So, we continue with our series of lectures and as I promised to you yesterday, so today we will speak about positivity of magic functions and how to prove it. So, in the previous lectures what we have done, we reduced the question about universal optimality of E8 lattice and Lich lattice to the following positivity statement. So, we constructed this function f tilde and we've also shown that if this function is non-negative for all real positive real non-negative values of error and for all purely imaginary tau in the upper half plane. So, if you could prove this in equality then this would apply that the E8 lattice and the Lich lattice are universally optimal. And so, what will be useful for us to try to prove this statement is that we also shown that this function f tilde, it has the following integral representation. And so, here, so f tilde is this, so sine squared which will generate double zeros for the function f tilde and the following integral from zero to infinity of this meromorphic function k which is defined on the product of two upper half planes. And we have seen that this integral representation it converges absolutely if tau is in the domain D and imaginary axis it belongs to domain D and also if r is bigger than square root of 2 and 0 minus 2 and n0 it's a number which depends on dimension. So, for dimension 8 and 0 is 1 and so this condition somehow just means that r has to be strictly positive which is actually fine for us it means that we can use this representation for all the purposes we want. And if dimension is 24 then what will happen is that this number n0 equals to 2 which tells us, so it means that the first possible lens in Lich lattice is missing, we have no vectors of lens square root of 2. And so this integral we can converge only if r is big enough because here I made a typo there should be a minus sign. It makes somehow because here if you have a minus sign here it is correctly should be then this will be a very fast decaying term which will compensate for poles of k hat. And so this is just to recall what what were the Meromorphic kernels we spoke about so this kernel k hat it was a compute defined it as a transformation of kernel k we worked a lot with so it's k it's a function of two variables for example tau and z and we apply slash operator with respect to the first variable and so also what so now what we would like to do we would like to give an explicit formula for this kernels kd and as we discussed it in one of the previous lectures it is convenient to certain to split this kernel into two parts so to say into a positive part and negative part and this positive part and negative part they are defined by the action of this evolution s and so so here are the explicit formulas for the kernels so we will write them in a following way so we will so here this is a column vector which consists of these functions phi minus 2 phi 0 phi 2 and we define these functions I guess in our second lecture and over the functions which generated the ring of functions in the class p which are annihilated by the ideal I and so in the next slide I will remind what these functions are and this is also for these are functions with a generate the ring the module functions which are a legate the deal I till I had two ideals I plus and I minus so these are for ideal I plus this are for ideal I plus tilde this are for ideal I minus and this are for the ideal I minus tilde and so for each of these functions we have a concrete description I will show it to in the next slide and what is here in the middle so in the middle we have a three by three matrix which I will also given in two slides from from now so here are the functions phi 2 phi 0 phi minus 2 so they are so to say they come from the world of quasi modular forms so the four functions psi psi 4 psi 2 and psi 0 they are a mixture of logarithms of lambda functions so here this calligraphical L it's a logarithm of lambda function and this is a logarithm of it of the lambda function acted by matrix S by linear fractional transformations and so the functions this psi 4 psi 2 they are some usual modular forms of weight 2 and 4 respectively and so they are modular forms for gamma 2 yeah so and here maybe I will write down so what are u v and w u v and w u they were the so they were the force powers of theta functions I think like this and so there is one linear relation between this four functions so one of them is the sum of two others and those two functions they actually generate the ring of all modular forms of for the group gamma 2 and so we also have this functions phi tilde and psi tilde and they are somehow they come from the same world as they are friends without tilde so here again we have some expression which is in terms of quasi modular forms and for psi t psi tilde we have again modular forms of level 2 and the logarithms logarithm of lambda so and now we come to the matrices so the matrices tried to write them in a in a way which would be somehow which couldn't cause we have now four different matrices two matrices for dimension 8 and two matrices for dimension 24 and so we tried to write it and somehow compact form so here we introduced some abbreviations for this so what so here we take this so this number number for functions of weight starting from minus 2 to 13 and for from them we will construct diagonal matrices and now each so the each of the the first matrix is defined like this so it's a diagonal matrix times this particular matrix so here we introduce this notation for Jane variance so that things look a bit nicer in inside of a matrix and so this what we've got here this will be sort of same matrix where objects they will be holomorphic at the upper half plane and possibly have poles at the cusp so I think in this case we don't know in these caves we do have maybe one cusp at infinity somewhere and here we divide by the difference of Jane variance and this will give us our poles at the points where tau and z are gum are cell to z equivalent and so similar representation we also write for this matrix which corresponds to the minus sign so somehow we tried to find some nice structure in these matrices which could give us a hint about positivity but we were not able to so maybe somebody else could could do it later and so here is what we have for dimension 24 so again structure is similar so we have a product of three matrices so this is a diagonal matrix this is this matrix and this is again a diagonal matrix and so sorry is there supposed to not be a j of tau minus j of z denominator oh yes I think it just disappeared somewhere or maybe maybe maybe it got absorbed somehow no no probably not no no probably not no okay yeah yeah yeah yeah yeah yeah yeah yeah yeah there is minus 1 so it's already in from here yeah so we see that like is somehow in dimension 24 we have more poles and after all expression got a bit more complicated but not too much. And so now when we have this explicit expressions we can what the next thing which we try to do is how to see the positivity of the function we are interested in and of f tilde from some properties of our kernel k. And so again just to we just recall the integral representation here and so if we see for example if in those cases here again minus is missing and again in those cases when this integral converges absolutely then for example just the positivity of k will imply the positivity of f. And for example this happens in dimension 8. This is the only thing we have to check. And in dimension 24 we have additional problem coming from the divergence in this integral so we will need to work separately with the small values of r. And so so here how we what will what we do we how address this problem in dimension 24 so here we use so to say a truncation. So it means that we are going to split our kernel k24 into two parts so one of them this e hat it will be a part which so to say contains the pole and the remaining part will grow at most polynomially on the imaginary axis of the second variable the imaginary axis goes to infinity. And so here again the here are the explicit expressions for the for this term which we have which we are going to consider separately. And so now what we do we set this parameter p which was somehow chosen to make our mnemerics work better. And so now we split this integral into the following two parts. Okay so it's from zero to infinity but here we have kind of just a bit slightly tricky definition of this part. And so now the advantage of this is that this second integral here it can be evaluated explicitly and so this is what we what we get. So here we got a pole of second order but you remember that we are also in our representation of function f till they were also multiplying it by sine squared. So this pole it will be compensated by factor of sine squared. And so now the positivity of f we will deduce it from the following statements about kernel k hat the kernel k truncated and the remaining part. So first we show that the kernels itself that they are positive if tau is in the imaginary axis the first variables in the imaginary axis and the second variable is also the imaginary axis. So now we should show the same for the truncated kernel and we also estimate the remaining term which comes from the integration of a pole. And so in this inequality it actually will be split into two simpler inequalities which we can prove which you are going to prove separately. And so now somehow what we are going to do because our now our function functions which we are interested in they are all defined on the product of two real half lines. But this is the product of two half lines it's a non-compact set and so doing numerics on it might be not very convenient. And so what we have done we have decided to instead of defining function on a product of two half lines to go to the to consider a function on a unit square. And so for this we will need to make a change of variables and so this is change of variables which we will do we will instead will take a modular lambda function which is a help module for the group gamma 2 as our new parameter. And so lambda it maps the imaginary axis into interval 0 1. And so now what we have to do we have to express all these functions in terms of lambda if our variable in the upper half plane is actually in the imaginary axis. And so for this which functions we will use we will use we will need for this polynomials also we will need logarithm because we had logarithm of lambda in our formulas. And now to express the quasi modular forms and modular forms of higher weight what we will need we will we need to introduce the elliptic integrals because the classical fact that the elliptic integrals they invert modular functions. And so here are the elliptic integrals so the elliptic integral of the first kind and the elliptic integral of second kind. And so here are the formulas which we use to express all the functions in terms of lambda so with curly L and curly L calligraphical L as it's easy it was just equal to the logarithm by definition. So the only way to check that the branches of the logarithm we are using here is the right ones and it is the case. So now for the modular forms we have expressions like this so they can be expressed in terms of square of this elliptic integral of a first kind. Now in some of the formulas we also use the just the variable on the upper half plane and so now it also can be expressed in terms of k and this way and here we have a formula for the quasi modular form e2. And now after we have done all this so we can make a substitution so now we have we can compute two functions well not two functions actually they are three functions so functions l ld and l truncated such that k of tau z it's equals to l evaluated lambda of tau and lambda of z and so the one this identity is to be again valid if the real parts of tau and z vanish. And so now we'll get all these expressions and then they can be expressed in terms of these functions in terms of for functions x logarithm of x logarithms of 1 1 minus x the elliptic integral e elliptic integral k and elliptic integral k of 1 minus x. And so I think also I can use the rithome slightly like technicality with this truncated kernel because here we have exponential to the power x so it will be yeah we will get some rather unpleasant term something like exponential to the expression in terms of of elliptic integrals so but then but then that one we estimated separately. And so now let me show you how how these expressions look like how long they will be if we express them in terms of this easy parts so here is a mathematical code for here it's a typo here should be sorry l8 so the function l8 so it is kind of lengthy but maybe not not too big and so here is the plot of this function and so in a plot you can see that it yeah somehow on one hand just by eye we can see it seems like it is positive on the other hand it is maybe not not exactly easy to see that because on the boundaries here our function it actually vanishes so it vanishes on these borders and it goes to infinity at this edge also we see that here on the diagonals we have so to say virtual singularities so the function itself is smooth there but because we had to decide by the difference of J invariance so the computer does not know how to evaluate the function here so it leaves the diagonals blank for us and so on the next slide we have so this is it here we show how what is the growth of functions at the edges so here as we have seen it before so so here so maybe I explain a little bit what it means so it means that this is so say the order of vanishing and it is also for example here if it's we're going to y equals to this edges y equals to one and asymptotically it means that here our function it will look like a logarithm of one minus y times some coefficient which still depends on x but we simply don't write it at this picture and so we see that somehow here we have the vanishing here we have vanishing and here we have actually growth and so so now what we somehow as we told you if we could not find the way how to prove the inequalities which I showed you before by some simple mathematical argument so what we do instead we do a computer computations but we also try to make them like a mathematically rigorous so in a sense that when we can compute value of a function at some point so we can do it just to say using if we have two numbers which we know exactly then we can use rational arithmetic and do some operations with them for example like two times two multiplied by four and this is mathematically rigorous statement on the other hand you can you can write your numbers in decimal representation and this is how it will look like then and this is often what people somehow see when they are using maybe making some computations a computer this is what we get however in reality what this really means often if you have this like something dot something it is not that this number is exactly the rational number represented with this decimal representation usually it means that we simply don't know what goes after the dot or we somehow we don't really want to know what it is we know that it's something not important for us and it works quite good for many practical purposes there are practical purposes for which this does not work that well and I think like 50 years ago people realized this that maybe it's better to have not only a representation like this but actually knowing so what happens if we know two numbers approximately then there is for example if you multiply them then they will also know their result only approximately and the error will also accumulate and so for this we what we can use is something what is called interval arithmetic so suppose we can like other way to interpret this equation here is that we know that we have some quantity which is 2 plus some error and then we'll multiply it by something else which is also 2 plus plus an error or what we can do we can say no that like our first number lies in this interval and our second number lies in this interval and then if you multiply them we obtain something which lies in this interval so here for example if you know our numbers with precision like this then we know the product we know our product will lie in some interval like this and so interval arithmetic it's attempt to to do the computations in this consistent way when we know all our variables with some precision then we say that the result belongs also to some interval so here we could write this interval explicitly and in some situations of course even the because evaluation is not so easy we will just give here some interval which definitely contains the result and we are sure rigorously sure about that and so our days there are actually quite many packages where this is implemented for example such packages exist inside of Mathematica so for our computations here we have used Mathematica and so also as you've seen on the plot so with our function it's not somehow it's not an easy function it has all those how peculiarities it it has problematic behavior sorry problematic behavior here at the edges and it has this like virtual problem at the diagonal where like in the diagonal of course this function is smooth but if you want to compute it we have to we cannot just compute it by dividing 0 by 0 we have to do something yeah something like that but still we have to do it Mathematica yeah it could be some legal issues because it's not public domain maybe we should use nature yeah maybe but we used license at first but also we don't know what's what's happens in set mistakes it's not really proof yeah yeah so I will pick about it maybe a bit later and so so so but it yes like one nice thing about commercial products is usually they're made to be liked by people so if you use it it's very convenient and easy but actually so Henry con and Abinav Kumar they did work on writing at least some of our procedures in Sage also and I'm I think in Sage writing or maybe working is it sometimes is more difficult but what we discovered that it was somehow it worked actually much faster but one might do one reason for that is that now like writing it for second times we are more experienced and can introduce some maybe better procedures but also it worked faster and so and so again like the problematic points which we had so they were like diagonals and the good point where two diagonals intersect it's like using lipidal rule rule twice and so we also have to do something about edges and maybe like most unpleasant points there are the small corners where because like here we have so to say three different singularities intersect like two edges and also one diagonal so that they require to our most most work and so here is the picture of like all all this each of these regions it was a positivity on it was checked by different program and so at the end what I can tell you also the running times of the program so they say like all the computations they were made of Mathematica and here are some technical details about computers these computers were these computations were run by Stephen Miller in Rutgers and so he used 16 cores to run Mathematica on it and so here we had like some small files to which you run pretty quickly so we had to write down our own estimates for elliptic integrals so some symbolic computations with kernels symbolic computations with so this is like dealing with the doing some parts of the truncation argument work and so here what so it looks in dimension 8 so in dimension 8 actually everything runs pretty fast yeah so it is somehow maybe everything will add up to a few hours maybe this one was seems like this is the longest thing also turns out that for checking numerically the longest was actually checking generic points you got algorithms which we had to run on the singularities they run pretty fast but for generic points for some reason it was actually longer longer to check to check them and for dimension 24 here the running times are much longer so here it already adds up like to a few this part adds up to a few days and so also for dimension 24 we also need to consider those small values of r separately and so for so these are the running times of programs which deal with the truncated part of the kernel and so maybe you have some questions sorry you didn't insist on every arithmetic you want a non rigorous competition could you do it much faster I mean okay I so so the I don't know like it depends on how on rigorous you want to be so like so like I don't know like this plot it computes it like in two seconds yeah but that okay but then like here like problems happen if you mean here probably like one thing which is necessary still to check that everything is fine on the in this proof on the singularities because like if you thoroughly try to rescale it and to come closer to the edge usually plot will show something very bad it will not look like it's positive it will look like it it will show the noise but it looked like the computations of the boundaries were much faster than yeah so this also okay so it could be that something could be implemented in a more efficient way or I don't know maybe there is some fundamental reason for that because actually like is from things which we computed actually like do doing for example tail because of the probably because of the boundary we have to somehow work harder do more mathematics and mathematics somehow speeds up computations so we have to compute Taylor series actually do more like more estimates and those generic points we are just lazy we just take the existing program and it should be much faster in principle in principle yes because like you said the hardest part mathematically was the most painful part was the corners where yes yes yeah but the but then probably we then there there we did all the work for I missed it actually Steve Steven did all the work for the computer expansion here at some first few terms some yeah it shouldn't be hard to get well like painful that's why I said yeah just like if you've the method of tail or a tailored for the for the boundary then somehow sometimes it's difficult to extend it far far far there that's that's that's certainly the danger did you try alternative hardware just to be sure yes I think actually so Henry con was also running these programs independently from Steven and also getting the most similar result so is it possible to write programs to check the results of the computations and then I don't know and then write another programs to check computations yeah so here so here I don't think it's for security you write something else to check this maybe this maybe it's more like it sounds like more like an statistical physics we're sure that this is true by like 09999% so I think this maybe can increase your security in the result but probably mathematically it cannot prove it anyways because if you if you don't believe in the first program then maybe a second problem the program is also corrupt or your second computer is also defective so yeah and of course now it would be very nice to have also a theoretical proof of this positivity but at the moment we have no idea how like whether it's how to achieve that or I'm maybe like even is there any good theoretical reason for it to be positive maybe it is just positive by accident so to say maybe have some more questions do you have such can work to remove the singularity a factorization that cannot be more singularity of the diagonals okay I tried I tried to do it but guess maybe what I can so like writing in some kind like an algebraic way right to divide by something so I tried to do that but not maybe not for very long time and not very so I can see like this kind of a big expression and then if you try try doing some kind of elimination of variables or it actually it gets much much much bigger probably if you ever like worked with you know because I get effectively if you have I worked with it it's like it's a function with like algebraically independent many many variables and so at the end I got like some really really huge result which I certainly could not handle by hand and so it again would be a computer computation only instead of maybe instead of computing to this like this interval arithmetic it would be computing huge symbolic expressions so I somehow it is it looked to me that it would take also very long time because I'm out of here we realized like especially try to write our expression more one more compact so it is small but if you try to do any kind of elimination then this expression just grows extremely fast but I mean like in this in this so I try to fucking vinyl or rename the variables and see if it's some nice function but it did not look like a nice function it's just like a some big big polynomial and I don't know how many it was like 10 no no 10 yeah but the metal breakers they may they make after all expression a bit smaller yes I tried to write it down as an expression of like of these of these how many they are like 12 variables but I could not see any particularly good structure in it so I think I think here either there should be some very like good good new idea why positivity should hold or yeah or probably any other method seems to be not much like not not more rigorous or much more elegant than the one we are already using here so suggestion your function looks like it doesn't have minimum yeah okay so minimum is like zero it's where we can prove that it's positive just so equation for critical point but how would this imply because you know it's there are a few types of minimum of the function because it seems it's not critical point inside this yes yes I think it might have no critical point not no okay if you need to find me on the bottom yeah I think it's not it looks it doesn't have no critical point at all inside yes so I think like I mean okay so maybe like bond of the boundaries because of this like logarithm I think it I don't know maybe maybe I don't know it can't can boundary count as a critical I think it will prove that the guy just yeah maybe I don't have other way to try it and like the reason with something it's maybe some simplification right which critical points it will get some question for this columnic functions which is easy to yeah it's actually be easy yeah maybe maybe we can try that one theoretical proof would be would be nice on the model are you derivating a few times your expression in order to get the positivity so on the guys on the bottom on which boundary on here on the nose like to hear with what we do we kind of just compute what the limit is so to say that like compute the expansion for example in like here if we take for example x going to zero here x going to zero so we just find an expansion in terms of x look at the first term and see and I get first term in the expansion it will be some explicit function again even in terms of and then check whether this function is positive and also bound the bound the rest yeah so here like at the boundary it's not exactly Taylor expansion because here we have we have also like logarithmic terms so it's like this you need to check something on the part no no you have to check this function is kind of this bounded below and to the boundary takes value zero zero infinity on the boundary nodes equal to zero and can continue to say probably for this one need some some time has to be in it maybe it's difficult to do it just like this could then probably we make a break the function you are showing depends on your location parameter so the one function I showed it was for dimension 8 so we did not depend on it truncation parameter because like in dimension 8 we don't have a truncation parameter yeah and it's okay so I just turned off the computer but and in principle I also were good to collect from picture from the functions I have I've chosen to show one but again I also make pictures so far so for 24 dimensional kernel but it looked very similar to this one so I thought maybe it will be not so interesting to show yes actually like we do have like this three different essentially things so that's like this kernel for the man like full kernel for dimension 8 full kernel for dimension 24 and also this truncated kernel for dimension 24 but all they look more or less like like this so that's for dimension 24 what we did we proved the inequalities for the like kernel itself which was like without truncation without modification and there was like another program which was running for the truncated part like kernel without without this like first pole and the pole was also handled separately but but actually considering pole it was much faster because it was essentially like function in one variable so it's easier to because it depended on this variable z in a very simple way I have another question is it possible that I don't remember x x and y but let's say the the boundary where it goes to infinity is x equals one y equals one is it possible that if you fix for example x and you increase y that the derivative is positive everywhere as the functions increasing from the bottom boundary to the top so we did not check this I don't I'm not so sure about that I'm not sure if it is actually if it is monotonic everywhere because it looked like it has some kind of fun well that's the turnaround so to speak going from one boundary word zero yeah I'm not so sure about that yes like also I can't think we look at this like with the presentation we have now if you take some kind of a couple derivatives of this function then expression also gets more and more complicated so this was the reason why we did not fight on derivatives but tried to address the function itself yes maybe maybe the second parts will be a bit shorter because I ran out of slides earlier than I expected but that's almost always situation with slides and yes maybe now I will speak a bit more about some implications of this result if we do believe in this our computer computation and believe in universal optimality then what kind of consequences will it will it have and so like wow one interesting question is the uniqueness of optimal configurations so suppose that we have some optimization problems like f would be some completely monotonic potential and suppose that we have some so what we have already proven so from universal optimality it means that if we take any point configuration see then its energy will be at least the same as the energy of d but now the question is what if we have equality here would this mean that C is the configuration C is isomorphic to our lettuce so the answer is yes and so why it happens so we can for this we can remember how we proved the con the con kumar bound so you remember that we had our function we had this function so so now we know that there exists a function fg such that we know that fg is bounded by g that its Fourier transform is non-negative and also that and that also we have the correct we need is that the condition about this has to be the energy of all the lettuce and so now if you remember the proof of of the linear problem programming bound by con and kumar okay so row is one case one so we have to do we have to also fix the density of course of our configuration so under from the proof of the theorem of con kumar we will see the linear programming bound it will tell us that for each so the only so the set of all Euclidean lenses of elements in this configuration see it has to be contained in in sight of the distances between like x and zero zero okay no alright sorry because we don't it's not the latest so we don't have so so the set of possible distances it has to coincide with the set of possible distances between elements in our lettuce and this happened because we when we proved the universal optimality of lambda D we I whispered this energy as a reason that an estimate for C and that estimated would be a sharp if and only if this condition holds so maybe so maybe here one thing so maybe maybe it's not for here an important thing is that so we would have so if we have our potential G which goes like this and this was the function f of G so now the uniqueness it will be true if what we need is that G equals the f of G only only four points are in this so to say in the set of possible lenses of two elements of our lettuce and for example we know that this will be true for if G is for example a Gaussian because in that case we have an explicit for formula for f G and and now that we have a qualities only on our square roots of even integers it's kind of step function yes you're spear backing step function maybe something like step function but which is also somehow infinity at the here here so probably step function would also work but step functions of how it does not belong to this it's not completely monotonic so it has to be so for the spearpacking the problem the function has to be something like this like here zero the specking radius here we have zero but here we have kind of infinity and then one could argue that this is a completely monotonic function and so and so as long as we have this condition satisfied then we see that we always have the also have the uniqueness and so uniqueness it says is a mouth it's argumented I seen it well first it was a paper of a con and elk is so now if we have some point configuration and it's a set of possible distances is the same as set of possible distances of our of one of our two lettuces then these two sets they have to be and then both sets have the same density of course then these two and I think also what we have to assume here that C is periodic otherwise it's difficult to speak about isometry because for example we could take a lattice and take a one point and this does not change the energy however it's not the same configuration anymore so we we should assume that C is periodic so now so the density of C is one and that the set of pairwise distances in C it will be the same as the set of pairwise distances and our lattice so it means that there exists some lattice such that like C shifted by this lattice is a for some lettuce you want equal set of distances or inclusion so I think even inclusion suffices so then we claim that C has to be isometric to to one of our lettuces and so how do we do it so first we see that like this set it has somehow a very special arithmetic structure so it is it's just will be the set of all square roots of even integers for integers bigger equal than n0 right and so for example it means that the distance squared between any two points it's always even integer and so here is a simple algebraic claim is that now we take we fix one point for example x0 and compute a scalar product like like this then we know that the scalar product like this it always has to be an integer just because if we know somehow if we know the distances between points then we also know the scalar products between them and so this is a usual there is I forgot that name of the formula which expresses the polarization formula right and so now we see that we fix this points and all that points x0 for example and we turn translate our set so that this x0 for example coincides with 0 so we got some set of points such that there are all the scalar products between them are integers and so now the claim here is that the set so this the linear span of the following set like c minus x0 it has to be is an integer less lattice integral this sorry no even so even so even lattice like it's actually means that so definition is like lambda is well it is even if first either norm of a squared is always an even number and some lambda or equivalently it means that the scalar product of two lattices has to be an integer no even means that you have in the basis metrics metric measures which is even numbers on yeah but this but this will mean that you have no no it's like you wouldn't be a second one it's not good it's not exactly between it I think I think it just removed yeah okay no it's equivalent to saying that it's Sophia yeah one implies another but not and so it has to be an even lattice and so now also we know that if it's an so so let's denote that lambda c be there I think it's yeah so from this condition so let so let lambda prime be the lattice which is spent by by c minus x0 yes yeah so this is what I was going to say that now because we know that somehow we know that c minus x0 is contained inside of lambda prime so this means that the density of lambda prime is at least one on the other hand because it's an even lattice it cannot have a higher density so from here we see that lambda prime is even it will actually mean that the density of lambda prime is also bounded by one and so we see that I see it's contained inside of lambda they have the same density and now since we assume that c was also periodic the only way those two sets can have the same density if they are equal so this way we can see that c is an even unimodular lattice and so in dimension 8 we know that there is only one even unimodular lattice up to isomorphism and it is the latest e8 and in dimension 24 we have 24 different lattices like this but only one of them has the same set of a pairwise distances as leach lattice whereas the first where the square root of 2 is omitted because all other they're called nemyer lattices and all they will contain vectors of length square root of 2 so this gives us the uniqueness of solutions of this optimization problems so we know that if some configurations some periodic configuration solves this problem then it has to be isometric to leach lattice or e8 lattice the assumption that c is periodic seems to have only been used the end to who it's equal to lambda is that correct or I get that c is inside even unimodular lattice of dimension d with density like the difference having density zero yes I guess I guess so yes okay so this also implies that any such c is this you just take for example e8 lattice and you move some densities your subject is that correct up to the translation as I'm just the proper probably you are right even though so maybe have to think it's think it's right and so maybe one more application of the theorem is the now what we can do we can look not only at the Schwarz potentials but also for example to pop our laws and in particular if we look not not at all configurations but only concentrated the lattices this result it also gives some can can be applied to the optimality of Epstein a zeta function among lattices so now what we can do we can also write that now that among all lattices are D with the term and one so the minimum value of the Epstein zeta function so I just recall the definition it's some over lattice points without zero and we take the length of a point and take it to the power minus 2s to the Epstein zeta function for if our parameter s is between zero and infinity yes yes so we will do the analytic continuation as well so easy shift and so yes we can extend so somehow it's so the thesis the it's more or less straightforward to obtain this where the Epstein zeta function converges it just follows from universal optimality and now for the analytic continuation what we do we can use the functional equation and so obtain it also for s in this range from zero to infinity because the smaller the value of this factor in the functional equation it will be positive so things will be fine and then actually for if s is negative there are something interest because there are the sign of the factor is not constant anymore it's either positive or negative so in some cases it will be maximum in the other cases it will be a minimum and also like one interesting thing is that we also can say something about so of course this zeta function it it has a pole at d divided by 2 but here we can still normalize the value of our function at this pole for example subtract the the pole from it and then we will get what is called the height of a torus defined by this lattice so and so also the if we take height and so the height is defined in the following case so it so it will be some constant which depends only on D and because it's constant it's not so interesting for us right now and the following limit and so and so this height is the smallest iso then so it is the smallest among among among all the dimensional flat volume one so it's the same as the lower regular sum of logarithm of legs probably you take some of legs six to four minus distance yeah the sense it will be and make pre-transforms so it's a constant which depends on dimension yeah but was a question to us and so like something what Henry Kahn observed is that here in for this if we the optimality for the Ipshti and zeta function it also somehow implies here also have uniqueness so the only optimizer will be the eight lattice or the leach lattice and so and so uniqueness and it will follow from the following formula so we can write the following integral representation for zeta function and from here because we already know that our lattices they are optimal for the values of theta function because of what the value of theta function it will be just the Gaussian energy of lattice okay I'll with the maybe with a theta function minus minus one which is value at one this will be the normalized Gaussian energy so and from here we know that we have you so that our lattices lambda d they are unique optimizers and so from here we see that for for the values of abstinence zeta function we also have the uniqueness so maybe for that maybe have some more questions one of the first lecture you mentioned that this six dimensional presentation is a polynomial growth and useful for say something about this polynomial growth was a function is it interesting story on this story this is how we use it we used it to prove the interpolation formula and to prove all the all the bounds so so I decided I somehow like it said no interesting around but so like here maybe I decided to I mean that part because it was a bit technical but maybe maybe I can speak about this more tomorrow if it is interesting so the pressure for it's not yet in my lecture this was the part which I did not did not do yes I guess it's not necessary for for the universal optimality so it's the most it's important for interpolation formula it assures that the this functions on the interpolating basis if we fix a point and to the for example make the index grow what we want to know we want to know that for example this value they will grow at most polynomially and this is where we use it yeah but I'm always simple I probably have more time than I expected that I can speak about it maybe tomorrow and so today maybe I wanted to speak about more like so many people ask the question so what is so special about dimensions 8 and 24 so maybe like at the remaining half an hour I will try to speculate about this so what is what is special about 8 and 24 and so here so and so I don't have a simple answer to this question so it's still not clear why what are the particular properties of these numbers which are important but what we observe are the following two phenomena which seem to be quite special to these two dimensions so first is that the energy minimization so it can be solved by linear programming and so rather by so say by by a concrete linear programming bound to which I explained before and this seems to be special to these dimensions maybe also including one and two and second also properties that it's a solution of linear program has so it has particularly nice structure so that in this case we were able to somehow for example give an explicit formula for this solution which probably would not work in general and so yes which are not minimizing but extremizing functional I think it I think it might be I think there are some results like this I think actually there are some results of that kind maybe maybe not for all lettuces but maybe like for for example for shells of lettuces there are things called perfect lettuces I think they have some might have some properties like that and so and so here maybe first speak about the first like why so why do we why we don't expect that energy minimization will be solved by this method in general so why there is something unusual which happens here and for this I will somehow introduce a new definition and so what we are going to do we want to so let C be a periodic configuration simplicity and what we would like to do we would like to somehow not only to consider the set of all pairwise distances in C but also to compute some kind of statistics of this pairwise distances so and so we introduce the following function we say that is a two-point correlation function this would be the radial distribution mu and for example we can take it in space which is dual to the space of radial Schwartz functions but we will see that actually it's not just a temporal distribution it's it's essentially a measure and so we define it in the following so maybe such that if we apply applying mu to any function it will it gives us energy of energy of configuration C so it's certainly a linear so this is a linear functional of our energy profile and if we assume that fdk is fast enough then it will be also well-defined and so here just to somehow to we also want to include zero which we excluded from computing self energy of point interaction so we include zero here so and so now this distribution it has a number of nice properties so so how can one could think about this correlation function so it will be like a sum of delta functions at those points which occur as a pairwise distances between two elements in C and the weight will be somehow it will measure how often this particular distance is met with some normalization so to say and so what we see that's obviously that this distribution is actually a non-negative and also if we somehow this is essentially what we've seen while proving the linear programming bound by Conant-Kumar is that the Fourier transform of this distribution if well defined I will not bother as this question like right now but if we can make sense of its Fourier transform then it also has to be non-negative and also what we know we know that if you restrict this mu is in the in the neighborhood of zero we will get just the delta function of zero and if we take its Fourier transform then in the neighborhood of zero it will look like the density of our configurations times the delta function at zero and so for example you can check that all this actually works if mu is a lattice for example and so now we see that like in this transformation of how knowing the complex hull of all such two point correlation functions it is equivalent to being able to solve all energy minimization problems but of course the difficulty here is exactly that we don't know we know very little about this convex hull except for these two conditions it's not that easy to think of any other restrictions which should be and so the what what is the linear programming method it is that the more we are trying to for example found chalk so if we have this for example set you know that by M which will depend on D so this would be the convex hull of all possible configurations and for example maybe with fixed density so it will be some difficult set we know very little about and now we know that some of this set is it's contained in intersections of two other convex sets we actually understand much better so one of them are all just all positive distributions and now there are so to say positive so those which have positive or non-negative Fourier transform and so maybe let's denote it this intersection of these two cones by L for the linear programming system and so now what what so what what so now what the universal optimality property means so the universal optimality means that our cone here it has so to say a corner point so this corner point it sticks out and it becomes a solution to many optimization problems so now universal optimality for some reasonable set of functions kind of it means that we have a corner point and so in particular what it means if for example lambda is universally optimal for a cone of functions for example we can denote it by s and in our case our cone of functions it was a cone of this completely monotonic functions of squared distance or the cone which was a which was a linear span of all real Gaussians and so now we see that lambda is universally optimal if and only if the set m which I will omit index D here it's actually it's contained inside of the dual of of this cone s plus the correlation function of lambda and so here so here as to all it will be just the set of all measures new such that the pairing between new and f is not negative for all functions f in the cone s and so the picture we will get here will be like this so so we have here our this will be the point new lambda this will be the cone m and it has to lie inside of a new lambda plus s dual of course everything happens in a infinite dimensional space so this picture with a corner is well in the dimensional space this kind of intuition might be quite misleading but now for so what what happens for the leaf and somehow we we don't know whether all all the cones MD whether they do have such corner corners for example now we know that such a corner it would exist for example in dimension 8 and 24 but in other dimensions it could be that which we simply don't have corners like like that so we don't have universally optimal configurations for at least maybe for not for this natural nice corner functions which we have selected before and so another know what is a special what is special about dimensions 8 and 24 it is that this the con l it actually for it this point m lambda it also somehow it has to be lie inside of to be between our cone it has to lie exactly here so it he needs to have exactly the same corner and in this case we can prove linear universal optimality by linear programming and so as we somehow numerical results maybe I'll speak about it about a bit more tomorrow so what they suggest is first that like if we go to other dimensions usually we will not have a corner like this so here indeed these dimensions so so the station when m has a corner at least for our nice set of functions so this is unusual at the same time but numeric shows that this con l it actually it seems like it always has a has a corner like this l has a corner this this seems to be a usual situation so is it usually a two-point correlation function of the lattice no no but like this thing that con l it doesn't it's not it just comes from these two conditions of about the positivity it's not related to any lattice so it's just like it's some virtual it will be some virtual distribution which does not correspond to anything and actually this is the case why sometimes or even very often why linear programming fails or the methods which we used right here so it could happen that we are optimizing we want to optimize for this con l but we don't have a nice description of it so it's very difficult to access it so what we are doing we are optimizing over a bigger con l and so this would be our objective for example and so very often we can find a solution here which will be optimal solution of this problem inside of l but it is not inside m so it cannot correspond to any to any actual configuration and for example this happens if we try to solve a sphere packing problem in dimension 3 by the con l case linear programming bound so we can find so to say some parasitic distribution and we know that somehow the distance from zero is too far and the weight of this first so to say first delta for first non zero first delta function which is not in that not zero the weight is too big and it for example contradicts what we know about possible number of points in a kissing configuration so we know that such a configuration with this particular correlation function cannot exist but the way the single questions in coding theory are also fine and good having distance and also the scobatianski which they learn some some this art and there's also maybe some extreme things like stuff yeah I don't know did you study this yes so I think from very nice cold yeah so so if so in this case like linear programming for for example for fine for finite codes it's it's not easier to work with it because there I have to work with polynomials everything is compact everything yes yes and there are there I think also somehow there is rather this codes which correspond to leach lattice and eight letters and they are also perfect codes and I think their optimality is proven by linear programming and and also also we know that for example like kiss you come to spherical codes than kissing number in dimension you see a number problem in dimension 8 and 24 it's also solved by linear programming and also solved like exactly unlike in other cases so it seems like these two lattices they so certainly friends with two point correlations maybe like last thing I would like to say is that another another special feature of dimensions 8 and 24 so it's numerically it seems that in all the dimensions we were able to find this corner here at least approximately we cannot describe it but it seems like it's exist but in all dimensions except for 1 2 8 and 24 usually this distribution it's some very transcendental and nasty thing and we cannot find any nice description of that and so like maybe another second feature it is that the solution it seems nice no no no they're just some just some real numbers nice only if D equals like 1 2 8 or 24 just so probably yeah of course one can add some bombastic things its dimension of super strings is 10 which is 8 plus 2 and for strings is 26 which is 24 plus 2 which is not accidental but I have I still have to discover what the connect connection is so I do things can happen for the high dimensions I we have not seen so far we made some experiments and that it seems like actually in high dimensions things kind of they'll look the same they kind of stabilize no the like it's very similar very similar behavior like understanding asymptotics is not that easy but we have not seen we have not seen for example other case when you have only square roots of integers or some unusual arithmetic behavior I think it seems like all the higher dimensions they all look like each other they are all transcendental so to say


Well, hello welcome in today and yes Imagine a time just imagine a time when accountability matters when you make a mistake instead of Tuck and tail and hiding I don't know behind ignorance or Maybe a miscommunication or whatever other excuse What if you instead Accepted the mistake and Changed things for the better and for the future and started doing things the right way. That's right Do not adjust your sets. You are at the 1985 PBS station Zapping you here Into a nice lesson for the CRT world now This is a new series and I'm kicking it off with a Live show so it's a bit of a hybrid I was describing it when I was teasing it and I'm calling it a hybrid because I'm there's going to be live Episodes where you can be involved and we can work on these things together and get the community involved And then there's going to be other episodes. I believe that will fall into the same Category and this same series that will be taped. Okay, and I'm sorry. I didn't have any good watchmen Rorschach music ready So it is a bit cheesy compared to what maybe you expected from the dark edgy Comic book and movie and everything else that's come from the watchmen. Hey So we're gonna get started here today, and this is all revolving this whole the Genesis behind the end this entire series is a conversation I had recently with Keith Rainey and most people in CRTs and into CRTs and on social media have Have heard of Keith and know his work and have seen and used his work in things like the 240p test suite and the Monoscope pattern and Anyway, I was having a conversation with him not too long ago and where we were discussing How he had been reviewing a service manual that he bought and This manual was just not available online at least details in it that were important to what we're talking about and That's adjusting some geometry settings on this specific model and that is the Sony PVM like 1340 series. So this is a 4-0 right here 1340 but this could be like 4 1 4 2 4 3 4 4 and it might even fall into the same category with those in Europe and other regions like the 1440s and this Adjustment is for the geometry on this set and Keith has Been kind enough to make a video for all of us. So I'm gonna switch over now We're gonna take a look at Keith's YouTube channel first off. I'm sorry. I haven't talked about this sooner But everybody should know that Keith does have a YouTube channel KH MR 3 3 and I have linked This channel I've linked this channel in the description for today's stream So if you'd like to go sub subscribe to him and check out some of these other great adjustment videos he's making he's been on streams with me before and So you can go over there and check him out, but this is a video he made Just under two weeks ago, and it's about setting the horizontal Phase frequency and basically centerness on a Sony 40 series, which is the exact same monitor I have right here next to me and personally I'll be honest. I've always avoided horizontal frequency adjustments because it was something that was a little wild and was never was never really properly understood until Keith broke it down in this video from the information he had extracted from the Manuals he purchased online. So we need to go in here and refer to his information and we're gonna use something that he and I discussed and Anyway, the reason all this goes back to this new series is he He sent me a message and I was like, well, this is brilliant You know, we've got it's great to find these new ways that we didn't know before That were actually the correct ways to adjust some of these CRT's and He said yes, there's a lot of things like this and even what I'm doing today could you know fall under under Keith's definition of Of of not perfect because I don't have the same kind of awesome signal generator that he has for his His screen right here. So he goes into much better detail We're just going to do what he says to do in his video. We're gonna do that live on this set And we're just gonna check it out. We're gonna try to adjust this set according to this Guide and use the tools that I have available Which will be available to most of you if you're adventurous enough to do this but By the way, it's all good to know these things and to know how to do it correctly And I know I'm teasing I'm moving my hands around and moving this. Oh nothing happened Keith Keith just joined us in a live chat here, but yeah, if you're in here and you're stopping by just Drop a like on it, but check Keith Keith had said Yeah, we're getting into a situation where It's who watches the watchmen and it's absolutely correct If I went around and just kept doing this the wrong way and didn't even have I don't have any pattern generators on my laser disc, Keith Ah, but Maybe but what we'll have to do with the only things I have is Super Nintendo or Sega Dreamcast, okay If I can find a laser disc That I Oh That's it. That's on my laser disc hot list is a pattern Laser disc, so if anybody finds a pattern laser disc and wants to send me that Listing I will check that out anyway So who watches the watchmen right so we all got to do a better job. I think sometimes of Watching what each other's doing in certain instances and making sure we're doing things the right way and There's going to be a lot of instances I could find probably in my years of discovery in this hobby and in growing my business into the progression of the you know Repair man you see before you over the years there are things that I've done in the past which I Could critique my own work for probably ten episodes of this series to begin with so today we will start with Keith's method to correctly set this horizontal Frequency phase and then center so that's the Keith Imagine this an expensive thing that will just have to be on the hunt list. Maybe I'll see it out in the wild somewhere this fall Will be a laser disc. Okay. I want to get around here and first off. This is the monitor It is in S video right now just looping some Gradius right there, so we'll let We'll let this roll for a second But what I'm going to show you Beyond that is what I have hooked up to composite and that is the Sega Dreamcast eBay 169 holy crap. Thank you koalakoa. All right guys I did the introduction everything set if you're liking the series so far I know this is live even if it's on a playback and you can hit the like button for me Hopefully this won't disappear into the algorithm of nothingness, but again, it will be part of a play writ playlist that Is a hybrid that progresses over time? But first off again, you're seeing just a nice wonderful image we have already gone through on the last stream and we Serviced this power supply, which actually had a big crack down it and we had to do some welding there and then we Recapped it reflowed all the solder cleaned it up and it's been working perfectly since then and relatively untouched since then So everybody thank you so much again for coming in a lot of people here that I see each time I do a stream and I'm really blown away Thank you all so much First off, I'll do some shout outs here for a second little pig Dan B my retro fix. Thank you all for coming Belmont Keith Rainey, of course koalakoa Felipe also and Ray Seroni, thank you guys all for showing up and everybody else who's here who I've missed before that who's been Really involved looks like we've got a lot of chat going on this morning, which is always fun So again, this is the monitor if I switch over to I think it's line a all right I've got already a pattern pulled up here Keith wants to give me any advice as to which pattern would be best to do this I'll be glad to say it. I think this is I Think this is gonna be one though that will show up good when I insert this dongle and It will Look really good on the screen. I think that's the most important part. Oh, hey snuffer-stuffer. Thanks. Absolutely Sorry about that Yeah, don't worry about it. Hey, it's not that big of a deal I appreciate you being here anybody even if you're at work and you're sneaking around and just listening Odyssey 113, thank you and We're gonna just get into it. But first I'm gonna show you Let's go back to our dashboard view on this video a little bit So Keith has his pattern pulled up here. Okay. He is like I said a great pattern great pattern generator Eric Thank you for showing up and What he's gonna do is I'm gonna summarize a lot of this but he's got a capacitor here that he's made I think with some attachments on maybe the ends we'll do we'll pull the color bars up to and What he's doing is he sticking it in this little spot right here in the circuit board, okay? Right next to this chip and again the monitors turned on So he's sticking it in there and he's jumping a ground point This is just a ground to some kind of voltage point and he's jumping it with a 100 micro farad capacitor I use 25 volt. I believe that's what he uses and as long as it's 16 volt or higher. You're okay So what I'm gonna do is I'm gonna show you what mine looks like close up because I was actually fortunate enough To where I was able to salvage a piece of plastic That is from this monitor. I showed you I think it was two weeks ago Yes, there. I had a video about salvaging parts and I showed all this extra wiring I come across well This is like one of the things I keep from that are some of these ends Thanks to Keith knowledge really he told me about this end Said grab it if you find one so this fits perfectly into This spot right here and it just slips right in and all I had to do was jump one side Let me show you Just in case you're lucky enough like me and you have one of these so you just I soldered one end To the negative side and one end to the positive side of the capacitor here and This came from the speaker input on this monitor. So that's where you would salvage this Part from 99% of the time is this is what's attached to the speaker that also goes into this board so that came out of there and on the speaker cable you just snip it real close and the red on the speaker side the red goes to your negative on your capacitor and The white goes to positive on this now I've never even tested this So if this is somehow wrong and all this explodes You will be here to see it live and We will all enjoy our Monday a little bit a little bit more than we thought we would and Let's see if we can talk find the color pattern EBU style that Keith referred to color bars EBU That's what he was referring to Maybe I'll turn the brightness down a bit just on it for what we're about to do I Will try not to overclock wise That's right. That's the important thing everybody Everybody will be good. I do have an interesting thing to to update you all on Yeah, if you remember the Sony PVM 1354 Q That was opened on a live stream That did not function that was refunded and The good news is is I don't believe they are gonna get it back I think they're just gonna leave it with me. It's been about two weeks and they were fun to me. Oh Almost a retire week ago and They filed a claim. Oh, so I don't know we might get that for parts and be able to experiment more on that one in live streams I don't quite know but we're on the verge of almost getting to just straight keep that one as parts Because they told me if they didn't if we didn't hear from FedEx that you just keep it as parts or dispose of it That they weren't gonna pay to ship it back to their facility But let's try it I've got another Another yeah fully refunded every bit of it View for you here, and I know you might have thought You might have thought this was just like a picture, but no that's a live shot right there live shot and What I'm gonna first do is I'm gonna stick. I'll show you I'll come over there And I'll show you I'm gonna stick this little part in that in that Spot So this goes down into there, right see my hand told you I was a bibbon. So that's going down in that chip spot So this is the destination point here, but I want you to be able to see the screen simultaneously Well that is true koalako it's always sucks to see one Hopefully I can salvage it the problem with this one. I believe is it's a tube issue So that might be a fun thing to diagnose on stream on Another episode like this. That's a perfect thing. I wanted to bring up as tubes to Rejuvenation because I got my rejuvenator mostly working and testing it can test the tubes All right, if we go back here to our Double view this should be This should be our best view. Maybe I will expand This a little bit So you can see a bit a bit better Because where I'm where I'm going here is Right at this chip I'm not sure if you can even see it on your cursor, but maybe you can my cursor on your screen But I'm going above this chip. We're gonna insert there and Then we're going to use this blue potentiometer back here to make the adjustment See if I'll do that Yes, okay All right Gonna turn the gain on my mic up so you can catch my voice from across the room I'll probably turn the music down just a touch Here's we're gonna insert this and then hopefully this this TV is gonna or this up. Sorry. This pvm is gonna scroll Because if it just sits mostly it's gonna scroll All right before let me show you before I really we got all that set up before we let me turn the microphone back down So it's not blasting your ear off All right What we do that just let me show you what happens when Keith does it's Keith puts the part in and it makes The screen scroll and make sure that's not playing the volume there and that's mostly good Tunage when it's scrolling nice and evenly but before that I believe it's It's really an erratic It's it's hard like scrolling look it'll it'll start scrolling back and forth And I think you want it to not scroll Or to scroll like that. Let's see He's gonna adjust it here To stick the screwdriver in and As you spin that it'll it'll it'll screw up more and then it starts to straighten out So you want it to be what we want it to be we're gonna do all this live We want to spin it. Oh You didn't dizzy yet, so it's like center like that Man, all right, who's ready to get their Disney's their Disney spell on today. I hope you guys are ready That's great Keith. He did awesome there Keith he did a great job Recording this okay, it's awesome and helpful Extremely sorry. I didn't mean to do that All right, let's go over here now and let's try it Let's try it. Let's try it live here friends I'm gonna insert the device. I'm gonna find my screwdriver to right. I can't Hang on. Oh, baby. Look at that. I found it. I found it Yeah, team, you know, thank you for coming. Yeah, I'm sorry everybody for getting dizzy Here we go. Let's adjust this Whoa Keith, what do we think do we pull it off? Maybe is that kind of what it should look like there? You get you for a close-up of that Whoops, sorry wrong one See how it sits there and like It's in the middle of that. It's very very precise on that potentiometer Cool. That's it was definitely off right when I turned it on It was off by a little bit Okay, so what I could do is just remove that capacitor now and then you Went through and adjusted the video phase But that's an interesting thing right there. So that's this is Well from what I understood you this is like the foundation point from where you need the first thing to be set would be this Particular Setting horizontal frequency Set this and then once you have this set you can set the other things down the blockchain kind of Or down the chain of Settings from this then video phase and horizontal center. I guess to use it at the end, right? That's what you're explaining. I think Keith if I remember everything correctly from the video. Let me remove the capacitor and We will Check out some other things on it now. We'll take a look at the screen without it in there All right, so I won't be able to I won't be able to Show you in the same manner that Keith does with his great pattern. I don't believe we can tell that Wherever we go from this point on If we look over here even We are off-center a little bit. I know it's hard to see probably on that screen. It's not off too much but it is Still scanning left to right a little bit to the right Okay, there we go. Good answer if somebody was asking what happens if this horizontal frequency is off Then our team you said it can throw off the geometry and the timing It'll all be basically set from a wrong position So you'll just more than likely in reality You'll see you'll just have Geometry imperfections that most likely happen when you're changing signals. I would think and Maybe things that you just can't get corrected And it's because possibly right that timing is off and Geometry will always slightly be off probably on some things. I could be wrong because again, I Want everybody to always know this I am like most of you my background did not come in like electrical engineering I have been most of a student my career here and I'm always learning new things and I did have a background in engineering, but it's pretty much only in It was in more Construction specifically in concrete was my field under scan. Oh this but You know, sorry Keith. I don't believe this monitor has an under scan Now this 1340 super basic. It doesn't have actually an under scan So if you want to go over Keith's using a better version of the four series that has an under scan button on there So if you start from that point, right? What if we took a second and reviewed what we do after that on Yeah This one is so basic. It has no under scan. There's only Other than the input buttons on the front There's only a blue blue only button and then on the back side. There is a switch for Color temperature between 9,300 and Then That's it like a v-hold knob. It's definitely the lowest and Yeah, they actually do they have it right there don't they There's a knob in there for adjusting under scan and vertical scan on your screen right there and For some reason it's still on there So we can get in here. We can definitely spend these potentiometers I'll do that for all you guys so you could see what happens on your screen Just I feel like sometimes seeing these procedures done Could Maybe make you feel a little more comfortable if you had to do this or just something to refer to You see somebody doing it in real life, but I also want to try to get this Vertical or I mean video phase and horizontal center done the right way so we should Check out maybe let's do this Let's just pause this bad boy here and I'm gonna go in and we'll try to see like So the problem is is I don't have this great same pattern that you have that she can adjust the timing so well from right Or Keith's not gonna hit me for copyright infringement. This is under fair use. I believe anyway All right, yeah Keith you can't tell you the cleaners just for going through this, okay? I was I know Keith's not gonna do that look So basically just telling you kind of what we've been walking through and talking through here that we need to start from that Horizontal frequency Adjustment that we did first off and then we can move on to these other adjustments which I hope is where we're at in this tutorial that he's given us and Again, this is in the this is in the description. So please go watch this Before you even consider doing this adjustment We're just again trying to interpolate this into a real-life scenario and do it here Resynchronize myself to that sink pulse. You're not actually drawing a picture That's precisely when you would want the fly back to energize and clean the screen So if those are out of sync, I think you see how clean this is on this side and how warped and weird it is on this side What you're seeing there I think is literally the video signal being sucked up into the Negative into the fly back pulse basically So we're gonna make a little adjustment here if I can remember which one's video phase You think I'd have this memorized. I don't have this Not a smart person I'm just persistent So that's probably All right, let's see what She makes the adjustment here It's also why video phase gets confused for horizontal center sometimes too. I mean you can use it to center, but sort of on accident we'll say so I think You want this to just start to disappear Just like that Now Think I need to tweak H blank. Let's move this back where I can see it real quick. It's a little bit smaller So we can sort of see what we're doing And blank Will literally make that disappear Right because basically you don't want to waste time drawing stuff that you shouldn't be seeing if you get too close to the edge of the Tube and the electrons go bounce off the edge of the tube Caused all kinds of problems According to the service manual Think I think you're supposed to leave that there It says Adjust H blink Make to blink the vertical I think it means Not completely gone, but touching it right, so That's too far obviously and Then we're out past that we wanted to just start to Okay, so we're gonna get in here and do this world will do our center adjustment here We'll probably have to shrink it down a little bit Maybe not we have to do the video phase adjustment though And I don't again. I don't have this awesome pattern with these numbers on I'm gonna be using the regular monoscope pattern I guess and then we'll do the blanking adjustment to try to get it right up next to this line here See what we can do. So let's uh Let's go back to this view And I'll try this a little bit No, no that this is gonna be I don't know this is gonna be greatly visible for you guys here, but we'll try it Try to do the blanking adjustment now, which is right next to that because there are a couple frames over there that Be an energized that there's nothing being drawn on So that's good right there. That's kind of good. That's what we just did is What Keith did here where we adjusted that horizontal blanking after our video phase And like I said Keith's really doing us a favor by explaining all this from the service manual So if we go back here, you can see I'm sure in the video when I was doing that you saw this move side to side especially when I was doing the Video phase adjustments. I don't know how much more of an adjustment this needs beyond that Keith if it looks good after this, right? And at the very end you can adjust it for Horizontal Okay, 92% screen phase adjustment Equal as the width of the white frame And as I said before we may have I mean this is all experimental This is the best closest adjustment thing I know that I have There are better things available and Keith points out that the video game signal is only about 92% of The NTSC signal. Yeah mirrors are great to use over clock wise. Good job. So the idea is that you've blanked it on this side Just enough to touch adjust the phase so that you can see an equal amount of the white on both sides brightness So you can see it's actually out beyond if you think about it. It's actually out beyond with it blanked, you know Certain amount. Sorry here guys. I didn't switch back to this other view Certainly as close as it needs to be on this little bit of a CRT Now the centering stuff is universal for under scan and over scan doesn't make any difference But we've done each frequency. We've done video phase right now. We're gonna hit under scan get out of there Where are we at? We're still very close to one on this side Not as close to one on this side So what we're gonna do go hunting for the big fat All right, so I know where this is and the last thing would just be to center this up from this point That you see here to center it up a little bit more and I will spend the center adjustment. I'll try to point it out to you from the Point here, but that would be like the third and final stop for your adjustment on horizontal And then everything else you can fall in line after that just everything after that point Because it's gonna be universal and especially on a TV like that or set monitor like this That only has a certain amount of adjustments and modes on it So this one is a pain in the neck to get to It's right there I don't know if you can even see my finger. I can't even get it in there right there it's like all the way back here behind the flyback and Here I don't see any reason to do this If it doesn't need the adjustment right now, but that's the potential or you got to get in there and mess with that one Sneak your hand in all that there it is so if We just look at our No We just look here at our screen I've got this centered really well thanks to the Information Keith's provided So it's not I'm not gonna even have to touch the vertical center because I've got it so good Using those three adjustments. We got to this point through his Tutorial, I'm sorry It's tutorial here that we don't actually need to get in there to the centerness at least not until I get in here and Unless I check this and I really need to I believe this is gonna be good enough It looks like it's right on from what I can see. I need to get the next level of testing here and That's pretty much it though on doing this the correct. This is building that this is building a Foundation for your calibration. So you're building the foundational blocks So that this is all set and your timing set and then you go from there what I'm understanding here and Build upon that and that will just give you better results and make things correct kind of on your CRT All right guys. Hey, hey to self-elected. Hey to over clockwise and hey to delusionals arcade. Hey, Dale and PO 17 thanks for shot for stopping by and Yes, here's this announcement. I made this a couple of weeks ago in a live stream I've talked about it a couple of times. I will be at Retro world expo This year, so I will be driving there. Yes. I will I'll I'm I'm getting things ready. I do have some CRTs. I have to get done before I actually get to go and That's Let me see here. I want to get a better view for you guys. Give you that one or How about the Desk view with me in it too. That's better probably and let's switch the screen over here to a different pattern but What I'm I am going to be at the retro world expo. See I'll be there absolutely and If you guys have any other questions about this stuff drop me a question here I didn't want this to be a hugely long episodes of people just want to watch it that's kind of the majority of What I wanted to do I want to do a live demonstration of what Keith had done and If there's anything else you want me to check out while we have it here We can do that but also just to kind of show you that and then you can Use these principles to get in there and you know change this if you want or just enjoy a show watching me try to do it So That's the day other things that have been going on. Hey mark. Hey moe I Have There's a lot of stuff that happened this weekend a lot of great content came out I mean, I'm not just trying to plug my own show. I had a Interview that I did with my good friend from the art museum. I know a lot of you guys watched that It was pretty universally liked for those who watched it it is about the museums and Why the museums? Still you CRT's and here's here's the thumbnail for it this one right here Just sat down with a good friend of mine from the museum. Let me turn some music back on and We had a great discussion About a lot of different topics. We went from how the museums acquire CRT's and how they maintain them how they how they try to use a network between one another of sharing the equipment and Other ideas that they do have how they save some from different disasters where they get them from and A lot of talk about the exhibits themselves. It's a lot of fun stuff to get to talk with him about. Hey Brian Harmon Yes, I do. I do have a CRT projector. I have not had time to mess with it.  Well, you'll come in and all the colors. Let me show you if you go back here to the Shop cam. Let's go back to the just the shop cam Not that cam if I can remember which one of these I'm trying to get you to this one We go up to a pattern Thank you demon child. Thank you for the five dollars super chat. I appreciate it a lot Do you know any techniques on how to shield a CRT from the magnets from bookshelf speakers? Okay, so the first thing you need to do is probably the easiest thing which is to Try to move the speakers a little bit Even if you have to add extra cabling and and hang them from somewhere If that's not possible and you're still having trouble There are methods you can take to attempt to shield a CRT similarly to what you see on the professional monitors where it has shielding behind the tube that's metal and If I go over here to this view for a second, I can show you exactly what I'm talking about Just let me make sure I get the right camera No, there's not much on this model, but you see this shielding up here right here that's all shielding and Sometimes so you got to do things like mimic that kind of shielding right so that could be anything Man that leaves a lot like a different things you could do there like I've seen Instances where people have tried to add metal inside the shell the CRT I've even as seen copper thin copper lined inside shells a CRT to try to help with Magnetism I'm actually supposed to be working on that project for the museums because they're having a big problems with these sets and interference from the subway which was one of the topics that Kirsten and I briefly talked about in the museum's video that that came out over the weekend So thank you demon child for the great question. I hope that helps a little bit But again, it's gonna be more about trying to make a homemade shell around a CRT or or fitting Some kind of shielding that you may salvage from some other CRT and try to retrofit that onto the back of the CRT It would be a lot of experimenting and and just trying to basically prevent that magnetism from getting in They the best the honestly easiest thing is to try to make it a set up like Keith just mentioned where You're actually separating that to the point where you don't have to interfere have the interference So the best idea is just to get the speakers away till they no longer interfere But if you get them close look at my channel, it shows you kind of right here What happens you get this discolorations from magnetism on your two purity problems, but yes, that's that video There's also an awesome interview from our friends and My your friend and my friend 8 bit Esquire and he had He had a video where he interviewed Mike Chi which was a lot of fun. So it's still really cool I enjoyed that over the weekend So if you guys have any other questions, you can definitely ask them right now so That's kind of what's been going on I Did enjoy those videos and A lot of stuff over the weekend so a lot of a lot of good content now Take a look over here. I keep forgetting which one of these I have them all I've chained them so many times I don't have them all marked the right way right now Translate the abbreviation some Mo was asking about a CRT from Samsung and translating service menu My best advice would be to try to find the service manual where it would give you a better explanation of what each line And the set says because a lot of times those are abbreviated and especially if there's a different language Yes, hang on one second. I have got to take this call. All right. Thank you guys. Sorry about that Appreciate you. Give me a second there. Oh I'll let that backlight on. All right. That's better So here's the deal As far as let me give you a little bit of a while we're doing this live again We'll expand here and just and just kind of chitchat about things. I'm gonna be Again at the end of August. So this is the end of July last day, right 31st wonderful month Thank you everybody again who's come in and I mean there's been a lot more activity on YouTube Well, more people watching a lot more people interacting the live shows have been awesome I've really enjoyed it. I'm thankful. We got everything kind of situated after our weird issues but Going to go to that convention at the end of August now. That's not gonna be That's gonna be a pretty tight convention. I'm not What I'm gonna do is I'm gonna be arriving Friday. So I'm gonna leave Friday morning and drive up And it's like an eight hour. I'll probably get there in seven to eight hours and then I'll Be there Friday evening. I'm staying at the Marriott, which is attached to the convention so I'll be there Friday evening in the Marriott and then Saturday morning, I'll get up and go up and I'll be at the convention all day Saturday and then That's again the last Saturday in August and then Sunday. There will be more convention But I will be leaving Sunday morning because then I've got to get some the rental car back Sunday evening because if I keep it another day, it's like a hundred and sixty dollars more to just leave Monday and Honestly, the show is a lot slower Sunday than Saturday Saturday is the big day That's a day.  I mean, that's not I'm sorry I said the exact wrong thing to say be there Saturday not Sunday. Okay Saturday not Sunday and We can we can chat there Also, if you're staying at the hotel and you see me in the lobby and you want to say hey absolutely say so Unless it's like me running to the convention for something important that I have to be there on the time limit for Saturday You know, most of the time Friday, I'll be going in there and I'll be socializing Hanging out and speaking with people So if you're staying at the hotel and you're coming down you see me you want to say hi, please do I love to chat about anything But that's the first convention The only reason I'm bringing all this up is kind of circle back around a lot of things you guys are talking about in the chat But then there's a second convention, which is the music city Multi-con, so let me show you and pull up something Many of you've probably seen this video Right, okay, I think this no Interesting enough I have done two videos about the music city multi-con Okay, one of them Trying to find them all here. I'm just typing in music need multi-con The first one was two years ago okay Let me show you this There's a video here and I and I go through and I show every CRT that they have and in the one last year did even better And I don't see it on here anyway Let me see if I can find I can't find my own video So there's like I say I go here and I do a course, okay? So I've done a couple courses. You can laugh at me with my silly hair This is the only one I actually go and do courses for is the music city multi-con And I don't know why my there it is okay. This was the one from last year last season. Oh my gosh live Look at that. Isn't that nice? Advertisement there from YouTube I have no idea. Oh my gosh. Anyway Here's the video I'm actually referring to And This one will show you all the CRTs that this guy has at his convention and what I really What I really want to do is I want to spend some time at that convention in my booth And I'm just gonna start grabbing these CRTs and I'm gonna video them I'm gonna open them up because they're all kinds of weird CRTs that I just never seen I'm really close with the owner of this show It's back in the Nashville area and that one is in October and like I know that my friends from my life in gaming will be there both try and Let's see. Let's just see who's on the lineup card Let's just see who's on this line up Sometimes I mean I don't even know if I'm on the guests like let's try now. Oh, look at this See guys This is where we have to meet to if you can be at this one either one look at this this one has But we're getting to the wrestling the wrestling amazing wrestling people. I know that if I wish Ape and Esquire was here so you can see this you got the million dollar man Jimmy Hart and IRS and look I have no I've never met them of course I don't know them this is a mixer of a con so it's got a lot of People from comic book industry. We've got all the guys who will be there. I'm sure at And at the Retro world, I'm sure I bet y'all three of these guys will be there and then oh look there I am, huh? Classic game room. I didn't know he was gonna be there mark Bustler will be there my life in gaming and look at that your boy Steve's still there and That's it. Okay. Cool. Lots of stuff to do. That's a fun show and We will be there so and also I'll be hanging out. I'm gonna be bringing a special guest at least I'll invite Chris from This place gamers to come with me should be fun That's the season for me as far as like conventions go 90% of the time those are the two I go to And I get over here. Let's go to this Let's let Let's let it go for a little bit on the desk view. There we go. I'm just let that roll So I'm excited about those things. I think it should be fun It's always a fun chance to come out there and see people and see what's going on actually in the real world As opposed to just the CRT bunker down here Mark be awesome to see there and I think Mark looks like he'll be at the I'm sure he's talking about the retro world I've got a secret minivan. I'll have to fill up a CRT. So I don't know Visual performance loss interesting question elf lover EF lover. Sorry Oh There I am with someone's name butchered it Right Yes, EF lover, I'm sorry So I Don't really think There would be a difference. It really would depend on the device and if the device does anything specific talking about some kind of a Mike Chi device, I would expect not really much of any loss performance not if you're using it in the CRT Experience I Will tell you if you are wanting to get maybe more Adjustability out of your CRT or your experience. I should say You could convert your scart over to component video if you have a component PVM and then you actually get the whole 240p experience plus you have the ability to adjust your colors in the front on things that you cannot Adjust cannot adjust on RGB Yeah, that's cool. I you know, I've talked about that too where the experiences of going to conventions It's good, but you really have a Challenge of Funding it. I was quite lucky. I worked at all the funding for both these shows, but it's still It's not something that you know Is cheap most of the time and But it's awesome to get to do it so I'm happy to do it when I can also it's a time-consuming Consuming experience, which is awesome to be able to do it, but at the same time it does I Take away from other things.  Is it like a medical monitor that only has one line for RGB and component? well I think that's gonna be probably it for today guys, I really enjoy coming in and hanging out and everybody asking all the great questions and Enjoying the stream today. I had a good time. I have a lot of stuff going on right now. I have to get ready to go back for a Fortunately for a funeral to him this week But I'll be back by the end of the week and I'm gonna try to do something special With some other people and have some guests on on an upcoming stream. Hopefully soon So if you're just coming in late We went through and we did this awesome adjustment the correct way Thanks to help from a video from Keith Rainey if you want to know more about that video Please check out the description of this video and there's a link to that video Everybody else go check it out and make sure you're subscribed to Keith in case you have any questions About repairs and things that he works on he puts out a lot of good content and that'll help you fix things too So anyway, thank you again everybody. We'll see you all next time Some more retro content


E.M. 3, it on his... Brass. Brass is good for the water. Yeah, it's good for the water. It's five rounds and go for the five-circuit. Yeah.