metric on x. It's a scalar metric. OK. So in this way, we can define a vibration over the domain omega so that the fiber over t corresponds to this h phi t. So I'm sometimes going to write that as h phi subscript t to indicate that it's a fiber. So part of Bernstein's theorem involves making statements about this as if it were a vector bundle. But it's not necessarily a vector bundle. And even if it is, because it's typically infinite dimensional, it's a little bit hard to say what that might mean. It's not something I want to wade into so much. So I try to make some simplifying assumptions. It still becomes a very useful theorem. The point, the thing you first do is that you put this x as a relatively compact domain inside some larger manifold y. And then I need some technical hypotheses that I don't want to go too deeply into. They are not 100% necessary, but they make everything easier. So I'm going to ask for this to be a Stein manifold. So most of you probably know what that is. But if you don't, it's a closed sub-manifold of some complex Euclidean space, complex sub-manifold. And then this domain shouldn't just be any domain. It should be so-called pseudo-convex. So if you don't know what that means, then it means that you have an exhaustion function of this thing. So there's a smooth function on x, which is strictly plurisubharmonic. And so the sub-level sets, so all the points below a certain given level, is relatively compact inside y. That's what pseudo-convexity means. In particular, this thing is also a Stein manifold. But the advantage is that now I can have my data be defined over here. And then the L I'm using is just a restriction to x of the ambiantly defined thing. I can also have my scalar metric coming from this ambient manifold. So in other words, this data here, it all extends to some larger space. And then you've got these holomorphic sections. So they're nice and smooth. And so if you're in a Hilbert space for any given t, then this same f is in the Hilbert space for all other t. So somehow what that means is that if you think of this vector space as a subspace of the holomorphic sections of L, then it's independent of t. So that's one thing. But also the norms that you get here, they're equivalent norms in the analysis sense. So these are all quasi-isometric. So you have a family of Hilbert spaces that are quasi-isometric. That's the situation we want to be in. OK, so now the next thing I need is to define sections of this vector bundle. OK, so what is a smooth section? So it's going to be a section of this line bundle here. So whose restriction, let's give this section a name, say s. So st, that's the section on the restriction to x cross t, but thought of as on x, naturally. So this st should be in hv t. So you automatically get some smooth things, but they're actually holomorphic in L2 on each fiber. Now the reason you do that is because you can now define a d-bar operator. Now you have a d-bar operator for this thing. You just take d-bar of s. And then you restrict it to fibers. You get 0, 1 forms in the horizontal direction. But because they're holomorphic on the fiber, you don't get any d-bar component vertically. OK, so we're sort of turning it into a holomorphic vector bundle at the same time. OK, so what's a holomorphic section? So maybe let me introduce notation. This will be written as s is in gamma. Yeah, no, it's the same. It's just what the fibers are by definition. So the holomorphic section is s in gamma of omega hv, such that it's actually a holomorphic section of this bundle. So in other words, d-bar of s is 0. And then the notation will be s is in gamma o of omega hv. OK, so if you remember the criterion for Griffith's positivity and involve the dual bundle, so now I need to give you a definition of a holomorphic section of the dual bundle. OK, so well, first of all, let's say that the dual bundle is the bundle of Hilbert spaces that are fiber-wise are the dual spaces. So I just remind you that the norm of a vector c in the dual space over t is the soup of, so you take some element f in hv t, f is going to be in hv t, and you pair it with c, which is an element of the dual, and then you divide by the norm with respect to t. And then, so now if you have a section, say it's going to be a section of this dual bundle, then you can ask about what is its regularity, like under what conditions, for example, is it holomorphic? Well, if you take any f in, say, one of these guys, let's just say hv 0, that f is automatically in all the other ones by our hypothesis, then you can look at the function that sends t and omega to this complex number, and this should have that regularity. So for example, if you want a holomorphic section, this should be a holomorphic function. If you want a smooth, then this should be smooth. If you want measurable, this should be measurable. It's more than that. So if it's holomorphic on each xt, I think you meant x cross t, it's a section of the pullback of L over x cross omega. Yes? No, it's more than that. It also varies holomorphically in t. Yeah, so it's both. If it's holomorphic, it's a holomorphic section of this whole thing. So it's holomorphic in the. So the restriction is always a holomorphic section of L. That's the definition of the vector bundle. In addition, you want holomorphicity in omega. Yeah, well, also L2 in the fiber. But I mean, a lot of times we're doing this shrinking of domains, so it's effectively under this hypothesis of shrinking and having all the data living from the ambient space. Because it's smooth beyond the boundary, and it's a compact set. I want to give some examples of sections. One, not holomorphic, and two, holomorphic, of the dual. You're just asking your questions too quickly. So here's an example of a smooth section. So let's take some section, which is a holomorphic section of, or I should say, is the holomorphic section of the original vector bundle, not the dualized bundle. And now you can define, so CT, this is going to define a section of the dual. So CT acting on some F, and by definition, the inner product of F with S, ST. So that is the inner product associated to this Hilbert space. So that clearly gives you a linear functional on every fiber, but it's almost never holomorphic. Even if this section, the section S that you started with, is holomorphic. So you can even put a complex conjugate here. Well, that's not right. And it's in the wrong Hilbert space. You can put it in L2 or something. So you might think it's not holomorphic because it has a complex conjugate in the inner product, but that's not it. The problem is really that the weight doesn't vary holomorphically. So this is an example of a non-holmor. So the second example is almost trivial. So if you take F and H, I was going to give an example of something in H. So let me just say that in words. If you take an F in H of phi 0, then it lives in H of phi t for all t. So that's a holomorphic section because it doesn't actually depend on t. So this is because this bundle is actually a trivial vector bundle. It's not only trivial, it's sort of trivialized. It's handed to you trivial. You don't have to trivialize it. So if you've got one vector, you can just constantly translate it and you get a holomorphic section. So that's not a very interesting example. Maybe a more interesting example is this one. So let's let x be a point in our manifold capital X. And let's define c tilde superscript x by c tilde superscript x acting on some section of H of phi is just the evaluation of this F, the point x. So point evaluation. OK, so for each x, that actually gives you an element not of, it's not a complex number, but it's almost a complex number. So the trouble is that this is in L, the fiber of L, over the point x. So if you knew what 1 was in L sub x, then you would know what this complex number is. But it's effectively a complex number. To get a complex number out of it, you need to pick some e in the dual bundle. And you can pick it in such a way that, say, e, I don't really care too much. So then if you take F of x tensor e, then that, if you redefine it, remove the tilde by putting tensor e here, then you really do get a complex number. And it's almost point. It's point evaluation given a vector in the fiber of the dual bundle. OK, so I'm going to kind of ignore this point. Just pretend that I do know how this is isomorphic to c. OK, so well, this is clearly something that takes a vector in h and assigns to it a complex number. But that, in itself, doesn't make it a section of HP star. Because the problem is this notion of dual. In infinite dimensions, duality is not just linear functionals. It's continuous linear functionals. So you have to know that this thing is continuous. And it is because this is a fact which is given as an exercise in the notes that I gave out. This is called Bergman's inequality. This is a general equation of it. So F of x squared e to the minus phi of x is less than or equal to some constant that may depend on x times the t norm of F. And the way we've done this is constant doesn't depend on t because all the data extends to a larger domain. But it could depend on t as well. So this tells you that you have a bounded linear functional. So this is actually a very well-known object. So let's drop the tilde, Cx F and F of x. Let me say a little bit about this object because we'll meet it again soon. So by the Reiss representation theorem, for each such x in x, you can find a section, let's call it k super x sub t in Hv t such that this number, in this case it's an element of Lx, is achieved by taking L2 inner product with respect to this section. So say F kx t inner product is equal to this F of x. So this is not exactly correct. This thing is not taking values in, I guess it is exactly correct now. Yeah, sorry. So it's a section of L. Question? The boundedness, the Bergman's inequality exactly means that this actually is an element of the dual. This says that the norm of this number is less than or equal to some constant times the norm of the vector in the Hilbert space. That's what boundedness. That's what continuity of the linear functional means. Well, yes, you want to show it's an h star. What does it mean? No, it's bounded linear functional. Otherwise this representation theorem doesn't hold. And then the output is F of x. Well, let me do this for each t. So it's a section, so F sub t if you want in ht. Yeah, but I'm evaluating it at particular x. I've chosen some x and I'm evaluating it at that particular x. Yeah, still depends on t. So I just want to check that it's in the dual space in each fiber. So I drop the dependence on t. It's you should, I guess. So I should really write this. And now I need to prove that it's bounded. No, it just says that for each t it's in the dual space. But it is actually because we've shrunk things, it is actually bounded uniformly in t. It doesn't matter here. Yeah, so this is the point I was trying to address before. So because it's an element of Lx, you can't talk about it being a complex number. So you have two choices. You can choose a vector. Or you can put another metric on this thing. And that's e to the minus phi is the metric on that line. So it's bounded with respect to that structure. OK, so then what you do is you put this. It's a valuation. It's point evaluation. So that's the most important example of a holomorphic section. It's like a delta function. So in some sense it's all the examples. All of them are some average of this. Right, so if you check what it means for this to be a holomorphic section, it means that if I plug in some f, this should depend holomorphically on t. But it's actually independent of t. Or if you start with a holomorphic section, f, it's holomorphic in t. And it's holomorphic. It's a little confusing point. Yeah, if you check the dependence on holomorphicity, if you look at that formula for the inner product, you'll see this phi sub t. Yeah. On this case, it also gets screwed up by the complex conjugation. But that's the less important part. OK, so then there's this. So this guy here, it depends holomorphically on some variable that's not x. But how does it depend on x? Well, so what we do is we define kt of x and y to be maybe bad notation. You take this k superscript x, plug in y, and take the complex conjugate. And this is a well-known object in complex analysis. It's called the Bergman kernel. So one thing that you can check, it's not difficult, but it's worth doing. So this kt actually is a holomorphic section of something. I have some non-standard notation here. Let me explain it. So this x dagger is the complex manifold expo with a complex conjugate structure. So that's, from this conjugation, it's clear that it depends anti-holomorphically on y. But if you put the complex conjugation, it depends holomorphically on y bar. Then it's also a section of the line bundle. So the fiber over x comma y is lx tensor with a complex conjugate of ly. Complex conjugate structure of l at the point y. OK, so that's one thing you can check. The other thing is that this is a kernel from this formula that when you integrate f times k sub t, you get the value of f at the point x. So it's basically the identity map written down. Well, it's a point evaluation. But so if you choose an orthonormal basis, if g i is an orthonormal basis for h, p, t, then this kt of x and y is the sum over i of g i of x, x tensor, g i of y conjugate. So that's really the usual formula you see in a complex analysis class for the Bergman kernel. Yeah, that's right. And that's what this is, the Bergman kernel for each t. Yeah, via the restrepresentation theorem and appropriate conjugation of some sort. That's right. Maybe there's one last thing that's worth knowing. And I'm going to put it almost invisible because I'm not going to use it. So you can actually compute this thing as a solution of some extremal problem. This is the soup over all g with norm t equal to 1 of g of x squared e to the minus vt. And the restrepresentation theorem, yeah. So you could do it that way, or you could do it from this statement by first choosing an orthonormal basis for the things that vanish at x. And that's a hyperplane because the evaluation is bounded. So there's only one other direction, and this guy is the guy in that direction. That's a kind of explicit way of finding the actual section. OK, now I can finally state Bernstein's theorem. No, I'm going to put it over here. Not like this. It's not. OK, so we can call this theorem 1, which is its number in Bernstein's annals paper. So let x be a relatively compact pseudo convex domain in the Stein-Kehler manifold. And then let l to x be a holomorphic line bundle with family smooth metrics e to the minus vt. So if the curvature of these, I shouldn't say it like this. Let me explain, and let me just write it down. So this is the phi as it depends both on the x variable and on the omega variable. So this d bar operator is in the space x cross omega. Then you have the projection to x. You pull back the Ricci curvature from x to x cross omega. In other words, this term doesn't depend on the omega variable. But if you compute this quantity, and this is greater than or equal to 0 or greater than 0, then the vector bundle h phi to omega, together with its Hermitian metric given by the Hilbert space norms over omega t, it's this norm squared sub t, which I just erased up there. This has non-negative, respectively positive, Nakano curvature. Curvature that is non-negative in the sense of Nakano. So that's finally the statement. And there's the one-dimensional version. Sorry? This thing? This one? This one. No, I mean it's a, this is a vector bundle. So it means that you have a Hermitian inner product in each fiber, Hilbert spaces. So remember, when we had a vector bundle, e over y, with a Hermitian metric, we can talk about the curvature of this Hermitian, the churn curvature of this Hermitian metric. So the h is this guy. So yeah? A section s? OK, it's to each fiber t, there's an 8, there's this norm sub t. I think there's no confusion. It's a metric on a vector bundle, which means it's fiber-wise a Hermitian inner product. But that's right. So the claim is that it's positive as soon as this guy is sort of fully sub-harmonic in omega. And the dd bar x is bigger than the Ricci curvature. So a lot of people, they don't look at sections of l. They look at sections of l tensor, the canonical. And that eliminates this Ricci curvature. And then the statement looks more concise, but I think it ultimately is a bit more confusing. So this is a special case of a one-dimensional base. So that e to the minus phi, the metric for the pullback of l to x cross omega. This is what I should have written there. So now I'm going to change omega. I just have a one-dimensional base, which I'll just think of as a unit disk. Assume that this metric satisfies the same condition. So dd bar phi plus phi pullback of Ricci of omega is greater than or equal to 0. And there's a corresponding statement for strict positivity. Then for any holomorphic section of the dual, that's not identically 0, let's say, the function t maps to log square norm is sub-harmonic. So this is the one-dimensional base version of that theorem. It generalizes two bases with a higher dimension. But the statement would be Griffith's positive, not Knoll Poglian. I'll have something more to say about that at the end, depending on how far I can get. So I want to get back to this Bergman kernel for, say, a little bit more about it. And then we'll end there. Next time we'll prove these two theorems in a reverse order. So let me say something about the Bergman projection. So we started out defining these Hilbert spaces of holomorphic sections. But the holomorphic part was kind of self-induced. You could avoid the holomorphic thing as well. So you could, for example, define L2 of phi t. So this is just a set of sections, such that, but not necessarily holomorphic. You could start with the smooth sections and then just take the Hilbert space closure. That's like the complex analytic geodesic definition. And then in measure theory, you prove that these things are measurable and square and integrable, and so on. And then you have this subspace, which was what we defined before. And this Bergman's inequality actually tells you that it's a closed subspace. But why does it tell you that? Well, remember, the Bergman's inequality, without writing the weights down, well, I'll write the weights down. x is less than or equal to the norm f t squared, when f is holomorphic. OK, so now suppose you have a sequence of fj's converging to f in L2. Well, you can look at fj minus f, and that will converge to 0. So maybe I'll just say it more quickly than that. This says that the L infinity norm is controlled by the L2 norm. So if you have a sequence of things converging in L2, then they actually converge locally, uniformly. And then Montel's theorem tells you that the limit is holomorphic. So that's what this means, that this is a closed subspace. Once you have a closed subspace of a Hilbert space, that's equivalent to having a bounded orthogonal projection. And that bounded orthogonal projection is exactly given by this Bergman kernel. You can see it from this formula, for instance, but probably from many other places. Right, so now we have this orthogonal projection, L2 of dt to h2 dt projection. And now I'm going to combine that with this Hormander theorem over there. Yeah, so did I not use 2 before? This is the Hilbert spaces I'm talking about. Sometimes I wrote h2, and sometimes I wrote h1. OK, right. So now suppose you want to, it seems like an aside, but this is the main reason I introduced Hormander's theorem. So suppose we seek to solve d bar u equals alpha with good estimates. Well, Hormander's theorem is the thing that gives us good estimates, but what would be the solution that would have the best estimates? Well, if you've got two sections whose d bar is the same alpha, then the difference is holomorphic. So if you want to get the one with the minimal norm, you need the one orthogonal to the holomorphic subspace. So another way of saying that is if you take u and subtract away the projection, then this thing will solve the equation d bar equals d bar u, and it will also be the solution of minimal norm. So in particular, Hormander's theorem will apply to it, and then you get that the integral of u minus pt u squared e to the minus phi t over omega, if you have a theta like in Hormander's theorem, this will be less than or equal to the integral, not omega, dv x d bar u. So this is a fact that has, you don't need to think about it directly as a statement about the solution of the d bar equation. It's just an estimate, and this should say theta. It's just an estimate that we need. And we will use it to, morally speaking, I won't use this language, but we're going to compute the curvature of this guy, and then the curvature of this guy will be given from the curvature of this guy by adding the second fundamental form. And we're going to want to estimate the second fundamental form, and that will be the key result that we use to estimate it. So that's, morally, what the proof is going to go like, but practically, I won't need to use those words. So OK, that's good for today, I think.


When you think of Yu-Gi-Oh, you think of the iconic characters, or maybe you think of the iconic card combos, or maybe, just maybe, you think of Rex and Weevil, and that is the level of iconic dueling we're trying. This is the regional championship right here, Rex versus Weevil. Just the fact that these guys won any championship with their whack-out cards. So, full disclosure, we recorded this one after the Usa versus Jack deck, and that was a lot of fun afterwards. We were talking about that. We were like, damn, there was actually combos. We were actually, yeah, to think. There was a lot of fun, a lot of fun, and now we're turning it all the way down. We go with Rex Raptor versus Weevil, original dual monsters. We're going to see what happens. These decks we found online, so they're supposed to be as canonical as possible, which also means they're awful. They're pretty bad. They're really bad. But I'm going to cook you though. I still got that confidance, bro.  Yeah, you got confidence, so do I. Let me see my opening hand and what it has to offer me. Draw. Deon. Big mistake, Deon, bro. I'm going to use my pot of greed replacement because pot of greed was banned. I'm going to draw two. Yeah, that's the only. Right on the first turn. That's the only difference we got is we don't have a pot of greed. Bro, you said you have 18 cards in your hand. You got something. Deon, you get it outplayed, bro, because I'm going to special summon Gileosaurus. Oh, brother. Yeah, usually that would have given you a summon from your graveyard, but not today. And then I'll also normal summon Urabi.   Yeah, yeah, yeah. I got dinos on the field, bro. What's your turn looking like? I don't know. I don't got a special summon. I'll tell you that much. That's actually crazy that I just special summoned. Oh my goodness. I'll play a card face down. You got spells and drives? What the? And I'll play a monster face down. He really is the regional champ, dude. Maybe I just got to step up my game. Oh my God. This card is awful. This card is useless. You could definitely play.  I do. I do. But I'll keep it low profile and go with Tyhone right now. You'll be losing that attack bonus when all of your monsters become insects. Come on, man. Come on. DNA surgery?  You can't attack a monster.  That's actually a devastated combo. I need red-eyes now. It gets worse. I'll play my laser cannon. What? To boost up my defense. You should save that for petite moth, bro. What if you got petite moth? It would not help petite moth. The petite moth has 300 attack. Yeah, but when you equip it with the cocoon, he gets the 2000. Oh, dang. I forgot about that angle. But that would, of course, mean that you'd have to play petite moth, and somehow he'd have to survive a turn on his own. Dang, I completely misunderstood my cocoon of evolution. All right, let's see. You just thought having cocoon out here would do that? Yeah, I was hoping that that would make it good. Bro, you need a moth in there, bro. Now I'm going to play Dipli. Dipli. Dipli is going to destroy your... Gileosaurus. Yeah, he's a flea, bro. Dang, I should have equipped Dipli with this.  I need speaking of boot home, brother. This is not good enough. If I could somehow go through the cycles of my moths and stuff, that'd be crazy. Your tribute summoning?  Oh, why are you crashing? Because I don't know what you got, bro. I'm keeping everything nice and safe right now. I'm keeping everything nice and safe. If I'm going to get over Weevil's strongest monster, which is cocoon of evolution, then I've got to play it nice and slow. DNA surgery being the insect, so that now I don't get my wasteland boost. I need a wasteland. I'd be strong enough to get over that thing. Oh, design this. What are you doing? I'll play this. Do you have petite moth? That's petite moth, isn't it? No. Well, even if... The thing is I can only equip it with, hypothetically, if that was petite moth. I'd have to be in attack mode. Yeah, but if you survive till next turn, oh yeah, you're right, actually. That's my point.  It was petite moth. Yeah, bro.  What is this? Wait, wait, wait, wait. It's some of the stegosaurus in defense mode. Really? It's a defensive dinosaur. Oh, that makes sense. You had the perfect opening hand, goddammit. No, I didn't. I did it because he would have got cooked with Kukunava. It doesn't protect it from battle. I would have just taken damage.  All right, I think...  Is that the same guy? Yeah, you wish, bro. Who is that? You'll never know. I got so many dinos in my deck. This is a dinosaur deck right here, bro. You wanted that petite moth play so bad. Yes! Who drove bug? Drove bug just here for real.  You had to tribute to summon face down. All right, this is enough. Now I'm waiting for my big time in the slot. All right, I'll go on the offensive then.  No, it's the answer. Okay, I'm just gonna hope... I'm just gonna believe in heart of the cards right now. I'm believing heart of the cards right now.  This has to work, dude. I'm never gonna win regional championships if I can't pull off a simple play like this. All right. Well, first, I gotta go for this one. Wait, no, this won't even work. I gotta attack with my drill bug and then my drill bug's effect activates. I place my parasite-parasite on top of my deck. You have combos. What is this? And then I'll tribute both of my monsters. You're tributing. To bring forth Instant Queen.  And truly, that's all I can do. How do I beat this thing? Bro, this is Panther Warrior, bro.   And I'm not a... Oh, DNA surgery. What a nice summon.  Play this. And I don't really want to attribute this card, so you're off scotch-free. Yeah, then you better hope you get something quick. Oh, brother. Actually, even if that is parasite-parasite, what's the worst that happens to me? Nothing. It just mixes into your deck. Yeah, parasite-parasite does nothing to me. In fact, it might even help. I'm gonna play into the parasite-parasite. Wait, wait, wait. Whoa, whoa, whoa. You don't understand how it works, bro. I do. No, you don't. It's getting added to my deck.  Oh. I told you you don't know what you're doing. That's me. Well, there goes the beat.  Bro, you don't got the tributes. That is true. All right, I'll play my swarm of scarabs. You have swarm of scarabs? Why are you so shocked? That card is so good. Anyway, you didn't got to worry about him too much, bro, because I'm gonna have to tribute him to make this attack. I swarmed of scarabs. And now, if I'm not mistaken, don't I get to do something for destroying your monster? Yeah, okay. I get to summon a token. Yeah. Oh, and now an attack mode. Now it's an attack mode, mate. Oh, why? Oh, brother, I can't get to break. Bro, you drew such a good hand, bro. Oh, my God. I need to win this duel, bro. I need to find a way out of this duel right now.  I'll tribute my token. The token's gone, but that doesn't help me too much. I got my gobble goo. I'm taking so much damage right now, bro. I'm taking so much damage right now, bro.  Oh, yeah, I am. Wait, no, I'm not for real. I wasn't thinking. I'll flip up my swarm of locusts. Warm of locusts. Destroy whatever you got here. You good, bro. You good. Yeah, you good, bro. Oh, perfect. What do you mean perfect? Perfect for you, Ivy. Hell, yeah, I was. Yeah, but what would you say if you're still cooked? How? You can't attack. Wait, I can't attack at all? Bro, you need tributes. Oh, yeah, okay. I'll play my petite moth. It's a gavagoo.  That was 500 points or less. Oh, my God. Looks like I do get one more third. Come on. Draw. Oh, no, this still isn't good, but it could be. It could be if I wasn't in such a bad situation. I just have to set one. That's literally my only hope is I just have to set.  That's my only back roll removal. I can hope that you don't. Yes. All right. This is the only thing I can do now. Oh, brother. I just have to hope that you can't beat me anymore. I'll play my petite moth. Again? Wrong. This insect queen is killing me. I'll play this.   Leave him alone. I just spared you, bro. Bro, I did not. It's my last petite moth, bro. All right. Thank you for it. I really do, but I cannot allow him to live, so I'm going to kill him. Bro, but how else will you ever see the perfectly ultimate great moth, bro? Oh, it don't matter. Why is you special summoning that guy, bro? God damn. You're making me strong, bro. I'm making a huge mistake playing these guys. Well, get out of here, petite moth. Scram. Skedaddle.  All three of my petite moth.  Bro, you could have had the big play, but sadly, it's hard. Oh, I got a big play for you. No, no, no. Relax. Relax for the relax. Hey, bro, you play too much. Well, I can't attack. Good, good, good, good. I need this. I need time. I like how the idea of Insect Queen seemed like such a strong card back in the day that they just, they were like, yeah, we can't allow this thing to attack. Same with Panther Warrior. Yeah. This card's too good. We have to balance it. Can attack. Well, even Panther Warrior is a little more understandable from, but Insect Queen is like, it's a level seven. I had to work to get this dumbass out here. I play my Gokibor. Wait, no, wouldn't a who and a what? Oh, it's Gokibor. Don't, don't mind him now. Oh, it's the old Gokibor. I wouldn't pay him too much. I got to pay a premium to attack with Insect Queen. So I guess I'll just attack with Gokibor, please. You could try. Oh, brother. You could definitely try, but it ain't going to be easy. And I don't want to sacrifice Gokibor. Damn it.  Leave Gokibor alone, man. Bro, there's just... You go into attack mode. I'm cooking you next turn.  It was. Okay. Okay. You just watch. Just watch. Bro, you ain't top decking a monster. So it's like it's not even a big deal. Yes, I am. I have a lot of them. I promise you. Oh yeah. Enjoy that spell card you're about to draw, bro. Oh, we go see. I already got a spell card in my hand and that's why it's going to seal your face. Oh, I got combos for you, Dotto. What do you mean combos? You got insects. First I'll play my Scopemark Ladybug. Oh my gosh. And then I'll play my Insect Armor with Laser Cannon. What? I would never in a million years be able to get over this. It does it up that I'm not a dinosaur.  Bro, if I was a dinosaur, I'd be living my best life. And I gain some more life points for this. Just let me be a dinosaur again. Now, the question is, do you make the mistake of going into attack position to attack my token again? I can't, no. Yeah, I've left you with no choice. Now you've got to leave my token alone. Oh, if only I had a petite moth in this situation, then you couldn't attack it. What are you doing? What are you up to? Oh my God. Bro, this is canonical. This is exactly what happened to Rex in the tournament. Oh, no. When it Rex needs to get to... What? What just happened? An error? What? Well, I don't think that's exactly what happened, but damn, what a way to win.  He fell off. He fell off of the thing. Hey, hey, you trying to sneak a quick jack versus you say duel in this video? Nah, bro, run that back. I am pissed. Damn, damn. I am pissed. Ain't no goddamn way that just happened. I'm gonna need you to stay mad, dude, because I'm just better. Well, I'm coming out swinging this time. I play Forrest. Man, I wonder what it's like to be able to have a field spell power your cards up, man. I'll play a card. Face it down. I ain't even doing it, boys. I'm angry. I'll play my giant flea. This guy mad for real. Oh my gosh, that is a strong flea. I cannot tell a lie.  Anyway, I'm gonna have to go ahead and beat you up now. I'm going to raise my body heat. Yeah, yeah. You ain't know about my body heat technique. I'm afraid I can't let you do that. You have back roll removal?   I'm not pulling any, but I'm beating the, I am tight. I'll play laser cannon armor, bro.   I've got to deal with this flea and fast. Deeply.  I also don't have time to play the game, dude. I can't be doing this for real. I can't be doing this for real. It's that queen out last time. All for nigh, man. For nigh, dude.  Hey, bro, what you got face down over there? I'm wondering what you got face down over there. What you got right there, bro? It was ita kaboom. Ita kaboom. Anyway, I can see the way this duel is going right now. It's so good for me. I still got defense points. Thank you. I was gonna say, yeah, I thought my Weevil deck was pretty bad. Your Rex deck kinda trash, bro. All right, all right, all right. I can get a little boost. I'm getting a little boost. Giant rat? Giant rat? Yeah, yeah, yeah.  What am I supposed to do? Oh, when he's destroyed by battle? Okay. Giant rat might not be a dinosaur, but he's a beast. Is he? Yeah, and... Man-eater buck. I needed to be destroyed by battle, bro. I've told you, bro.  I'm getting swarmed.  Heard of the cards. Yes. Maybe. Yes. Ain't no yes. I mean, it's the best thing I can... It's all I have right now, dude.  Oh, no, not my Diffley. Yeah, Diffley leaving, bro. Yeah, plus 700 is kinda crazy. Yeah, but it'll fall off. Yeah, but at the rate it falls off, it's gonna be... Oh, dang. It'll be a little wild, bro. Yeah, this would have been great last game. I've got a... I'm stimmed up right now. Defense mode, defense mode. You can run, but you can't hide, brother. Well, boy, I say I don't like this. I'm getting out of the shoes on the other foot. Anyway, check this piercing damage out, bro. Wait, it's piercing? Yeah, yeah. He should have read. My dino's got pierce on him. Whoo, now I'm in control.   Damn, another standby phase means another 200 points down the drain.  Yeah, okay, brother.  Yeah, no, I wish I did, though. I'm about to, though, cause Sangam! Damn, he actually is spitting. Sangam's gonna allow him to draw. Damn, I can't play like this, man. Sangam is just your giant rat, bro. Or would this be smarter? Could be a play and a half. It could be a play and a half. But no, let's go with the smarter option, I guess. Oh, brother, it's a cocoon. You know, DNA surgery would kind of hit right now. At least then I get some boost. DNA surgery would be the end of you, bro. It would be. Oh, thank God, okay. Now I get to play my fake version of Pot of Greed. Oh, come on. That's the worst time for you to draw it. Wait, what?  Okay. You running for real, bro. I have no choice. All right. Wait, you're just gonna keep getting weaker until you have zero.  Bro, you know what I got. What are you doing? You know what I have face down. I was just checking. I suppose. I don't know. I don't even know. I don't even know. It's like my third day out here. What is wrong with you? My third day out here, bro. I don't know. What if you try to pull a fast one on me, bro? Because what if that was like petite mob, bro? You use a moron, bro. All right.  I only won last time because you got an error. I know. And I'm like one duel up right now. So I'm like, you know, I'm pretty big in terms of dueling community. Just don't draw red eyes, bro. Red eyes would be really bad for me.   Like I can't cook you with just a thousand damage. You ain't got to like that. Bro, don't you sleep on me. Bro, I promise don't you dare ever sleep on me. I promise you shouldn't have ever slept on me, bro. What do you mean by that?  You ain't got to like that, brother. I'll play Pean Chopper. Okay. That's a lot. And first I'll activate my pineapple blast. Now you got to remove monsters from your side of the field. So you have the same amount of monsters as me. Okay. Kind of a powerful card. Did you think that was all? Now I'll play my tribute doll. Once my pinch hopper is sent away, I can activate my pinch hopper's effect. What? Why you got combos? I don't even need that. Because now I got insect queen. Oh my gosh. And just so you know, if I did have DNA surgery, insect barrier. If you had all insects, you wouldn't be able to attack at all. Oh, that really would just end the duel. And now I will go in for... Wait, I can't attack the turn that I used tribute doll. Yep. Yep. Yep. That is the rule. Okay. Showed my whole hand with that one. Don't know how I get out of this one. Better go in defense mode, bro. And hope. Truly is my only play. Dotto. What? Oh, Dotto. Oh my God. Don't worry. I don't really want to sacrifice my cards yet. You lucky. I want this great model play so bad, bro. You ain't getting it, bro. You ain't getting it.   Better not. Come here, bro. Come here.   What are you thinking? I'm going to give you a little piercing damage, bro. Yeah. You better have a good face down card. Oh, you already know I do. You already know I do. Better.  Yes, sir. Yes, sir. I'm taking the bait, bro. Let's go. Let's go. Damn. So the thing about...   Think about that. Think about that as like I didn't count the numbers correctly. What? I didn't just think... I didn't think you'd be able to kill me. What do you talk? You had 1,000 life points left. Yeah, yeah. I know.   Yes, I did. Yeah. No, I made a lot of mistakes. Yeah. Oh, my God. Rex... Like props to Rex for even making it to people's level, bro. Because like Rex can't play the game with these cards. Oh, I got the card in my hand that I told you is the worst card in the game. I'll tell you that much. Dang, you scared already in defense mode. The duel just started. I don't got nothing scary out yet, bro. Special summon in defense mode. Bro, I'm just trying to play my game, bro. I'm just trying to play my game, bro. Man, traumatized. Bro, this deck is trash.  When somebody tell Kodami to release an official updated structure deck, bro. I gotta play this card face down. Oh, now you're bold and brash. Oh, brother. Stop, bro.  Yep, yep. You beat basic insect, bro. That name is basic insect.  Yeah, but it's such a good thing. Why? Ow! Yeah, I'm still out here, though. You is? Oh, my God. You're not a lie. What? What? Yeah, you know what? I'll just start with this. This isn't what I was reacting to, but I'll start with this. My God. I know what it is, bro.  Hey, bro. How 400 damage sound do you, bro? God, damn it. I knew it, too.  I'll play my Skullmark Ladybug in attack mode. I got my goo.  Bro, you're just helping me. Yeah, man. Let me get some white points. Enjoy the 1,000 white points, bro. That's big in these duels. All right. Well, as long as you don't draw red eyes, I'm chilling. Yeah, you're probably chilling. You're probably right. Yeah, you're probably right. Anyway, I'm also going to enjoy some white points. Anyway, my body heat is rising.  Overflowing, allowing me to equip it to twin-headed King Rex for the perfect 2,100 beat stick. Yeah. Yeah, better go run and tell your insides that somebody else is in charge now. Yeah. All right. Yeah. Now, all of a sudden, the Wasteland diamonds I got a combo for you. You ain't got the time. You ain't got the time for a combo to do that right now. Oh, I got a combo for you, brother. I'll summon my Sengan in attack, and then I'll play my Tribute Doll. Oh, my gosh. By tributing my Sengan, I can special summon a level 7 monster, my Insect Queen. That's just so powerful. That's just so powerful. I can pick up any card I want. I wish I could draw into my level 7. Please. Please. I'm not even, I'm tired of begging, bro. Red eyes, if you're out there, if you're listening. I'll just pick this up. No wonder you chose Joey, bro. Red eyes, please listen to me. Please listen and come to my head. I need you now. It has to be right now. I can't attack this, sir. I know. I get one more turn to play Red eyes. I need tributes. Red eyes. Oh, it's like I really don't have time to do this. I couldn't tell. Oh, no. Not two headed King Wrest. Why are you in all attack mode? Bro, you know I'm going to be choice.  I'm getting some ideas now. Hold on. You better stay. Have an idea. Let's keep my promise you.  I promise you. No, you can't make that. Don't lie to them. I'm not lying. I'm not lying.  Don't be that way. Bro, don't be that way. Still a chance. Still time, Red eyes. If you want to take me up on that offer. Just please leave my tokens alone, man. Not happening, brother. You should at least make you attack it instead of, like, other insects. Bro, are you really trying to make that card good, but it's just not going to happen? I was hoping. Why attack with the lowest attack points I have? I don't know. Good question.  These tokens are risky, though, man.   You got to keep tributing monsters if you're going to keep getting tokens. I don't want tokens.   Ah.  We're kind of at a standstill, guys. I don't want to attack you and risk putting more tokens out. It's just free damage for you.   Man, it's about to have a Link 4 play in a second. Ah. Elkentime? No, bro. Hey, so listen. Here's what we're going to do. You're going to hit me with one of them tokens, bro. Wait, wait, wait. What's going on here? What do you mean what's going on here, bro? You don't know which is which. Yeah, okay, bro. Come here. Come here, bro. Hey, come here. Brother!  Get him out of here. Damn, I really wanted to flip this card up without you attacking it. No. Now you need to start tripping some monsters, huh?  You can try it. You can try it. Here's big insect, bro. Big insect, bro. This guy's a literal. Oh, yeah.  Why did you do that?   He's dead. Yeah, you want to play with these equip smells, bro. Let's talk about it, bro. What's up? What's good with you? Okay, so this is really bad. This is really bad, dude. Let's talk about it. Go to the fence, bro. You was talking.    As soon as I figure out a plan on how to get out of the situation right now.  You got rid of my parasite. Parasite, bro. Damn, I wanted to flip that card up. I just wanted that bit one time for you to just get a good draw and then take a thousand damage.  Oh, I wonder what that could be. You ain't even know, bro.   But you were the big insect. The big insect really out here. Just being a big insect. You know what I'm talking about? It's a bland name. Big insect. Basic insect. Insect queen.  Gorewa.   You don't go in defense mode, bro. Bro, your time is up, bro. You're done. Dude, you keep talking, bro. That's why you had to tribute some of the monster and put it in defense mode, because it couldn't beat big insects.  I don't know why you're being so stubborn putting it in attack mode. Because there's no reason for it not to be in attack mode, bro. What are you going to do?  Well, I'm just saying that damage adds up, bro.  I didn't do math. You're incorrect. Straight up not logical decision, man. Damn it. He only defends me until I get an equip spell. Then you're cooked, bro. Unless you got MSD. You ain't getting a word equip spell. Cut.   That's a point. Once you lose because of an 800 life point difference, you're going to be sad.  You're trying to bait me. You're trying to bait me into destroying the rat. You know what? Be successful. I'm about to beat you out. Yeah, I am. I want this rat. Go on, bro. Don't get him. Ain't no way you're teasing me by having a monster out there, bro. What you doing? What you trying to get into for real? Negate attack. And end battle fit. All right.  That's all I have. Yo, help me. Police. Police. Police. Oh, there ain't no way, brother. There ain't no goddamn way, brother.  What are you doing? Oh, you just... I'm tired of waiting. I'm going to squirt myself off the premises. Oh, my God. I would have had to destroy him eventually, bro. What? What's even the big play with this?  Are you so invasive? You lose so many life points for this. Don't submit a third one.  See, I don't see it like that, bro. I see the world a little different, I guess. See, I paid you back. I paid you back a nice 900.  This is the worst card I could have drawn. Keep drawing back cards, bro.  I don't know. So it was actually 900 damage for... What do you got? Oh, brother. My man's got draw baller. Hey, bro, why are you hooking? No reason. You got a red eyes?  You trap hole.  Yes! Now it's my turn to draw, too, dude. Oh, my God. It feels like a million years ago. The card is so good.  All right, bro. So we're going to... Damn, but now I actually can't even get over that. God. I should have saved some of your equip spells for red eyes, bro. Nah, because it's like whatever. Because honestly, like, you're cooked, bro. You're done, bro. You better trap homie. Hey, you got an animation, bro. You better trap homie, bro. Please don't, dope. Please don't, bro. Yeah, I truly don't have one. Let's go. Let's go. Yeah, get him out of here. Get him out of here. That does weaken me to your level. Look at us. Look at us even. It's the way you think I ain't going to crash. I got 2,400 defense, too. Damn, he's smart for real. I need a Stimpak. Oh, my gosh. I'm waiting, bro. I'm waiting. Dino's getting hungry. Dino's getting hungry. Oh, my God. I knew the Dino was real bad, dude. Bro, you're saying that, bro? I'm fighting for my life over here. I had that giant rat twice, bro. The rat. Oh, my God. Hold on. Let me go ahead and get it. Let me calm down. That's what I need, bro. Like, that's honestly what I need. Bro, you should be at 4,200 right now. Damn, you look... Yeah, I can't get through that. Bro, you better hope I don't draw, like, DNA surgery.  Dude, I'm constantly hoping you don't draw DNA surgery. What is this even for? This is the most unlikely card to ever happen, like, ever. Please. All these face down cards. Please.   This actually does nothing for red eyes. Because red eyes is not a dinosaur. Red eyes is not a dinosaur. Rex is dumb.  Rex, bro, put your deck to read, Rex. This makes it look like a dinosaur to me. I guess it kind of does look like a dinosaur. I wish you could see by hand.  Please. I can't keep drawing. I need to get my moth out of here. You're not getting a moth. You just wait. Oh, my God. What I need right now is either one specific dinosaur or... Hey, I'm going to go into attack position real quick.  Oh, my gosh. Weevil can actually read. Wait, you can't attack without a tribute, though. Yeah, I can't. I can't. You're right, but I don't have to be afraid in defense mode anymore. You better stay afraid, because I'm drawing Stimpak right now. I wonder if this is how the finals actually looked. Oh, my God. Anyway.  No, no. Anyway, I'm going to go ahead and attack now.  Oh, this duel is over. I'm sending you back to regional finals. I really didn't want to... What do you mean? All right, not yet, not yet. I should have flipped some other monsters face up. Finally, Red-Eyes Black Dragon is here, baby. He's stemmed up. All right, I'm going to play. What do you mean?  He was instructed never to use by your sensor. I was just, I wanted to save this card for something else for my moth, but I'm not going to be able to because you put the pressure on me.  All right. What do you mean by that? So first, I'm going to clear out your field. Brother, this guy practically the mascot. I'll activate my pineapple blast. Now you have to remove cards from your field so you have as many as I do. Hey, bro, get rid of that Red-Eyes. Nah, bro, he gets to stay. All right, but now you can destroy me via battle. Yeah. Damn it. All right, now I'll play my Call of the Haunted. What? We've got good cards. Oh my God, man. Is it not good enough? Well, I guess there's only one option. If that's the case, I'll be my Insect Queen. Pretty good option, I guess. I promised I would summit my ultimate right now.  Call of the Haunted petite moth in defense mode so then I could attach it and it would be safe. Yeah, it would have been a safe play. It would have been the move. If there's any way to do it, it would have been that way. Yeah, that was the big play. I have no back removal. What's the play? Why do I only got 500 life? What's the play here, bro? Could I fancy you to not destroy my giant cleat? Hey, no way. I was giving you a holy drop.  And then I'm really cornered. What are we talking about? You kind of shitting. I will tell you, I only got one call of the haunted. Well, I guess we don't like entertainment, though.  Oh my God. I don't even know what we're talking about. Yeah. There you go. Watch the 5D's duel as well. Other than that, watch that one. Other than that, this is the end of the video. Bye.


The study refines a multi-state level forest carbon monitoring framework that addresses spatial inconsistencies caused by variability in data quality and modeling techniques to generate a consistent 30 m pixel forest above ground carbon map covering 11 states in the regional greenhouse gas initiative region of the USA. This article was authored by Haotang, Leymar, Andrew Lister, and others.