Bootsrap attack may be a common problem of all chains with finalization. Let's talk about the difficulty and the impact of launching a successful history bootsrap-poinsoning attack in our system.

First, you have to find a history point where there are enough empty accounts that had more stakes than the average total online stakes after that history point. Apparently the longer history the point is ,the more available accounts you can get. But the longer history you look back, the less impact the event of force majeure will have, which limits the history length of that point.

Second, whatever an attack aims for, the cost will not allow you to afford so many stakes.
As the example I gave, the users who sold their empty accounts to the attacker are actually risking their assets (if the attacker succeeds ,their current assets A' and B' will become useless.) for a short-term profit which is the cost of the attack. And that risk cost should not be low enough for one to bear.  At least he can't attack constantly, that makes the influence  of the bootstrap poisoning attack limited (maybe a fork with a few victims, which won't last long).

Under the circumstance you described, the history attack could succeed. But if you can't control the time of your attack, what's the point of the attack?
Besides, if there is a chain with the ability of finalization, I will not confirm my transactions untill the final state is established when I am going to make an important deal.

Yes I have read that before, and the paper, which is nice.
And the original post about the "history attack" of yours, good thinking, by the way.

For the historical attacks that construct new branches, we provide two layers of protection.

One is the save point. Save point is a finalized block which will limit the history attacks to its escendants. It means that the attacker must collect enough stakes after the last save point which may be less than an hour earlier. That seems much harder.

The other one is the branch priority decision strategy:The branches with higher online stakes will definitely be heavier. Therefore, unless the historical stakes that an attacker possesses exceed all the online stakes of the current main branch, it will not succeed.  For example: the total stakes are made up of three equal part A，B and C. If you collect the private keys of part A and B at a history point, that's 2/3 of the total and you plan to build a new fork from the history point and replace the original one. But the owner of stake A and B must have moved their stakes to other accounts, like A', B', before they give the old private keys to you. So the original branch will have the active stakes of A'+B'+C and your branch will have the stakes of A+B. Your branch will never heavier than the original one under my strategy. Besides, your account A and B will become invalid when a new save point is established.

Not if most of the users don't break the rule and choose to paticipate in , which probably will happen because the cost of breaking it (like renting alot of VPSs over the plannet) is higher than the benifits (mining reward which is not so big, or double spending which is nearly impossible).

Stake weighting, not with network dispersity but with accumulated stakes. Sybil attacks are also not so easy and not even valuable for attackers to apply, and it is no big deal if it really happens.
Please at least read the answer I just replied, I don't want to explain the same stuff repeatedly.
The main idea of the paper was introduced here https://bitcointalk.org/index.php?topic=5094909.msg49129375#msg49129375.

First of all, thank you for your concern. But you don't have to be offensive because I am not your enemy but a guy who wants to share something and discuss them with someone interested. Maybe I have offended you with some unappropriate words that I didn't noticed, I appologize for that.  Anyway, all questions are welcome.

If the key issue you mentioned means the "VPS" problem, maybe you have missed the main idea of the paper or maybe I missguided you by my previous posts, I am sorry for that. Although I have a preference for it because it's objective and seems "elegant" to me, "Network Dispersity" is just one of the abilities to "accumulate stakes". If it fails, the security and fairness will not be affected because:
1.
And the competition of accumulate stakes is still fair and objective.
Even if the accumulating process is subjective, you could consider it as a sort of "public" DPoS protocol in this respect.
2.
It means that the chains will remain strong whether the "network dispersity" works or not, and the motivation of breaking the rules of network dispersity is low because of the negative ROIs.

This problem was discussed in section 6(2).
Under some circumstances PoAS works like DPoS. Please read the 4th section of the summary post: https://bitcointalk.org/index.php?topic=5094909.msg49129375#msg49129375

Modified for better understanding.

The first voting is to determine the right to generate the next block.
The second voitng is to determine the main branch from different forks.

About the previous question, maybe I misunderstood you.
The "Confirms" you mentioned should not be "votes" from stakeholders. Sorry about that.
Anyone can provide many confirms to those signals, but he can't fake the fastest confirm to most of them, because the network latency and the physical distance between nodes.

"Confirms" is votes from the stakeholders. He can vote for anyone he want anyway, but can not vote with the stake belonging to others.
Thank you for the advice! I'll consider about it.

Sorry I didn't notice this question yesterday.
Network dispersity is a concept that means how much dispersed terminals in the network. Network dispersity reflects the ability to grab informations randomly appearing in the network. Like a honeycomb full of worker  bees, the more bees working out side, the better chance they grab a random flower. it cant be fabricated easily unless you cooperate with the signal senders.
I'm not saying I eliminates NAS, which is impossible . It just resolves the most serious problems caused by NaS.

gatherers belongs to the miners competing for those broadcasted signals to win their votes.
That is why wallets should paticipate in the profit distribution.

It doesn't work like checksum.

I am not going to publish any coin in any form. It is just a technique discussion, shouldn't it be post here?

Maybe I was wrong, it doesn't matter. Please focus on the main content of the paper other than the opening words. I am not here to debate "PoS or PoW?which one is better" problems.
I'll be preciated if you spend some time to understand the design, thank you.

modified

The article primarily deals with the major problems of the PoS system trying to make it more suitable for the use of cryptocurrency and become the mainstream protocol in the future.

It can be summarized to the following points:
1. Wealth distribution
The distribution of social wealth usually obeys the Pareto’s law as the following curve shows:
    If everyone’s wealth grows at the same rate, the distribution will not change. As the green line shows:

    In the field of cryptocurrencies, an overall growth of coins means inflation. Inflation is an incentive for the stakeholders to work. They have to earn more coins by working in order to compensate the wealth reduction caused by the inflation. To approach the ideal curve (the green line) in a PoS system, the ability of earning should depend on the number of coins they already have, or called stakes. It means that for some of the users who don’t have much coins, they also don’t have the ability to compensate the wealth reductions because their work costs are more than the earning. Those users have to choose not to work and then lose their wealth gradually (assume that the total value of the coin is not changed). It is the basic wealth redistribution rule of PoS currencies. As the red line shows:

    As shown above, the users owning less coins than w tend not to participate in the wealth redistribution, and they will be constantly “robbed” by the richer ones. As time goes on, the poorer users will eventually disappear. The lower value w has, the more users will remain.

    Considering the factors influencing the value of w, there will be the following approximate equation

w*R(Inflation Rate)/(R+1) (The wealth reduction) = C(Work cost) - F(Transaction fees acquired by working)  ,
that is : w=(C-F)*(1+1/R)

   So we have three ways to lower the value of w: increase F (Transaction fees), increase R (Inflation rate) or decrease C (Work cost)

   Traditional PoS protocol works as the first way or the second way, which causes serious inflation or high transaction fees.

   Our design works as the third way. We reduce the work cost of stakeholders from working fulltime to logging in once in between 100 hours. That reduces the work time to about one ten-thousandth of before, and the value of w will decrease substantially. In addition, since we have sharply reduced the value of C, we don’t have to increase the inflation rate or the transaction fees to a fairly high level. It makes the wealth distribution model of PoS systems much more acceptable.


2. Double voting and history attack
Stakeholders participate in the wealth redistribution by handing over their stakes to the miners through an accumulating process, which will be introduced later.

   The miner plays the role of working fulltime maintaining the network. The maintenance work includes two parts: generating blocks and voting for branches. I am going to explain the branch voting process here because it is related to the solution of the most serious problems caused by “Nothing at Stake”, starting with the “double voting” problem.

   Briefly speaking, the double voting problem is a strategy for miners to vote on each fork of the chain. But in PoAS systems, the miners cyclically vote for the current main branch and publish to the network as transactions which will be recorded in the next block. We ensure that the total voting information of every branch are recorded in each chain (introduced in section 3.2.2). Thus, each vote will go public before it takes effect. Then through a specific method of counting (introduced in section 3.2.1), we guarantee that each stake will be counted no more than once no matter which part of the branch are counted. Therefore, there will be no space to make multiple votes.

   Another major problem caused by NaS is the “history attacks”: the attacker rebuilds a new branch from a historical block trying to replace the original one. This is caused by the PoS consensus mechanism itself but we considered another aspect of it: the property of “Stake”. Unlike the other competition resources such as electricity, hashpower or storage space, stake is an inner state of the blockchains and therefore the total amount of stake is fixed. As it is introduced above, no multiple voting, we can easily conclude that a branch shouldn’t have any competitor if the stakes voted to it are more than half of the total stakes.

   As it is shown above, the stakes voted to the branch are more than the rest, then the root of this branch (with the red frame) will have no chance to be replaced, or to say, it’s finalized (introduced in section 3.2.1). The finalized block that we call save point limits the history attacks to its descendants, making the attacks much more difficult. There is another factor that helps out with the history attack problem but it will not be explained here (introduced in section 3.3).
   Before now, the NaS problems were solved through some complex and subjective methods, which also needs the users to perform additional operations. As it was discussed before, additional operations usually mean higher work cost, which is not healthy in the long term.

3. Wallet applications
Wallet applications usually don’t participate in the wealth redistribution because they are not involved in the process of mining. But in PoAS, wallet applications play an important role in the process of accumulating stakes which is the first stage of mining. They could profit from the system in different ways. (introduced in section 4.1), besides the wallets accumulate most of the transaction fees (introduced in section 5.1) which is not negligible because of the lower inflation rate. It will encourage the developers to be more active in making better wallet applications and that is a progress of decentralized development. In addition, it could encourage them to create sidechains with the clear profit model, which will be a progress of resolving the scalability problem.

4 Accumulating process
There are two ways of accumulating stakes: active voting and competition with network dispersity. The former one works like the delegated proof of stake: users have to choose the miners they already know about and vote their stakes to them. The latter method works more objectively and needs less operations by user: miners compete with each other using the ability called “Network dispersity”.

   Network dispersity is a concept that reflects how many dispersed units of a group are distributed to the network, which is also the ability to grab random signals on the network. As a honeycomb works: the more workers working out there, the better chance they find a usable flower, a Miner with more online Gatherers has better chance to find and win the vote from a random stakeholder. Because it is based on the network latencies which is inevitable and non-simulatable, network dispersity could be an objective resource for the miners to compete with.

   It doesn’t affect the security or fairness no matter which way we choose to accumulate stakes because most of the stakes are owned by the richest users who will tend to be balanced. (introduced in section 5.2)


full paper:
https://docdro.id/uanMOWk
or
https://www.keepandshare.com/doc15/19928/researchpaper-3-0-pdf-928k

Yes, you can say it's an ability to "control" the network. But the ability of network dispersity is not the only ability involved in the competition. Actually there will be three types of competitor with three types of abilities. The risk that attackers will control the network by dominating one type of ability, like you mentioned, will be reduced. You could refer to the section "4. Compete for Voters" for more details.

Hi:
I have been working on this consense mechanism since I posted it last time.
This is a new version of research paper after struggling with the language expression skills.
Let me introduce the protocol in brief.
1)This study aims to determine a pow-like protocol with less energy consumption.

2)The ability "Nertwork dispersity" is defined as
And it is involved into the system along with the "Stake" property to avoid the common problems of PoS like "Nothing at stake" and wealth concentration issue. So the protocol can be seemed as a kind of PoS mechanism.

3)Block can be finalized.

4)It's a fully discentralized system and doesn't need any special nodes like "Validators". The process of deposit and authentication are not needed either. We can think it in this way: it achieves the main purpose of "Casper", but it's much simpler and more effective.

The full paper is shown here(disabled).

If there are any questions, please let me know. Thank you.

大家好，上次发帖已经很久了，这几个月我又重新修改了一下协议的内容，基本上可以称为2.0版了，这里是在英文区发的贴：
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当然在咱们中文区我这里还有中文版：
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欢迎指正，谢谢！