 Thanks to all of our session speakers. So first question, I'm going to draw out this question and just ask you to answer it in real time here. Would you explain how a theory of two is not secure as mentioned in the last slide. Yes. Yeah, so it turns out that the beacon chain, as it's currently specified, and as it's described in gasper this kind of academic simplified version of it. So the beacon chain consists of two parts. One is a fork choice rule called LMD ghost. And the other part is a finality gadget called Casper FFG. And it turns out that this fork choice rule is susceptible to balancing attacks. The adversary can schedule their messages in a slightly careful way, and then make the network built even even even an adversary with almost no stake can make the network build two parallel chains, two forks that just go on indefinitely. And the network will never reach consensus. And the network is based on slack to two E three search posts where these attacks are described in detail. I was just wondering why four secure signatures were not being considered. Yeah, I've just checked the slack message and I think, yeah, pretty much everything is said is that I think this, like, like key evolving thing. So let's assume that some participant needs that the participant needs to be honest at the time of when they are doing the protocol, but really they don't really have an incentive to delete their keys right. So I think that's the main thing is like, oh when in a rational model that it's it's a trick that doesn't really apply in the rational model so that's, that's the thing. Why, why, why were we are doing this is to be more more robust even against rational rational players. I think this arguments at the at the beginning that you know we should think of of Bitcoin in in a different way so so potentially not not as a payment system but as a potential root of trust for for other protocols and other chains, this is the checkpointing into proof of work discussions. How do you see the future of of Bitcoin and its usefulness and also going to to the biggest point that Marco to the bigger point that Marco was making. How do you perceive the energy waste or energy usage of Bitcoin compared to the advantage that that it provides and it's the requirement of a proof of work chain for for checkpointing. It's true that you know that checkpointing into Bitcoin also like there could be the argument of all word, but then it's not really like proof of stake you know we are not really like improving the security, but, and that's that's like a valid argument that indeed it is like relying on on proof of work but also like this is like kind of like the cost of security, and, and if we have you know one big secure proof of work chain, and then all the other project that are less like more efficient that's also like a good, maybe a good thing of less less proof of work but at least some proof of work for for the security warranties. I have a question here so so if Bitcoin is to become like the root of trust for everything. And everything depends on it, and we might have a problem because it could be argued that, you know, the energy burned to maintain the proof of work system should be proportional to the value that is secured. So if it secures everything then it means that the energy burned because of what a craze, right, because otherwise it will be too easy to attack it so does this argument hold or is there flowing this arguments. That's an excellent question if I may answer it. It enforces the consensus on the root of trust. I believe it enforces the social consensus it goes that way it enforces the social consensus on what is the root of trust. And then yes you are expanding energy to secure whatever needs to be secure but this energy is not wasted because it secures what needs to be secure. So the argument that the energy consumption is proportional to to what's at stake basically correct, meaning that the more things around Bitcoin than the more energy will consume. So I think the more definitely consume more energy. If you want to attack the system you always have the dilemma that Satoshi mentioned in the white paper. So if you can attack the system. Do you want to bring it down or do you want to join to actually participate with it. That's always the dilemma for the attacker imagine a really powerful nation like there are very few nations that get attacked at this moment, but they would be facing this dilemma. So they need to engage this power to attack Bitcoin, and that's only basically to double spend and certain things like they're basically this case. Subvert our solution to check pointing are you only because you go and double spend and things, but there is only a certain number of attacks for example you cannot attack monetary policy right and there's certain that is that you're not able to pull up. But at that moment you're deciding okay am I going to engage all this power available to me to actually play the game, or to attack the game, and as the as the power physically of the Bitcoin grows on that comparison to, you know, as much energy as Poland or something like this grows on that list, the danger of the attack reduces from nation states, because you cannot mount the attack. Unless you have a breakthrough unless you have nuclear plants and unless you have fusion reactors in future. So we are playing here as a, as a planet as a species we are playing a very interesting game. So from game theory perspective this is incredible. But and just to finish on this I think indeed it's it's a very good point and that indeed if we do this like there is going to be more at stake on the Bitcoin like blockchain and it's true that maybe then you will need like more power to be secure but also there is the proof of state that is not going to do like to going to have other assumption about the security right so there is this kind of like two level of security there is like the power that you need to get in the to attack the Bitcoin blockchain but also, you know if you really want to mount like this attack, you also need to have the to mount the attack on the second layer which is the proof of state so there is this kind of like to level to level of security basically, and it's a good question on like how should, like, how should the security be spread between the two like can they be combined can that's that's an open question. So my question is kind of similar to the previous one but on a more moral and abstract level. So, for me, one of the big selling points of trying to move towards proof of stake or different kinds of consensus is that a lot of people argue that the big power drill from Bitcoin is actually a bad thing. My question was specifically for Sarah, aren't you, aren't you not quite moving in the right direction by trying to tie back security properties to Bitcoin, whereas we should be trying to escape from using Bitcoin or proof of Yeah, I mean I think the argument here is like even though well so first you know not everyone agrees whether it's wasteful or no Bitcoin as Marco already talked about but like the point is like even if it's wasteful like I mean our observation is like today we just don't have the same security warranties right so that's why we are we are doing this so yeah sure like there is some again like it's kind of so it's kind of like not the pure proof of stake energy efficient system that we can have but then if we want to have like the security and if you think that anyway, if you're going to have like proof of stake system you're going to have like Bitcoin is not going to disappear right so so at least in the meantime, I think it's a good way to secure secure proof of stake system, maybe one day I don't know like I don't know what the future is going to be, but at the moment it's like a choice of like security. Thanks everyone for jumping in and initiating some conversation.