larry_vw_1955
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November 15, 2021, 07:11:58 AM |
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The electricity will be reduced by the fact that Round 1 is not computing-intensive
Regardless of the complexity, if I use more power to increase my hash rate, then I will have a better chance of getting to the second round. Right? So, why wouldn't I use as much power as I can to get into the second round? You could but if I'm understanding the OP proposal correctly is that he will only allow a certain # of miners into round 2, such as 100. How those would get chosen he said it is based on the first 100 that solve the puzzle. So in that sense, if you increased your hash rate then it would increase your chances of getting into round 2. So your question is valid. The answer is you would use as much power as is necessary to be in the top 100 but no more. ![Grin](https://bitcointalk.org/Smileys/default/grin.gif) I think a solution would be to eliminate the PoW in the second round and simply make it a random selection (somehow). That would cut the expected block reward by a factor of N2, which would cut the power usage in the first round by that same factor.
Not sure on that. But why not just have a single round 1 and just select the winner at random without eliminating anyone? Why wouldn't that work?
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Epictetus (OP)
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November 15, 2021, 07:29:41 AM |
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tl;dr - total electric consumption will not be reduced by implementing the OP's proposal.
I'm sure the miners wouldn't be supporting such a thing because it just makes it even harder for them to get a reward. Also, if there are millions of miners and you randomly select 100 of them, you encourage the rest of the miners to form mining pools. Then, you will end up in a situation where 100 miners are selected as before, but there are only 100 huge mining pools, they always get everything and distribute that to smaller miners. Almost no solo miner will follow your system if that miner will be rewarded once per month, because the risk of price drop after entering exchange is higher than the potential reward from solo mining.
I wonder if the people that wrote that paper realized that. that's thinking ahead! ![Grin](https://bitcointalk.org/Smileys/default/grin.gif) the bitcoin mining system is really hard to make changes to without causing things to get "out of whack" ![Grin](https://bitcointalk.org/Smileys/default/grin.gif) This is similar to say that miners will organize themselves in big pools to organize a 51% attack on Bitcoin network. It did not happen so far.
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PrimeNumber7
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November 15, 2021, 07:41:20 AM |
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tl;dr - total electric consumption will not be reduced by implementing the OP's proposal.
I'm sure the miners wouldn't be supporting such a thing because it just makes it even harder for them to get a reward. Also, if there are millions of miners and you randomly select 100 of them, you encourage the rest of the miners to form mining pools. Then, you will end up in a situation where 100 miners are selected as before, but there are only 100 huge mining pools, they always get everything and distribute that to smaller miners. Almost no solo miner will follow your system if that miner will be rewarded once per month, because the risk of price drop after entering exchange is higher than the potential reward from solo mining.
I wonder if the people that wrote that paper realized that. that's thinking ahead! ![Grin](https://bitcointalk.org/Smileys/default/grin.gif) the bitcoin mining system is really hard to make changes to without causing things to get "out of whack" ![Grin](https://bitcointalk.org/Smileys/default/grin.gif) This is similar to say that miners will organize themselves in big pools to organize a 51% attack on Bitcoin network. It did not happen so far. No. The miners have incentives to not 51% attack the network. If they try this, the value of their equipment to drop >99% overnight. Miners engaging in activity similar to what I described is similar to miners attempting to keeping their equipment that has a limited shelf life working as much as possible.
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vjudeu
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November 15, 2021, 07:50:21 AM |
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In an ideal world with TRPoW, most miners will spend their time moving from one Block Round 1 to another Block Round 1 because the round 2 is limited only to the fastest few N2 miners. In a real world with TRPoW, most miners will spend their time working on Block Round 1, because the round 2 is limited only to the fastest few N2 miners, so attacking by kicking someone from that top100 and taking its place is more profitable than honestly waiting for the next block. Because kicking other miners from top100 is more profitable than doing nothing, everything can be reduced just to phase one, then phase two is the easiest part, needed only because consensus rules says so. Also read this: https://www.truthcoin.info/blog/pow-cheapest/#nonproductive-investments-are-wasteful. Not only it explains why other solutions like Proof of Stake or Proof of Capacity are worse, but it also explains why any two-phases or N-phases solutions are pointless (and can be reduced to the old, plain, unobscured version of single-phase Proof of Work). The reason is the same: you have some simple economic rules, miners are trying to maximize their income, and making some official version that is "honest" is not enough to stop the coin from attacks. Even if your version is eco-friendly and stops mining when you didn't get into the second phase, other nodes may still keep mining, then an alternative version can be more popular, as it happened in many successful coins (including Bitcoin, because mining pools have their own optimized versions, they are not mining with their CPU's by using Bitcoin Core's default mining implementation). Luck is using two phases of PoW to reduce the domination of large mining pools. While TRPoW is using two phases PoW but to reduce the network electricity consumption. It does not matter what is your goal. If you use the same tools to reach it, you will encounter the same problems. Even source code for Luck is still on GitHub, so you can still download it, see how they splitted the whole process into two phases and why it does not work as expected. Also you can see their Discord channel and watch some charts showing how some parameters of each phase changed in time, and how one huge mining pool reached 51% by gaming the first phase with his own software. Also I described it here, how they calculate their parameters: https://www.publish0x.com/vjudeu/two-phase-proof-of-work-as-a-solution-to-mining-pools-xrommelI'm sure the miners wouldn't be supporting such a thing because it just makes it even harder for them to get a reward. I think there will be only a few miners in the testnet (assuming testnet coins will be worthless or destroyed after testing), a lot of miners in the first seconds after releasing the software (so that if it will be published on centralized servers, they could reach Error 500 because of too much traffic), then the difficulty will skyrocket and the coin will be worth a lot in some Discord-based P2P trades. And then it will enter some exchange, everyone will cash out and the price will go from All Time High to All Time Low. This is similar to say that miners will organize themselves in big pools to organize a 51% attack on Bitcoin network. It did not happen so far. But it happened in many altcoins, including Luck, when they splitted mining into two phases, many people were mining with the original software, and one mining pool gamed the whole system and reached 51% quite quickly. Also some FPGA miners gamed the system, they competed with CPU's, so they win, because mining algorithm was not resistant to that. Also, the question is: which hash function you are going to use? If you use just sha256d as Bitcoin, the competition will eat you one minute after release.
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Epictetus (OP)
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November 15, 2021, 08:31:39 AM |
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In an ideal world with TRPoW, most miners will spend their time moving from one Block Round 1 to another Block Round 1 because the round 2 is limited only to the fastest few N2 miners. In a real world with TRPoW, most miners will spend their time working on Block Round 1, because the round 2 is limited only to the fastest few N2 miners, so attacking by kicking someone from that top100 and taking its place is more profitable than honestly waiting for the next block. Because kicking other miners from top100 is more profitable than doing nothing, everything can be reduced just to phase one, then phase two is the easiest part, needed only because consensus rules says so. Could you please explain to me how you are going to attack by kicking someone from Top100 ? Keep in mind that in order to move to Round 2 you need to Announce it to the network by Broadcasting your solution of Nonce1 and your list of N2** miners up to the moment you found your nonce1. For the round 2 you hash the following: Hash(BlockHead + PublicKey + Nonce1 + RandomNonce) So you will always need to show that you were in Round 1 at some points. And if you are late, the network will have already formed its lists of N2 and you will be outside of it. And your block will be accepted ONLY if your name was in the List of N2 of other miners. Thank you
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Epictetus (OP)
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November 15, 2021, 08:42:40 AM |
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I think a solution would be to eliminate the PoW in the second round and simply make it a random selection (somehow). That would cut the expected block reward by a factor of N2, which would cut the power usage in the first round by that same factor.
Not sure on that. But why not just have a single round 1 and just select the winner at random without eliminating anyone? Why wouldn't that work? The PoW job is also to maintain the Block Time at 10min. We can achieve that by just making everyone wait for that 10min minus delay/network broadcasting time etc. I think you need to have some skin in the game if you want to have long term serious players in the network. PoW is achieving this skin in the game by asking for CPU power and PoS is achieving the same by asking for stakes.
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Epictetus (OP)
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November 15, 2021, 08:49:23 AM |
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tl;dr - total electric consumption will not be reduced by implementing the OP's proposal.
I'm sure the miners wouldn't be supporting such a thing because it just makes it even harder for them to get a reward. Also, if there are millions of miners and you randomly select 100 of them, you encourage the rest of the miners to form mining pools. Then, you will end up in a situation where 100 miners are selected as before, but there are only 100 huge mining pools, they always get everything and distribute that to smaller miners. Almost no solo miner will follow your system if that miner will be rewarded once per month, because the risk of price drop after entering exchange is higher than the potential reward from solo mining.
I wonder if the people that wrote that paper realized that. that's thinking ahead! ![Grin](https://bitcointalk.org/Smileys/default/grin.gif) the bitcoin mining system is really hard to make changes to without causing things to get "out of whack" ![Grin](https://bitcointalk.org/Smileys/default/grin.gif) This is similar to say that miners will organize themselves in big pools to organize a 51% attack on Bitcoin network. It did not happen so far. No. The miners have incentives to not 51% attack the network. If they try this, the value of their equipment to drop >99% overnight. Miners engaging in activity similar to what I described is similar to miners attempting to keeping their equipment that has a limited shelf life working as much as possible. The N2 number of miners of the second Round is also adjustable like the complexity algorithm in PoW that is adjusted every 2016 Block. Plus In Round 1 we are hashing Hash(Block Head + PublicKey + Nonce). So I don't know how this is going to force miners to organize in big pools. The Public Key of a miner has the benefit of limiting the formation of pools. In BTC PoW there is no public key in the hash. In TRPoW, the hash result is public key dependent.
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vjudeu
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November 15, 2021, 08:52:54 AM |
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So you will always need to show that you were in Round 1 at some points. And if you are late, the network will have already formed its lists of N2 and you will be outside of it. But you can pretend that you were. How it is decided who were in the first round? By Proof of Work, right? So if you have some higher Proof of Work, you can pretend that the miner with the lower work came later. And if the total Proof of Work is used to decide who tells the truth, then miners with more power always win. And your block will be accepted ONLY if your name was in the List of N2 of other miners. So each group of 100 miners can pretend that they were first. When you join the network after they are formed in some groups, how are you going to choose the right chain? You can see 100 honest miners with some Proof of Work and 100 dishonest miners with another Proof of Work. If the most Proof of Work after two phases dictates the truth, then people are encouraged to kick other players from top100 by creating their own lists of top100. You cannot assume that all miners are online 24/7, you have to assume that someone can be offline for a while and then there should be some way to know which chain is the right one. The same is true for new miners, they know nothing about the network, they connect for the first time and they see some groups of top100 miners from the first phase. They have to know somehow, which group is the right one. Also, Luck coin encountered the same problem in the early stage. When the difficulty was low, everyone could pretend to be a true winner in the first phase. There were some alternative chains, the official block explorer showed block 500-something, but people were stuck at 200-something or 300-something. Then, when difficulty raised to some higher levels, everyone received the right chain, but then small miners were kicked and mined one block per week or so. The N2 number of miners of the second is also adjustable like the complexity algorithm in PoW that is adjusted every 2016 Block. If there is no upper limit for the N2 number of miners, then it will grow exponentially ad infinitum, people will spam the chain by pretending there are millions of miners, even if there will really be only 10 or 20. But if there will be some limit, for example there will be max 5000 miners, then you will reach that maximum and then the second phase will behave exactly as any other single-phase Proof of Work.
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Epictetus (OP)
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November 15, 2021, 09:05:53 AM |
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Thank you very much Bro. I tried this morning on Way back machine but I did not find it. Thank you for taking time to share it here. Much Appreciated. miner will hash the block header plus its public key plus an ounce repeatedly. The public key is added into the hash to avoid a miner using the result of other miner as its own result during the broadcasting But you know that Bitcoin blocks are produced in a similar way? Small miners include public keys for mining pools, so even if all blocks will be signed by miner's keys, it won't change anything. You can have one phase, two phases or N phases, it doesn't matter. Pools are going to download your client and behave like any other network participants. Then, they will be connected with hundreds of nodes and rewarding them "per share", no matter how complex that single share will be and how many phases will be needed to get it. Yea. I can see its use for mining pools. The electricity will be reduced by the fact that Round 1 is not computing-intensive If you have something that is not computing-intensive, then the energy consumption is reduced, but along with security. I guess the same thing could happen as in Luck: if you have two phases and they are not equally hard, then miners can game the system by dividing it differently between those two phases than you did in the original software. For example, your official client can mine the first phase for a short time and spend the most of the time on the second phase. But some optimized version could do the opposite: spend a lot of time on the first phase to pretend there are millions of miners, and then quickly solve the easiest blocks by completing the second phase. You can't game because of the public key in the hash. Plus in order to move to Round 2 you will need to announce it to the network by broadcasting your nonce1. So if you are a bit late your name won't on the list of N2 miners in other miners lists. In the second round you hash the following: Hash(Block Head + Public Key + Nonce1 + Nonce). So if you cheat, other miners will detect you and ignore your block. Exactly like Bitcoin. Or maybe they will find an equillibrium somewhere in between, maybe with the same amount of time for each phase, maybe 2/3 for the first and 1/3 for the second one, it really depends on your network parameters. In Luck it reached the highest limits they chose, as far as I remember their "alpha" value exponentially increased to the maximum value and stayed there, because that case was the most profitable for huge miners. In their first version there was no such limit, so without their first hard-fork, the network would be dominated by the biggest miners forever.
I do think that TRPoW is doing something different from Luck. We are not solving the same problems. I did not read all the Luck whitepaper, but from what I saw, we are already different. most of the miners won't be "allowed" by the rules (if followed) to advance to the second round You cannot assume that all miners will follow the rules, just because you placed them in your client. Rules have to be wired in the protocol to be followed, if some rule is only client-specific, it can be bypassed. For every successful coin you can find custom miner software, where miners optimize things far beyond what you gave them in the official version. Yes. But like in Bitcoin, You can cheat and not follow the rules. But the network will simply ignore you by using the longest chain. You will be served better by following the rules. Also, if there are millions of miners and you randomly select 100 of them, you encourage the rest of the miners to form mining pools. Then, you will end up in a situation where 100 miners are selected as before, but there are only 100 huge mining pools, they always get everything and distribute that to smaller miners. Almost no solo miner will follow your system if that miner will be rewarded once per month, because the risk of price drop after entering exchange is higher than the potential reward from solo mining.
The N2 number of miners of the second Round is also adjustable like the complexity algorithm in PoW that is adjusted every 2016 Block. Plus In Round 1 we are hashing Hash(Block Head + PublicKey + Nonce). So I don't know how this is going to force miners to organize in big pools. The Public Key of a miner has the benefit of limiting the formation of pools. In BTC PoW there is no public key in the hash. In TRPoW, the hash result is public key dependent
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Epictetus (OP)
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November 15, 2021, 09:25:46 AM |
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So you will always need to show that you were in Round 1 at some points. And if you are late, the network will have already formed its lists of N2 and you will be outside of it. But you can pretend that you were. How it is decided who were in the first round? By Proof of Work, right? So if you have some higher Proof of Work, you can pretend that the miner with the lower work came later. And if the total Proof of Work is used to decide who tells the truth, then miners with more power always win. And your block will be accepted ONLY if your name was in the List of N2 of other miners. So each group of 100 miners can pretend that they were first. When you join the network after they are formed in some groups, how are you going to choose the right chain? You can see 100 honest miners with some Proof of Work and 100 dishonest miners with another Proof of Work. If the most Proof of Work after two phases dictates the truth, then people are encouraged to kick other players from top100 by creating their own lists of top100. You cannot assume that all miners are online 24/7, you have to assume that someone can be offline for a while and then there should be some way to know which chain is the right one. The same is true for new miners, they know nothing about the network, they connect for the first time and they see some groups of top100 miners from the first phase. They have to know somehow, which group is the right one. Also, Luck coin encountered the same problem in the early stage. When the difficulty was low, everyone could pretend to be a true winner in the first phase. There were some alternative chains, the official block explorer showed block 500-something, but people were stuck at 200-something or 300-something. Then, when difficulty raised to some higher levels, everyone received the right chain, but then small miners were kicked and mined one block per week or so. The N2 number of miners of the second is also adjustable like the complexity algorithm in PoW that is adjusted every 2016 Block. If there is no upper limit for the N2 number of miners, then it will grow exponentially ad infinitum, people will spam the chain by pretending there are millions of miners, even if there will really be only 10 or 20. But if there will be some limit, for example there will be max 5000 miners, then you will reach that maximum and then the second phase will behave exactly as any other single-phase Proof of Work. Did you see these instructions ? TRPoW miners will execute the following instructions: - 1- If a miner receive $N_2$ $nonce1$ or more broadcast from other miners before finding its own $nonce1$, it will broadcast the list of the first $N_2$ winners and drop the current block competition and move to the next block. In this case it failed the first round and the block reward.
- 2- If it finds its $nonce1$ before receiving $N_2 - 1$ solutions from other miners, it will broadcast its $nonce1$ with the list of all the miners that found the solution before it including itself. it will continue listening the network to build the full list of the first $N_2$ winners. And at the same time move to the next round competition. In this case it succeed the first round.
- 3- If it didn't find its $nonce1$ yet and did not receive yet the full list of $N_2$ winners, it will continue solving for its first round $nonce1$ and listening to the network broadcasting to build its list of $N_2$ winners. In this case it is still running the first round.
- 4- If it finds its $nonce2$ before receiving any valid $nonce2$, it will broadcast its $nonce2$ and update the ledger and register the block reward for itself. And move to the next block. In this case it won the current block reward.
- 5- If it receive an $nonce2$, it will verify the solution and verify that the miner is in its list of winners of the first round. If all is fine, it will move to the next block competition having failed the current block comeptition. If the miner is not in its list of winners of the first round, it will ignore what it received and continue solving for its own $nonce1$ or / and $nonce2$ and listening to the network.
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Epictetus (OP)
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November 15, 2021, 09:36:23 AM |
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So you will always need to show that you were in Round 1 at some points. And if you are late, the network will have already formed its lists of N2 and you will be outside of it. But you can pretend that you were. How it is decided who were in the first round? By Proof of Work, right? So if you have some higher Proof of Work, you can pretend that the miner with the lower work came later. And if the total Proof of Work is used to decide who tells the truth, then miners with more power always win. you can pretend, but if you don't follow the TRPoW instructions, you will be ignored by the network. Keep in mind that in order to win a block reward, you need to be in the list of N2 miners of other miners. You can pretend and create a fork. but your block will be ignored in similar fashion like in Bitcoin. No difference here with Bitcoin.
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Epictetus (OP)
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November 15, 2021, 09:43:09 AM |
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And your block will be accepted ONLY if your name was in the List of N2 of other miners. So each group of 100 miners can pretend that they were first. When you join the network after they are formed in some groups, how are you going to choose the right chain? Again like in Bitcoin, we take the longest chain. No difference with Bitcoin. The honest and fastest miner will always win in the long run.
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LoyceV
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November 15, 2021, 09:47:36 AM |
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I don't believe your proposal reduces energy consumption. Energy consumption in PoW is limited by the value of the block reward This is a good point, but slightly incomplete: it's the total of resource consumption that depends on the value of the block reward. So if the energy consumption goes down, competing miners would buy more hardware, which moves the pollution to a different location. The electricity will be reduced by the fact that Round 1 is not computing-intensive and most of the miners won't be "allowed" by the rules (if followed) to advance to the second round. What's stopping the remaining miners from doing a "51% attack", trying to beat the select few by creating their own new Round 1 followed by their own Round 2?
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Epictetus (OP)
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November 15, 2021, 09:49:29 AM |
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The N2 number of miners of the second is also adjustable like the complexity algorithm in PoW that is adjusted every 2016 Block. If there is no upper limit for the N2 number of miners, then it will grow exponentially ad infinitum, people will spam the chain by pretending there are millions of miners, even if there will really be only 10 or 20. But if there will be some limit, for example there will be max 5000 miners, then you will reach that maximum and then the second phase will behave exactly as any other single-phase Proof of Work. There is an upper limit for N2 otherwise, the whole thing will be worthless. The idea is to limit the electricity consumption so N2 <<< N1 = number of all miners. Thank you for your great sharing and ideas. Much appreciated.
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larry_vw_1955
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November 15, 2021, 09:57:28 AM |
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I think a solution would be to eliminate the PoW in the second round and simply make it a random selection (somehow). That would cut the expected block reward by a factor of N2, which would cut the power usage in the first round by that same factor.
Not sure on that. But why not just have a single round 1 and just select the winner at random without eliminating anyone? Why wouldn't that work? The PoW job is also to maintain the Block Time at 10min. We can achieve that by just making everyone wait for that 10min minus delay/network broadcasting time etc. Say round 1 only takes 2 minutes to get 100 miners. Then you just wait 8 minutes to select the "winner". That's a 10 minute block time. So it saves 8 minutes of hashing. Less global warming.
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odolvlobo
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November 15, 2021, 09:58:03 AM Last edit: November 15, 2021, 10:08:14 AM by odolvlobo Merited by vjudeu (10), BlackHatCoiner (2) |
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Keep in mind that in order to win a block reward, you need to be in the list of N2 miners of other miners.
The first N2 solutions received by one miner could be different from the first N2 received by another. Do you have a way to achieve consensus on who is in the list? If there are different lists, then the network will split when miners don't agree on who is in the list. Again like in Bitcoin, we take the longest chain. No difference with Bitcoin. The honest and fastest miner will always win in the long run.
If you don't accept a block by someone not in your list, then you can't follow the actual longest chain. If you allow a block from a miner not in your list then every miner can include themselves in their own list (as soon as they complete round 1), which you must accept in order to resolve a split.
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Epictetus (OP)
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November 15, 2021, 10:07:31 AM |
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I don't believe your proposal reduces energy consumption. Energy consumption in PoW is limited by the value of the block reward This is a good point, but slightly incomplete: it's the total of resource consumption that depends on the value of the block reward. So if the energy consumption goes down, competing miners would buy more hardware, which moves the pollution to a different location. The electricity will be reduced by the fact that Round 1 is not computing-intensive and most of the miners won't be "allowed" by the rules (if followed) to advance to the second round. What's stopping the remaining miners from doing a "51% attack", trying to beat the select few by creating their own new Round 1 followed by their own Round 2? We can imagine that a lot of fastest miners will always be in the second Round 2. So those will win the race for the Block. In short the honest and fastest will win in the long run. Those disqualified in the first Round will lag behind and the block they will create will be a fork and it will discounted by the network as most miners will always go with the longest chain.
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Epictetus (OP)
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November 15, 2021, 10:18:50 AM |
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I think a solution would be to eliminate the PoW in the second round and simply make it a random selection (somehow). That would cut the expected block reward by a factor of N2, which would cut the power usage in the first round by that same factor.
Not sure on that. But why not just have a single round 1 and just select the winner at random without eliminating anyone? Why wouldn't that work? The PoW job is also to maintain the Block Time at 10min. We can achieve that by just making everyone wait for that 10min minus delay/network broadcasting time etc. Say round 1 only takes 2 minutes to get 100 miners. Then you just wait 8 minutes to select the "winner". That's a 10 minute block time. So it saves 8 minutes of hashing. Less global warming. This is true... But I think miners need to have some skin in the game if we want to have long term serious players in the network. PoW is achieving this skin in the game by asking for CPU power and PoS is achieving the same by asking for stakes.
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odolvlobo
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November 15, 2021, 10:29:45 AM |
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The PoW job is also to maintain the Block Time at 10min. We can achieve that by just making everyone wait for that 10min minus delay/network broadcasting time etc.
Say round 1 only takes 2 minutes to get 100 miners. Then you just wait 8 minutes to select the "winner". That's a 10 minute block time. So it saves 8 minutes of hashing. Less global warming. You would need a way to prevent the knowledge of the winner for 8 minutes so that nobody can start on the next block before the 10 minutes have past.
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Epictetus (OP)
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November 15, 2021, 12:41:09 PM Last edit: November 15, 2021, 03:14:36 PM by Epictetus |
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Keep in mind that in order to win a block reward, you need to be in the list of N2 miners of other miners.
The first N2 solutions received by one miner could be different from the first N2 received by another. Do you have a way to achieve consensus on who is in the list? If there are different lists, then the network will split when miners don't agree on who is in the list. No. But we don't need it. If there are different lists the network with go with the longest chain like in BTC. Again like in Bitcoin, we take the longest chain. No difference with Bitcoin. The honest and fastest miner will always win in the long run.
If you don't accept a block by someone not in your list, then you can't follow the actual longest chain. If you allow a block from a miner not in your list then every miner can include themselves in their own list (as soon as they complete round 1), which you must accept in order to resolve a split. Please Read instructions 1) and 5) below. ===========TRPoW miners will execute the following instructions============================ 1- If a miner receive $N_2$ $nonce1$ or more broadcast from other miners before finding its own $nonce1$, it will broadcast the list of the first $N_2$ winners and drop the current block competition and move to the next block. In this case it failed the first round and the block reward. 2- If it finds its $nonce1$ before receiving $N_2 - 1$ solutions from other miners, it will broadcast its $nonce1$ with the list of all the miners that found the solution before it including itself. it will continue listening the network to build the full list of the first $N_2$ winners. And at the same time move to the next round competition. In this case it succeed the first round. 3- If it didn't find its $nonce1$ yet and did not receive yet the full list of $N_2$ winners, it will continue solving for its first round $nonce1$ and listening to the network broadcasting to build its list of $N_2$ winners. In this case it is still running the first round. 4- If it finds its $nonce2$ before receiving any valid $nonce2$, it will broadcast its $nonce2$ and update the ledger and register the block reward for itself. And move to the next block. In this case it won the current block reward. 5- If it receive an $nonce2$, it will verify the solution and verify that the miner is in its list of winners of the first round. If all is fine, it will move to the next block competition having failed the current block competition. If the miner is not in its list of winners of the first round, it will ignore what it received and continue solving for its own $nonce1$ or / and $nonce2$ and listening to the network.
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