Stabilizing the Staking Rate, Dynamically Distributed Inflation and Delay Induced Oscillations

Transcript

to an optimal level because that's was how the cryptoeconomics work. Everybody wants uh uh the the staking rate to be at an optimal level. But how do the how do we design it? The design is typically follow the standard process in which there is some curve around inflationary regime and it increases uh the yield kind of increases when the staking rate is below target and it decreasing the yield when the staking rate is above the target. That's a standard design for most of the proof ofstake chains. Uh the problem with here is this one of the bigger problem is that that it's volatile. Why it is volatile? Because economic literature has identified that

all of this is financial dynamics related to some reactivity. There are like stakers who maintain the staking rate according to some external yield properties and also there is decisional lags like one of the biggest decisional lags in crypto currency staking is that validators needs to stake unstake due to some external factors and uh by default if you look at the um the the chain design or the economics design of it you'll see that uh uh it does have uh some kind of a delayed withdrawal period. Most of them has like you and that if you add this up, this increases the volatility. And the key finding to our uh research uh is that like there is

if there is an high sensitivity to the yield and if there is inherent delay in the staking rate uh delay in the staking rate or the decision making that can generate uh um inherent oxillation. So what we propose here is a uh a mechanism uh which we call stability corridor and try to prove using simulations and some um uh mathematical uh linearity nonlinearity around the system is that uh it's it's better than the current design. So that's where um you know the motivations or the problem statement call. I I would like this is like external looking but the most uh you know why we started this project because when um I started uh my own project

Palora which is actually uh multi-party uh uh compute nodes are there where you can monetize the data confidentially and securely that's a different kind of a system think of it like it's something uh different than Ethereum which has this definitive validator framework which has consensus it has this arbitrary node so when we We're doing this we uh when we ran the simulations on our own design the oxillations were like around 10 to 20 times. So that's why where you know where the number of parties increases exponentially and their uh interactions with the economic system uh system increases exponentially. This makes the system more volatile. So I'll start with uh uh

some of the kn cases or some of the uh examples uh where u you know uh we'll see what the curve characteristics are then uh we'll talk about like what are the changes around that like uh one of the example is polar like reward many people are familiar with that it's um it's a it's a it's an example of dynamic reward mechanism um and where there is a peace-wise ut peacewise inflationary function And uh one of the one of the key one of the key characteristics of this is like people want to stabilize a staking rate at some target level. In this case, one of the example like that's an uh white paper example. Uh generally governance

move it here and there it's around 50%. And there is some annual inflation rate uh which in our simulations and our design we set up to uh 03. Um there is something of a curve where it reaches some inflation and it goes dynamically down. There is a decay parameter. Uh the the equation looks like uh uh this. But the most important part here if you will see uh is that uh uh it increases up to certain point and uh that's what the maximum inflation and then it decreases exponentially. uh it follows the same design right uh that where we uh say that uh uh if the inflation rate is below some target we need to incentivize

people and it depends upon us how uh vastly the economic system incentivizes maybe linearly nonlinearly but there is a progressively stronger uh incentive to stake and on the other side if we fall onto the other side there is a disincentivization created I'm Now um polka dot u created the disincentivization in a more exponential decay format. Uh we'll see you know the next curve ethereum we'll see it it follows a different methodology. Um but the idea remains same. Uh I I'll just go through the chart. The first chart actually if you see in here uh the polar dot like inflation this is what I was

talking about like it's it goes uh it increases linear uh linearly the inflation and then this is an exponential decay and this follows the staking rate uh some staking rate equation where there's a kink around the system. uh the another interesting um the constant inflation. This is exactly what how Ethereum has modeled the proof ofstake dynamics. You'll see it's a nearly constant inflation with uh uh inflation yield u follows some kind of a follow some kind of a curve. I'm I'm I'm sure you would have followed the big discussions around moving this curve here and there uh because the yields of in are u pretty low sometimes but that's that's actually a different discussion

uh but the first one is uh the polar dot and second one is like generic um rather than closing into Ethereum it's like a very generic curve um [clears throat] so uh we talk now we try to uh this is just an example which uh I wanted to show in the simulation. We can run uh many um you know uh variations of this the stability corridor. It's just a way to mathematically and simulation wise uh show that uh this has better fundamentals. So the idea behind this is um to create uh instead of that sharp kink around uh the stab uh around the

inflation curve the idea is to have a stable in uh corridor that means the stability corridor. Um so if you see the curve is designed in such a way I'll go through you know how like the sample design and then we can uh you know talk about the variations and various executions which we can do but the target staking rate is defined if you see on that around kink a bit of a 40 to 60% uh a regime is created in the staking rate and the inverse uh inflationary uh curve is calculated so that it follows this uh stability ility regime and uh the characteristics are made in such a way that it somehow

resembles the curve the polar dot like curve which we have shown we can as I can say we can have uh uh multiple variations but the idea is to create this inverse mapping where the staking rate uh uh remains uh flat and the inflation is matched according to that maybe it's algorithmically maybe it's through the governance but we'll see like you know our objective is to show that you know how does the oxillations behave around this point. So yeah, so this is one of the schematic as I said changing it uh the stability corridor around 40 to 60 trying to keep the inflationary regime as 3% and 10%. Um and then making the curve like uh this

uh [clears throat] now uh I'll just show you the schematic of uh what the model inherent model is. Uh uh the paper is online. Uh we uh I presented it uh recently at financial cryptography uh conference. So uh you know the manuscript is online. It would be uh there on the Springer series as well. But uh uh the intuition of the model is very important like you know how we do it some of the artifacts right now if you see there are uh changeable for example one thing which staker can decide to increase or decrease the staking according to target yield parameter I kept it very high 16.6 six uh uh it's an arbitrary number right now

with our match matches the our curve we can do anything uh there is also a representation of an sensitivity like uh how the means taker uh uh uh means taker deviates if the yield deviates u this the fundamental b term can also be related to this financial like how much of your sensitivity towards any beta of the market you are multi- uh multi threedimensional portfolio. You don't only invest in cryptocurrencies. You have multiple other things going around.

So this is the sensitivity around that. It's taken from the system uh as a parameter because we are not designing the whole portfolio management side of it. Uh though that would be very interesting uh as a marketwide uh phenomena. So and the other thing in the model which is taken which is very important is that uh kind of a 7-day delay and this is what when I started as a motivation um that uh uh that in most of the proof ofstake chains there is uh you cannot withdraw your uh you know stake amount immediately. there is something uh inherent uh uh decision lag which is enforced in the system. We took a 7 days

delay to model the parameters uh in the equation. It's an empirical observation of nearly all the proof ofstake system. um we can change it. The more severe it becomes like you know the 10day 30-day withdrawal time the more severe sometimes the oxillations are uh but it does have a great sensitivity around that. The idea is that the critical idea is that uh uh if uh uh if you want to have change your staking rate, you need to follow some of the sensitivities that's a parameter beta B which we are saying and also you have to follow the change taking rate according to your t minus one time period right and then adjust is according to the mean

taking rate of uh your withdrawal uh time which is like 7 days average which we have taken Um and this this is what will be able to change your target staking rate. U then um um it's it's again that this is a time series equation which is being modeled. The important part is like you know the reduced form third equation which I was just telling you the staking um you know is clammed around the valid range n minus one n minus 7 is what just explained it's an uh 7-day withdrawal kind of a decision parameters and then there is a sensitivity around that the the important uh again one of the

critical part here is that uh this equation is endogenous. If you look at uh yield at day n minus 7 which is my uh decision factor it itself is dependent on uh inflation distribution curve because that is fixed uh by the protocol right. So this is very endogenous equation and these and this equation is what uh gives you that uh fundamental volatility and uh this is what we wanted to show under uh simulation and uh these are like one snap of the result which I can go uh one by one uh the the the first uh I I'll just go through how to

read the charts. uh the blue line and the red line represents uh the staking rate and APY. Um and uh the way to read this charts are uh the traffic light kind of a signal. The red in this chart means like people are moving towards reducing the staking rate. The uh the yellow is maintain and the uh green is increase. Uh these three charts represent uh one is the polar dot like inflation we chatted. The last one is constant inflation. We chatted about ethereum like and the stability corridor design is what uh we are you know uh saying that it's a little bit better.

The first chart as you can clearly see it's really bad. It's really bad in the terms of the inherent oxillations the inherent volatility is induced around the intuition is very same. there is a arbitrary kink around some stability rate and it makes uh the system unstable for a longer longer point of time. U anyone who follows that kind of inflationary regime is bound to have oxillations that goes days and days out like it doesn't stop like it's very unstable system. Uh if you see the uh staking rate it just oxillates and also uh in the background there is this uh you know the corridors which we are talking about the green and the red

there's a lot of fluctuation you can't see but as you can see right you know there is some uh red and the yellow so which is like a constant flip-flop happening because at one point of time um you like you really the ar your margin of errors are really very bad because you're operating around the kink sometime sometimes and uh uh on the last uh yeah we think the constant inflation curve is um you know would be way way way better but it's not the case uh it's not the case because if you look at uh uh the stability around first 45 days of simulation it's not as it's not it's not absolutely what do you

saw perfect it does is it is better than the first benchmark our case uh in the constant inflationary part but it's not it's not so good and this is like a clear artifact also inherent uh uh volatility which we see in uh uh this proof of stake chains uh where uh there is a constant inflation and the decay uh staking rate is found under that. Um so you can see the red uh reds of uh it's it does stabilizes after 90 days but uh it's not uh perfect. Um the one uh the benchmark the our proposed idea of being an stability corridor is is better is

better in the sense it does stabilizes and is has very less oxillations. Um one thing which I wanted to uh tell you about uh this chart is that uh this is a single short uh uh uh uh uh simulation done in a real economy. We will have these multiple uh snapshots coming at a play. The reason is that the reason is that uh because uh imagine you are having a fluctuation right now but also the future fluctuation also impacts the uh you know the fluctuations of the back end. Remember the B parameter and those sensitivity parameter those are time independent but in an real uh sense

they are also time dependent. So the more uh um you know the to give an example the first chart the more oxillations you have the worst sensitivity it belongs to the last chart. So it's it's it's also uh I was trying just I was trying to say that uh this is like you know the base good case the worst case can be you know uh way way way better than this because of this uh uh sensitivity around the time dependent sensitivity can increase. Um [clears throat] so uh one of the empirical uh exercise which is very standard in the literature around these things are out trying to find the stability near the equilibrium.

Uh when we say the equilibrium like that's a target yield right now um and how does those uh oxilation emerge around the local area. So trying to find the local stability around that and what does this uh uh directly correlates with the parameters. Um so it's it's a standard procedure in the literature where you linearize and uh where you have uh some equilibrium conditions. We do have like you know the the arbitrary target yield 16.6. We can linearize it around that point and then uh you know we can have uh an expansion first order degree and then we bunch of

uh uh you know uh the the cosiness and other functions you create the you try to back trace the stability regime around that local area using what parameters are u you know what are the ranges of that parameter which enforces that stability. Um so one of the parameter which we were interested which was the time invariant that is the B remember the sensitivity parameter we wanted to see that how broader the range of those parameters can be. So to put it into the more uh you know stable equilibria um so for the constant inflation model and uh the parameter range is around 0 to 1.4 4 which is

quite good but if you see uh the other benchmark it's like literally 0 to. 2 uh it's it's the so what does it show that uh even the stability corridor which we are proposing the range of stabil the range uh of B parameter increases so you have larger degrees of freedom to play around that it's it's it's the biggest what we find according to you know some of the average simulations which we did uh but it's way way way better than one of the uh polarit style benchmark but it is even better than the constant inflationary regime times.

Yeah. Uh the linearization I think uh uh these are the uh methodology which we adopted which is uh uh how to how to show you this uh B ranges. Um it's it's as I as I told you earlier it walks around the tailor expansion and the linear difference equation. Um the methodology works like the polomial exponential uh and again uh it does have uh uh the characteristics which you can solve around uh local stability module the it's a unit circle approach where you can have uh some kind of a uh stability around the net parameters and then the you need to back trace the

equilibri equilibrium point in our previous equation that is equation number two I think which you saw which talks about the time series around that. So you get that uh um the parameter dependence on the inflationary curve. So it's a broader methodology which I wanted to show that so that where the numbers these numbers are coming to um uh I I'll just try to uh conclude uh so the conclusion here is uh uh that uh sensitivity uh of the of the yield together with this delayed uh reactions which we you can model it as validator reaction or any other arbitrary reaction they are enough to create the oxillations in the cryp uh in our system

this proof ofstake kind of inflationary regime system. Um this we have done in this paper some qualitative analysis which does show that it they are uh you know the source is this and we can do little bit better in terms of u not little bit actually way better in creating the stability corridor. It all depends on us like you know how dynamically we want to enforce stability corridors in the system. Um but uh uh it's there like you know something needs to be done to uh maintain the staking rate as well as maintain the induced oxilation. That's what you know the study talks about. There are certain

future work which uh uh we plan to do and if happy to you know take more uh suggestions and contributions if people are interested. uh it's a single agent model by single agent I mean uh on the staking the behavior of a stakers they are one behavior only they do according to the equation but we know in the real world there are multiple types of stakers like home stakers what we call it institutional stakers they all take care into different regimes of their sensitivity so the multi- aent model can u make uh uh uh this uh uh our research more stronger in the sense and more validated across multiple behavior. So

that's what we are planning to do and also there is one synchronization uh phenomena which can play an important role. Um we we deliberately excluded that uh because uh then um it just expands it to the different uh uh line of research but that's also very important uh which uh we want to uh propose. And the next thing um you know uh which uh which we have not written but it's there in the paper. We are implementing this in the palora system uh which uh we are doing and uh so we we are running a a test net in which we are seeing better results and we are hoping that uh in the mainet when more nodes join as a compute uh artifact uh doing

confidential computation it would be the our system would be much more stable. So we will have like a real results as well in few months of time. Uh thank you so much. Um Alejandra if you're here you're welcome to come and set up your computer. Um Stefan. >> Yeah. So I have a question. Um is this like the beer game or is this a different thing? Have you heard of the beer game? Uh >> it's like the beer like beer as in drink beer. It's a very famous experiment where you every MBA class does it. So you have like a chain of people who so

you have like the orders coming in through at the beginning and then every chain needs to every every block in the chain needs to order for the for like one day ahead or whatever. >> Mhm. >> And this always blows up as well. It's kind of that that gets like infinite oscillations. If you play this, it's like, oh, they always plays an NBA class and there's infinite oscillations. And I don't quite remember what it is, but the solution mathematically is that effectively you look at the matrix and the matrix has an value bigger than one. And so then exponentially uh disappears.

And it looks like this delay plus delay plus correction is essentially exactly what makes a beer game explode. And I wonder whether this is something uh that you looked at and whether it's the same mechanism or it's a similar similar >> uh thank you for explaining the beer game. I didn't know about that but uh I I have uh you know some of the feedbacks from the market micro structure side in the order book uh phenomena we know that uh you know in the fast order book uh the market participants especially the makers actually adjust towards the prices and uh they adjust the volumes as well. So there are certain exchanges

which uh allow you uh very big block of volumes in intermittent right and when there is a little bit of a shock in the market little bit panic in the market the research shows that these kind of exchanges blow up uh uh very early on then the clob you know the slicing dicing people. So yes it do correlates with that kind of a that kind of an oxilation behavior which is unstable and it which is in finite regime. So the solution of that problem which they found in the traditional finance is that have a circuit breaker.

I just stop it right there. Right? Let everyone start from day zero. Um the solution that solution is not applicable uh not at all applicable in block proof ofstake blockchain. you can't say like you know pause the chain let's start from day zero but yeah thanks thanks for I think that >> I uh one question the for the polka dot for the polka dot staking regime um there was a clear sort of peacewise definition right for how that staking curve looked like um for your stable corridor one as well I think right was this also peacewise but then sort of linear at the end or is that a continuous curve >> um [clears throat] Yeah. Yeah. Um so uh

so to answer uh it's a two-part answer actually. Let me so uh we chose that a sample uh showing of that you know trying to maintain as much closer to the polar dot but trying to enforce the stability corridor around some means taking rate so that uh you know our solution does not look uh drastically different right. Uh the other part is that uh uh you can enforce microstability corridor in any peace-wise uh linear or nonlinear inflationary regimes right and like for example in the constant inflation uh rate of uh Ethereum like uh properties uh you can have uh some kind of a

stability corridor around your uh uh targeted means taking rate and I think at one point of time the community was also discussing something around on that uh like I think 6 to 8 months before that and uh they never discussed it about this having the less uh volatility over the ecosystem but that would have been the first order effect apart from having the higher yield forced higher yield better answers. Thanks. >> Please thank me in thanking AIT. Okay, next up to the stage um is Alejandro Rashel Padrosa who works at the SE lab. say is a Andra, please introduce yourself and and begin your talk whenever you like.

>> All right. Hello. Um let me test out a little bit of the audience. Who's familiar here with uh so who thinks here that transactions in Ethereum are private? Raise your hand. Okay. Who thinks that transactions are not private? Okay, good. Who's familiar with inclusion list or like fossil Ethereum? Okay. Braates multi-proposer designs. Yeah, more or less. Okay. Okay. Well, I'll I'll take it slowly. Okay. So, um first let me explain what multiconurren proposes are. Um and let me explain it with two different u consensus protocols. Who's not familiar with consensus protocols or what is consensus? Okay. So, yeah, for those of you who are not familiar, consensus

protocols are at the core of uh blockchain designs. They're what decide the ordering of transactions. And um I'm going to argue that single leader which are the typical traditional consensus protocols uh for BFT chains give too much power of ordering to the leader. So we have here at the bottom an example of a leader design leader based design. So we have the leader in this case process zero proposer zero proposing a value and then there's two rounds of voting and the value is decided right. Um at the top we have an example of a multi- concongurrent proposal design uh where we have four different proposers each proposing a different value and then there's some consensus protocol that decides some of them to be included in some particular order and some of them not to be included. So there's no single

leader that controls ordering of the transactions and this is a very popular design at the moment NCP chains there's sui there's atos there's aera now sana's latest consensus proposal from last week so the upgrade to alenlow is also based on mcp with ethereum as I said we have fossil which is kind of a step in that direction we have brakes which is explicit multic concongurren proposer uh design for ethereum and the reason is because it provides uh censorship resistance and for some definition of privacy it could provide Well, not privacy but it can provide MVB protection. I'm going to argue however okay who thinks that multiurren proposers like is said typically by the Solana guys by the guys etc is a

solution for me protection or for censorship again like to provide censorship resistance who thinks that is enough okay good um so yeah I agree with you guys I don't think it's enough um and the reason is uh because of this three-way trade-off so if I'm a user and I want my transaction to get included and not get censored um um what I can do is if I have a multi-current proposal design, I send the transaction to one proposer at a time, right? Um and that gives me the guarantee that I'm not going to pay for the transaction more than once. And if the proposer doesn't include it in this lot, then in the next lot, I try a different proposer, right?

This is something that you can already do in Ethereum because we you have rotating leaders. If um I want to exploit some low latency opportunity, I don't know, I see some arbitrage opportunity and it's either now or never, I can send a transaction. And if it doesn't get included then you know I don't try anymore because that opportunity is gone but then I don't get sensor resistance right I get low latency but I don't get sensor pistance and if I want both then because it's a multicurren proposer design then I send a transaction to all the proposers and then I'm guaranteed that I unless all of them are trying to censor me as long as one is not trying to censor me I can include the transaction but somebody has to pay for that because that transaction is going to if I want censorship resistance against F proposers then I

need to send the transaction to F plus one proposers. which means that somebody has to pay F plus one times the price of including the transaction and there's two different designs on one side we have um the SUI guys for like in production we have the SUI guys the ATOS guys or Falcoin which Falcoin is also an MCP chain where the cost of including the transaction is absorbed by the system is subsidized by the system. So effectively what means is that the user is only charged once but he can include the transaction a 100 times for example which means that the goodput you know if the throughput of the system is a thousand transactions per second then it reduces to a good a useful throughput of 10 transactions per second and then on the other side in production we have

hideera that says hey you know we provide this multicurren proposal design you can use it to pro to you know uh leverage sensor resistance but you're going to pay for it and so if I user wants to get censorship resistance against 99 proposers, he's going to have to pay for the transaction 100 times. So yeah, it's censorship resistance, but it's not really affordable, is it? Um, also I note that the way the reason why this is well to answer the original question that I did is Ethereum or this chain censorship resistance. It actually depends, right? It depends on your assumptions on the adversary and whatnot. We are seeing in Ethereum big me being extracted, you know, from users. So it's an obvious answer that is not really essentially resistant or me protected

um in this chain. The way this is actually alleviated is with a trusted RPC, right? So is the RPC the one that selects which proposer to send the transaction to and for how many duplicates and that's why you know we're not seeing an attack vector in which the good is reduced by 100x in these chains but that is trusted and so in a way I see the evolution of providing sensory resistance in blockchains um in these steps. So first we have the traditional step of leaderbased consensus. From there we uh some people in the space argued we can do better with MCP providing sensory resistance and we could say the the suitors and falcon guys are there.

Then the hideera guys realize oh this is an attack vector. If we really do want if we really want to do this in a trustless way we need to charge users for this. And then finally um realizing that this is too high a cost for users to pay and try to alleviate this cost and this is the work that I'm going to be presenting that uh I'm do I'm doing at say um although actually it was uh say with some collaborators researchers from so and so here's the solution it's very simple um the traditional way as I said of of getting sensory resistant benefits from a user would be to just replicate the transaction and send it to different proposers and then as long as one of them proposes it to be included in the blockchain and we're good. Um, which that means is to get a to get a

censorship resistance uh that is uh that protects you against a linear number of proposers you need to pay a linear number of fees. Um, and the good part of the system is reduced linearly as well. What we propose is sharding. So the transaction is sharded into smaller chunks, smaller pieces sent to different proposers such that as long as enough of these proposers include their chunks, you can reconstruct the transaction. And so as a result you get the same or like um uh you get the same tolerance in the linear number of proposers uh for sensory resistance but you pay a constant cost and you also get a constant fraction of the throughput in goodut so it's a street improvement in these terms so um I have a presentation on Thursday about how this protocol

works in particular and the bison default tolerance on the protocol etc. Um I'm going to just kind of like skip through that now to get into the economics. So how what is the me cost the pro the me protection cost using SENA using the solution that of sharding. So for that let's first define the problem and apply the protocol in a naive way. So we have here a number of proposers a user that is sharding his transactions sending it to different proposers such that if enough of them include their chunks we reconstruct the transaction. Um now what the user what the attacker can do is you know we have a coalition a cartel of uh a number of proposers that is going to try to

reconstruct the transaction with the chunks privately before it's onchain in order to exploit me because they if they just get some chunks they cannot really know the content of the transaction. Um so instead of sharing the and then they can decide also to censor or not to not share the chunks. So for example here one of the members of the cartel of the coalition decides not to include their chunk but because uh there were more chunks than needed the transaction is still reconstructed. This is what we call as slack of one. So one chunk can be not included and still the transaction can be reconstructed.

What about two? So now with two the number of chunks that have been included on chain is not enough to reconstruct the transaction. So at that point censorship has occurred and also the cartel can privately share the chunk as I said and reconstruct the transaction on their end and they get one extra slot where they can uh you know basically uh extract me from this transaction. And here we analyze also two different uh risk that can occur with SNAP or like that not that are not fully uh solved by setup by this charging solution. One is the multi-lot one which is the one I've shown the transaction gets censored and so you need one more slot of consensus one more round of consensus in order to include the transaction. The other one is the within slot delay. So even if the

transaction is going to make it on chain in that same slot, if the cartel, if the coalition is very well connected, they might still manage to get the chunks first, reconstruct it on time and uh wait for that and then once they have reconstructed the transaction, make their own proposal knowing the content of the transaction to try and still frontr run that transaction. So we analyze the two of them. The first thing that we notice is this very interesting kind of like inverse sawtooth where um so the user has a lot of parameters that he can uh tweak to its benefit. You know it's a userfacing protocol. The user can decide how many chunks to split the transaction into to how many lanes to share to how many proposers to send

chunks uh how many chunks per proposer etc. What we see is uh the important parameter is what I was calling the slack, right? The slack is how many extra chunks the user can tolerate to uh not to to not be included and still reconstruct the transaction. So um the interesting bit is that as the lack so in this case we have 100 proposers the user is going to choose 20 of them at random per round of consensus and we assume the cartel the coalition is also controlling 20 lanes. some of the 100 20 of the 100 and uh the here at the bottom the x- axis is the decode threshold. So how many uh chunks are needed to reconstruct the transaction.

So one thing that is interesting is here before I was explaining in the case of one round but you can actually the user could actually and it's actually beneficial for the user to split the transaction across rounds. So basically to require more chunks that are that that he sends in one round. Um but what we see here is like kind of like a frequent pattern that repeats over the over the slack. So um over basically the number of chunks needed for the construction modulus the uh the number of lanes that are conducted.

And what is interesting is here Q micro is the um probability of the attackers managing to get enough chunks to reconstruct the transaction within one slot before it's included even if censorship doesn't happen. And for this one, as the decode threshold gets closer um so this decode threshold gets closer to a slack of zero actually the probability decreases. Whereas for the multi-lot delay happens the opposite. The higher the slack the harder it is for the attackers to um to delay uh the transaction by one slot. Because for example, if the slack is 19 and I send uh that means that I send a transaction

to 19 extra proposers in this slot. So I can afford 19 of them to sensor if one includes it. So it's really hard to delay one multiple slot. But that also means that uh that I only need one extra chunk to reconstruct the transaction. So it's a lot easier if that extra chunk one of the those 20 belongs to the coalition. It's very easy for them to reconstruct the transaction quickly. So it's kind of like an inverse sawtooth. But this is the strongman approach.