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      "author": "alwaysnew",
      "permlink": "taproot-graftroot-to-the-bitcoin-development-mailing-list",
      "title": "taproot/graftroot to the #bitcoin development mailing list.",
      "body": "[bitcoin-dev] Taproot (and graftroot) complexity\nBryan Bishop kanzure at gmail.com\nSun Feb 9 20:19:55 UTC 2020\nPrevious message: [bitcoin-dev] Purge attacks (spin on sabotage attacks)\nNext message: [bitcoin-dev] An alternative deployment path for taproot technology (Re: Taproot (and graftroot) complexity)\nMessages sorted by: [ date ] [ thread ] [ subject ] [ author ]\nThe following is a message forwarded from an anonymous email that, for\nwhatever reason, couldn't be relayed through the mailing list without my\nassistance.\n\nThis email is the first of a collection of sentiments from a group of\ndevelopers\nwho in aggregate prefer to remain anonymous. These emails have been sent\nunder a\npseudonym so as to keep the focus of discussion on the merits of the\ntechnical\nissues, rather than miring the discussion in personal politics. Our goal\nisn't\nto cause a schism, but rather to help figure out what the path forward is\nwith\nTaproot. To that end, we:\n\n1) Discuss the merits of Taproot's design versus simpler alternatives (see\nthread subject, \"Taproot (and Graftroot) Complexity\").\n2) Propose an alternative path to deploying the technologies described in\nBIP-340, BIP-341, and BIP-342 (see thread subject, \"An Alternative\nDeployment\nPath for Taproot Technologies\").\n3) Suggest a modification to Taproot to reduce some of the overhead (see\nthread\nsubject, \"Taproot Public NUMS Optimization\").\n\nNow that the BIP has moved to draft we felt that now was the time to\nprioritize\nreview to make sure it was an acceptable change for our activities. As a\ngroup,\nwe're excited about the totality of what Taproot has to offer. However,\nafter\nour review, we're left perplexed about the development of Taproot (and\nGraftroot, to a lesser extent).\n\nWe also want to convey that we have nothing but respect for the developers\nand\ncommunity who have poured their heart and soul into preparing Taproot. Self\nevidently, it is an impressive synthesis of ideas. We believe that the\nhighest\nform of respect to pay such a synthesis of ideas is a detailed and critical\nreview, as it's pertinent to closely consider changes to Bitcoin.\n\n\nIn essence, Taproot is fundamentally the same as doing\nhttps://github.com/bitcoin/bips/blob/master/bip-0114.mediawiki and Schnorr\nsignatures separately.\n\nThe main reason for putting them together -- as mentioned in the BIP -- is a\ngain in efficiency. But this efficiency pre-supposes a specific use case and\nprobability distribution of use cases.\n\nCompare:\n\nSuppose a MAST for {a,b,c,d,e,f,g,h} spending conditions it looks something\nlike this:\n\n      /\\\n     /  \\\n    /    \\\n   /      \\\n  /\\      /\\\n /  \\    /  \\\n/\\  /\\  /\\  /\\\na b c d e f g h\n\nIf we want this to be functionally equivalent to Taproot, we add a new path:\n\n       /\\\n      /\\ \n     /  \\\n    /    \\\n   /      \\\n  /\\      /\\\n /  \\    /  \\\n/\\  /\\  /\\  /\\\na b c d e f g h\n\nNow, to spend from this MBV you have to reveal 32 bytes on the stack for\nthe not\ntaken branch, and 35 bytes for the  schnorr_checksig (1 byte push, 33\nbytes\nPK, 1 byte checksig).\n\nThis is 67 bytes more than Taproot would require for the same spending\ncondition.\n\nHowever, suppose we wanted to use one of the script paths instead. We still\nneed\nto have one extra hash for the  schnorr_checksig} (depending on if we\nput\nthe key in this position or not--see below). But now we can spend with just\na\nlogarithmic control program path.\n\nHowever, if we do the same script via taproot, we now need to provide the\nbase\npublic key (33 bytes) as well as the root hash (32 bytes) and path and then\nthe\nactual scripts. With the need for 2 push bytes, this ends up being back at\n67\nbytes extra.\n\nIs Taproot just a probability assumption about the frequency and likelihood\nof\nthe signature case over the script case? Is this a good assumption?  The BIP\nonly goes as far as to claim that the advantage is apparent if the outputs\n*could be spent* as an N of N, but doesn't make representations about how\nlikely\nthat N of N case would be in practice compared to the script paths. Perhaps\namong use cases, more than half of the ones we expect people to be doing\ncould be\nspent as an N of N. But how frequently would that path get used? Further,\nwhile\nthe *use cases* might skew toward things with N of N opt-out, we might end\nup in\na power law case where it's the one case that doesn't use an N of N opt out\nat\nall (or at a de minimis level) that becomes very popular, thereby making\nTaproot\nmore costly then beneficial.\n\nFurther, if you don't want to use a Taproot top-level key (e.g., you need\nto be\nable to audit that no one can spend outside of one of the script\nconditions),\nthen you need to use a NUMS (nothing up my sleeve) point. This forces users\nwho\ndon't want Taproot to pay the expense, when if they just had a MAST based\nwitness type they would be cheaper. So if this use case is at all common,\nTaproot leaves them worse off in terms of fees. Given that script paths are\nusually done in the case where there is some contested close, it's actually\nin\nthe interest of protocol developers that the contested script path be as\nefficient as possible so that the fees paid maximally increase the feerate.\nWe\nthink this can be fixed simply in Taproot though, as noted below.\n\n\n\nOn privacy, we're also a bit confused as to the goal of Taproot over MAST\nand\nSchnorr. Earlier, we presented a design with MAST which is very close to\nTaproot.\nHowever, it'd also be possible to just add schnorr_checksig} to the\nset\n{a,b,c,d,e,f,g,h}, shuffle them, and compute some MAST structure (perhaps\nprobability encoded) on them. This has the effect of not having much\nadditional\nfees for adding the extra Schnorr path at redeem time (only 1 extra branch\non\n2/8 script paths), e.g.\n\n      /\\\n     /  \\\n    /    \\\n   /      \\\n  /\\      /\\\n /  \\    /  \\\n/\\  /\\  /\\  /\\\na b c d e f/\\\n          g  h\n\nWe could argue that this is more private than Taproot, because we don't\ndistinguish between the Schnorr key case and other cases by default, so\nchain\nanalyzers can't tell if the signature came from the Taproot case or from\none of\nthe Script paths. There's also no NUMS point required, which means chain\nanalyzers can't tell when you spend that there was no top level key if the\nNUMS\npoint is not per-output indistinguishable. By using a semi-randomized MAST\nstructure, chain analyzers also can't tell exactly how big your spend\ncondition\nMAST was. In particular, you care more about privacy when you are\ncontesting a\nclose of a channel or other script path because then the miners could be\nmore\nlikely to extract a rent from you as \"ransom\" for properly closing your\nchannel\n(or in other words, in a contested close the value of the closing\ntransaction is\nlarger than usual).\n\nIt would also be possible to do something really simple which is to allow\nthe\nwitness type to be either a MAST hash OR a schnorr key (but not a Taproot).\nThis\nallows you to not completely fracture the anonymity set between people who\nwant\nplain Schnorr and people who want MAST (at least until they go to spend).\nThis\nfix can also be used in Taproot in place of a NUMS point, to decrease extra\nfees. It's unclear if this plays negatively with any future batch validation\nmechanism though, but the contextual checks to exclude a witness program\nfrom\nthe batch are relatively simple. See thread subject, \"Taproot Public NUMS\nOptimization\".\n\nThe considerations around Graftroot, a proposed delegation mechanism, is a\nbit\nsimilar. Delegation is a mechanism by which a UTXO with script S can sign a\nscript R which can then be executed in addition to S without requiring a\ntransaction. This allows an output to monotonically and dynamically\nincrease the\nnumber of conditions under which it can be spent. As noted by Pieter Wiulle\nhere:\n://github.com/kanzure/diyhpluswiki/commit/a03f6567d714f8733b578de263a4b149441cd058\ndelegation was originally possible in Bitcoin, but got broken during an\nemergency fork to split the scriptSig and scriptpubkey separation. Rather\nthan\nadding some fancy delegation mechanism in Bitcoin, why not just have a\nP2SH-like\nsemantic which allows a delegated script to be evaluated? See BIP-117\n://github.com/bitcoin/bips/blob/master/bip-0117.mediawiki. This way we\naren't special casing where delegation can occur, and we can allow taproot\nnested spending conditions (i.e., with timelocks) to generate their own\ndelegations. As I've seen Graftroot discussed thus far, it is as a top-level\nwitness program version like Taproot and non-recursive. Similar to the above\ndiscussion, top-level is more efficient if you suspect that delegation will\nbe\nmost likely occurring at the top level, but it's not clear that's a good\nassumption as it may be common to want to allow different scripts to\ndelegate.\n\n\nOverall, we are left with concerns both about the merit of doing Taproot\nversus alternatives, as well as the process through which we got to be here.\n\n1) Is Taproot actually more private than bare MAST and Schnorr separately?\nWhat\nare the actual anonymity set benefits compared to doing the separately?\n2) Is Taproot actually cheaper than bare MAST and Schnorr separately? What\nevidence do we have that the assumption it will be more common to use\nTaproot\nwith a key will outweigh Script cases?\n3) Is Taproot riskier than bare MAST and Schnorr separately given the new\ncrypto? How well reviewed is the actual crypto parts? None of us personally\nfeel\ncomfortable reviewing the crypto in Schnorr -- what's the set of people who\nhave\nthoroughly reviewed the crypto and aren't just ACKing because they trust\nother\ndevelopers to have looked at it close enough?\n4) Design wise, couldn't we forego the NUMS point requirement and be able to\ncheck if it's a hash root directly? This would encumber users who don't\nneed the\nkey path a cheaper spend path. See thread subject, \"Taproot Public NUMS\nOptimization\".\n5) Is the development model of trying to jam a bunch of features into\nBitcoin\nall at once good for Bitcoin development? Would we be better off if we\nembraced\nincremental improvements that can work together (e.g., MAST and then\nSchnorr)?\nAlthough the BIP raises some points about anonymity sets being why to do\nthem\nall at once, it's not clear to me this argument holds water (same goes for\nbusinesses not upgrading). If we can take things as smaller steps, we are\nnot\nonly more secure, but we also have more time to dedicate review to each\nchange\nindependently. We also end up co-mingling changes that people end up\naccepting\nonly because they want one and they're bundled (e.g., MAST and Schnorr, MAST\nseems like a much less risky addition versus Schnorr). See thread subject,\n\"An\nAlternative Deployment Path for Taproot Technologies\".\n\n\n\n\nOur provocation with this email is primarily that we think we should more\ncarefully consider the benefits of Taproot over simpler primitives that are\nnot\nonly easier to review, but could have been made available much sooner rather\nthan waiting on putting everything all together for an unclear aggregate\nbenefit.\n\nWe do think that most of the developers have been honest about the benefits\nof\nTaproot, but that on closer look we feel the general ecosystem has oversold\nTaproot as being the key enabler for a collection of techniques that we\ncould do\nwith much simpler building blocks.\n\n\nAt the end of the day, we do not strongly advocate not deploying Taproot at\nthis\npoint in the review cycle. We think the Taproot Public NUMS Optimization\nmay be\na good idea, worth considering if it's not insecure, as it cuts through the\ncase\nwhere you would otherwise need a NUMS point. Things like TapScript and its\nMAST\nmechanisms are well designed and offer exciting new deployment paths, and\nwould\nbe something we would use even if we opted for MAST instead of Taproot.\nHowever,\nwe also believe it is our duty to raise these concerns and suggestions, and\nwe\nlook forward to listening to the responses of the community.\n\nGreat thanks,\n\nThe Group\n\nSUBJECT: An Alternative Deployment Path for Taproot Technologies\n\nThis email is the second of a collection of sentiments from a group of\ndevelopers\nwho in aggregate prefer to remain anonymous. These emails have been sent\nunder a\npseudonym so as to keep the focus of discussion on the merits of the\ntechnical\nissues, rather than miring the discussion in personal politics. Our goal\nisn't\nto cause a schism, but rather to help figure out what the path forward is\nwith\nTaproot. To that end, we:\n\n1) Discuss the merits of Taproot's design versus simpler alternatives (see\nthread subject, \"Taproot (and Graftroot) Complexity\").\n2) Propose an alternative path to deploying the technologies described in\nBIP-340, BIP-341, and BIP-342 (see thread subject, \"An Alternative\nDeployment\nPath for Taproot Technologies\").\n3) Suggest a modification to Taproot to reduce some of the overhead (see\nthread\nsubject, \"Taproot Public NUMS Optimization\").\n\nAs a follow up to our prior message, we propose a different path forward\nfor the\nTaproot family of changes:\n\n1) A separate soft-fork for Merkle Branch Witnesses based on Taproot;\n2) A separate soft-fork for Schnorr Signatures\n3) A separate follow up soft-fork which enables Taproot and Graftroot\n\nWe think that the first 2 forks can be offered at the same time or one at a\ntime.\n\nTaproot, as a follow up to changes 1 and 2, can be enabled as a soft-fork\non the\nexisting semantics, but requiring a new witness version. With the Public\nNUMS Optimization, wallets could upgrade by just changing one version byte\nto be\nin the same anonymity set as Taproot.\n\nIt's not clear to us that the time to prepare a BIP and implementation for\n1 and\n2 at this point would be any less than the time to do Taproot as currently\nproposed. However, we believe that such a deployment plan is a reasonable\noption\nas it is more conservative, as Merkle Branch witnesses are relatively\nsimple and\nusers only have to use Schnorr signing if they want to, and can otherwise\ncontinue to use ECDSA. A further benefit of waiting on 3 is that we get to\ncollect real world protocol engineering experience to see how frequently the\nTaproot frequency of use assumption holds, and if it is worth doing or not.\n\n\nGreat thanks,\n\nThe Group\n\n-- \n- Bryan\n://heybryan.org/\n1 512 203 0507\n-------------- next part --------------\nAn attachment was scrubbed...\nURL: <http://lists.linuxfoundation.org/pipermail/bitcoin-dev/attachments/20200209/94a71b6f/attachment-0001.html>\nPrevious message: [bitcoin-dev] Purge attacks (spin on sabotage attacks)\nNext message: [bitcoin-dev] An alternative deployment path for taproot technology (Re: Taproot (and graftroot) complexity)\nMessages sorted by: [ date ] [ thread ] [ subject ] [ author ]\nMore information about the bitcoin-dev mailing list\n\n\n://lists.linuxfoundation.org/pipermail/bitcoin-dev/2020-February/017615.html",
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      "permlink": "steemitboard-notify-alwaysnew-20191222t171805000z",
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      "body": "Congratulations @alwaysnew! You received a personal award!\n\n<table><tr><td>https://steemitimages.com/70x70/http://steemitboard.com/@alwaysnew/birthday2.png</td><td>Happy Birthday! - You are on the Steem blockchain for 2 years!</td></tr></table>\n\n<sub>_You can view [your badges on your Steem Board](https://steemitboard.com/@alwaysnew) and compare to others on the [Steem Ranking](https://steemitboard.com/ranking/index.php?name=alwaysnew)_</sub>\n\n\n###### [Vote for @Steemitboard as a witness](https://v2.steemconnect.com/sign/account-witness-vote?witness=steemitboard&approve=1) to get one more award and increased upvotes!",
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      "body": "Constructing a Taproot output and spending it in the \"everyone agrees\" case. Shamelessly simplified.\n\n\n![EJgkKcRVUAIhX0p.jpg](https://cdn.steemitimages.com/DQmbddkqd1uH2uDepN87HGoZrDt26A6C9KdzyF1GGGj9Yak/EJgkKcRVUAIhX0p.jpg)",
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      "body": "Hi! I am a robot. I just upvoted you! I found similar content that readers might be interested in:\nhttps://busy.org/@yabapmatt/sps-proposal-for-steem-keychain-development",
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      "author": "alwaysnew",
      "permlink": "steem-browser-extension",
      "title": "steem browser extension",
      "body": "Steem Keychain is a browser extension currently available for the Chrome, Brave, and Firefox web browsers that allows users to securely store their Steem keys for multiple accounts and seamlessly interact with nearly all available Steem apps. It also provides a number of convenient features right within the extension such as:\n\n\n![yyyy.png](https://cdn.steemitimages.com/DQmdDHUftkHRrq27zMrF6Fs8sYKfAEsiPtERbD4vompDxh9/yyyy.png)\n\n\n\nChecking balances, resource credits, and voting power;\nTransferring STEEM / SBD and viewing transaction history;\nManaging power ups, power downs, and SP delegations;\nManaging witness votes; and\nViewing and transferring Steem Engine tokens.\nIt is available to download and install from the following locations:\n\nChrome / Brave: https://chrome.google.com/webstore/detail/steem-keychain/lkcjlnjfpbikmcmbachjpdbijejflpcm?hl=en\nFirefox: https://addons.mozilla.org/en-US/firefox/addon/steem-keychain/\nSource Code: https://github.com/MattyIce/steem-keychain\nRequest for Funding\n@aggroed and I have been personally funding the initial creation and ongoing development of the Steem Keychain extension over the past year or so and we are extremely fortunate to have been in a position to do that - all thanks to the Steem platform and community.\n\nGoing forward, we would like to utilize the new Steem Proposal System to ask the Steem community to help support the costs of continued development and maintenance of this project in the future.\n\nWe are requesting 100 SBD per day for the next 6 months. This comes to 3000 SBD per month, which is approximately $2000 USD per month at current market prices for SBD.\n\nThe funds will be used to pay for development and/or design work to add new features to the extension, keep it updated with any changes released to Steem or Steem Engine, and fix bugs and issues that are reported. The amount of funds requested is an estimate of what may be needed based on past history, and any unused funds will be returned to the @steem.dao account to be put back into other projects.\n\nAt the end of each month we will publish a report detailing what work was done and what funds were used for the community to review. The list of tasks currently in progress or planned for the near future are as follows:\n\nAdd the ability for apps to choose which RPC node the extension should use to broadcast transactions (from a pre-approved list of available nodes only for security reasons)\nAllow a default RPC node to be set and updated remotely by the development team\nCode cleanup and refactor\nAdd ability for sites/apps that create accounts to automatically add the new account to the keychain extension if it is available\nAdvanced design and planning for SMT / communities integration\nImproved documentation & error messaging\nLocalization support\nWhy This is Important for Steem\nSteem is a platform primarily focused on powering web applications, and as such it's very important that it be as simple and secure as possible for users to interact with those applications if we want to have any hope of serious growth. While there are a number of different ways to store keys and sign/broadcast transactions, a browser extension provides the best overall user experience without trading off security, which is essential.\n\nSteem, unfortunately, doesn't have the best reputation within the cryptocurrency community, so if we want to have any chance of changing that perception we need to not only have all of the tools users are expecting, but they must be easy to use, well designed, and be actively updated and maintained.\n\nProfessional, user-friendly, well maintained products give people confidence in a project while buggy, complicated, and poorly-designed products drive people away. If Steem can inspire confidence in the community through the quality of its products and apps then that confidence should eventually be reflected in the markets.\n\nOf course, professional, user-friendly, well maintained products require funding to create. It's usually pretty easy to tell which products were created by a couple people in their spare time vs the ones that have a properly funded team. Many of the projects on Steem in the past have fallen in the former category, but our hope is that via the new Steem Proposal System that will start to change.\n\nThat's why the SPS is such an important addition to the Steem ecosystem, but it won't achieve that goal by itself. It will require good teams to submit and deliver on great proposals, and it will require the Steem stakeholders to make smart decisions in the allocation of the available funds and to ensure that the teams behind funded projects actually deliver at the level of quality that we need.\n\nWe Need Your Vote!\nThe Steem Keychain extension currently has over 5000 users and growing (according to data from the Chrome and Mozilla web stores), and I like to think that the team behind it (including myself, @aggroed, @stoodkev, and @nateaguila) has a decent track record of delivering results. So if you feel that this is a worthwhile project and would like it to receive funding through the SPS, please consider giving it your vote!\n\nYou can view and vote for proposals at the following sites:\n\nVote for this Proposal using SteemConnect\nSteem Proposals: https://steemproposals.com/proposal/55\nSteemPeak: https://steempeak.com/me/proposals\nSteemit Wallet: https://steemitwallet.com/proposals",
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      "body": "Hi! I am a robot. I just upvoted you! I found similar content that readers might be interested in:\nhttps://boxmining.com/dcep/",
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      "author": "alwaysnew",
      "permlink": "dcep-china-s-national-digital-currency-overview",
      "title": "DCEP: China’s National Digital Currency Overview",
      "body": "Digital Currency DCEP (Digitial Currency Electronic Payment, DC/EP) is a national digital currency of the China built with Blockchain and Cryptographic technology. The currency is pegged 1:1 to the Chinese National Currency – the RenMinBi (RMB). The overall objective of the currency is to increase the circulation of the RMB and international reach – with eventual hopes that the RMB will the a global currency like the US Dollar. DCEP is the only legal digital currency in China (cryptocurrency such as Bitcoin are not legal tender in China).\n\nHuang Qifan (Chairman of the China International Economic Exchange Center) said they have been working on DCEP for five to six years now and is fully confident it can be introduced as the country’s financial system. It’s currently being rolled out, with the People’s Bank of China (PBoC) issuing the currency.\n\nDCEP CAN ACHIEVE REAL-TIME COLLECTION OF DATA RELATED TO MONEY CREATION, BOOKKEEPING, ETC, PROVIDING USEFUL REFERENCE FOR THE PROVISION OF MONEY AND THE IMPLEMENTATION OF MONETARY POLICIES\n\n\n![DCEP-security-1024x573.jpg](https://cdn.steemitimages.com/DQmNxbDTe1WpAyC2TbjfyQs2Q1rqSC6EqfrtUzCzefZ8Vn9/DCEP-security-1024x573.jpg)\n\nDeployment and Distribution\nDCEP will initially be distributed to all commercial banks affiliated with the Chinese Central Bank such as ICBC and Agriculture Bank of China. The significance of DCEP is that it’s designed as a replacement of the Reserve Money (M0) system, cutting back the cost and friction of bank transfers. This initial deployment will serve as an official production test for the currency system, where the network and security will be validated. In the second phase, DCEP will be distributed to large fintech companies such as Tencent and Alibaba to be used in WeChat Pay and AliPay respectively.\n\nMandate to adopt Blockchain\nPresident Xi JinPing has mandated that the ‘country’s development of blockchain technology should be sped up ‘ on Oct 24th in front of the Political Bureau. This speech has also been echoed by Li Wei, head of the People’s Bank of China. China has adopted the “Blockchain, not Cryptocurrency”, whereby the benefits of Blockchain is highlighted. On the other hand, cryptocurrencies that are native to Blockchain are suppressed as Cryptocurrency Exchanges and ICOs are banned in the country.\n\n![maxresdefault.jpg](https://cdn.steemitimages.com/DQmYVLKrYnS9Ef7cJsbfHbi79VscBHaPsBP1CYZSXcXah9N/maxresdefault.jpg)\n\n\nDCEP is a Centralized Currency\nDCEP is a digital currency that is run on a centralized private network – the Central Bank of China has complete access and control of the currency. This is a huge contrast to Bitcoin, which has an open decentralized network where there is no centralized leader. In the case with DCEP, the Central bank of China has the ability to create or destroy DCEP.\n\nNote: Previous publications have referred to the national currency as CBDC.\n\nSources:\nhttps://venturebeat.com/2019/09/15/wake-up-us-federal-reserve-china-just-showed-how-digital-currency-is-done/\nhttps://www.reuters.com/article/us-china-blockchain-idUSKBN1X704A\nhttps://u.today/just-in-chinese-central-bank-to-launch-digital-currency-called-dcep\nhttps://beincrypto.com/chinas-dcep-to-be-worlds-first-national-digital-currency-says-ccie-vice-chairman/\nhttps://qz.com/1710850/chinas-central-bank-could-gain-from-a-digital-yuan-cbdc/",
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      "permlink": "mimblewimble",
      "title": "Mimblewimble",
      "body": "Mimblewimble is a blockchain-based distributed registry design that differs in many ways from that of Bitcoin. It offers interesting differences from the point of view of the confidentiality of transactions and \"scripting\" at the cost of a sacrifice in terms of functionality or even transaction throughput per second. However, the operating principles of Lightning Network, in a simplified version, could apply to Mimblewimble which reduces the importance of the latter disadvantage in terms of loss of flow.\n\nMimblewimble builds on the ideas of Blockstream Confidential Transaction and adds the ability to combine transactions with each other, remove the \"outputs\" that are no longer expendable (UTXO) to keep only the unspent \"outputs\" that reduce that makes the total size of the chain considerably.\n\nThis ability to reduce the size of the blockchain over time is important, especially in the context of confidential transactions: in fact, the fact of masking the amount of the transactions is accompanied by an increase in information that is related to the transaction and ensure that the amount of the output does not behave like a negative amount which would lead to an attack to create money from scratch. To give an order of magnitude, if the bitcoin blockchain implemented the confidential transaction technology of \"Ct Element\" the total size of the string would exceed 1 Tera byte.\n\nMimbleWimble therefore allows newcomers to the network not to download the history of past (spent) outputs and to suppress the \"inputs\" to keep only \"unspent outputs\" and money creation inputs.\n\nIt is nevertheless impossible to claim that a transaction did not take place even if the input and output were erased because the combined transactions contain a cryptographic trace (sum of \"Excess\") of all the transactions including those which have been deleted.\n\nThis technology, in a first approach, seems to make the scripting impossible because they can not be the object of operation of addition or subtraction like the amounts and the keys. In addition, deleting the history of past transactions would not allow nodes to replay the scripts related to the outputs. But that nay! The magic of signatures (\"magicking digital signatures\" in the words of Andrew Poelstra) means that some of them can be created only through the good faith execution of a computer program. If we combine this capacity with the principles underlying Lightning Network's HTLCs, we then have funds that can only be released after the successful execution of a program, ie the publication of the signature. adequate. The scripts would no longer be executed by the nodes of the blockchain (as happens on Ethereum or Bitcoin) but only on the computers of the actors concerned: only the signature and the public key proving the execution of a program would be visible.\n\nThis is a considerable advance in terms of the confidentiality of the interactions between the actors of a contract because the \"Scriptless Script\" are stored and executed outside blockchain. These \"scripts\", however, have limitations. They will be the subject of a future study by project contributors.\n\nTo date, Mimblewimble is in the process of specification and development and is not yet usable. The implementation could be done in several ways in the future: an extension on the Bitcoin network via a softfork, a sidechain or in the form of an altcoin.",
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      "body": "good project",
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      "body": "Hi! I am a robot. I just upvoted you! I found similar content that readers might be interested in:\nhttps://hackernoon.com/building-your-own-bitcoin-satellite-node-6061d3c93e7",
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      "permlink": "building-your-own-bitcoin-satellite-node",
      "title": "Building Your Own Bitcoin Satellite Node",
      "body": "![1_gN909Ok7Ei98Fdl-Zx94NQ.png](https://cdn.steemitimages.com/DQmXt1HjrFHA7bH14UbrdNApwZtpAtf2z2MkSiabk19w9pm/1_gN909Ok7Ei98Fdl-Zx94NQ.png)\n\n\nHardware requirements:\nNote: The Amazon affiliate links are just to show what parts to get. You can undoubtedly find the parts on eBay if you want to. I realize some of the parts may be sold out on Amazon at this time. This guide was written for the parts on this list.\n\nA computer with Linux installed. This guide uses Fedora 26. I went with Fedora because it is free, it is compatible with the software required, and because it has a large user base. Make sure to have an i5 or a similarly performant processor: https://amzn.to/2x6G86r\nNote: It is now possible to run the Satellite receiver software on a Raspberry Pi or similar device! If using Ubuntu or another Debian-based distro, you can just add the PPA and apt install satellite !\n\nAmple storage space (roughly 4GB for a pruned node, 150GB+ for non-pruned)\nAt least a 46cm (18\") satellite dish: https://amzn.to/2wBtPzK\nSoftware Defined Radio Interface: https://amzn.to/2g8Nu2O\nLinear Polarization PLL LNB: https://amzn.to/2w0Zk4C\nLNB Mounting Bracket: https://amzn.to/2xgotXU\nLNB Power Supply: https://amzn.to/2KUGouq\nCoax Cable: https://amzn.to/2w7N4xQ\nF Connector to SMA Coax Adapter: https://amzn.to/2gajpAh\nScrewdriver and pliers (or similar tool) for adjusting fittings\n(Optional. My node uses this, but a roof mount is a better permanent option) 3 Ft Satellite Tripod: https://amzn.to/2w81RZm\nOther requirements:\nSmartphone satellite alignment app and/or compass\nPatience, some elbow grease, and the will to learn!\nHardware assembly:\nNote: Before you mount the dish assembly to the tripod, make absolutely sure the tripod is level. If the tripod is not level, you will run into difficulties when aligning the dish.\n\nThis image should give you a pretty good idea of how the assembly goes, sans the LNB part. We have a different LNB and LNB mounting bracket which is mounted slightly different than pictured here. The tripod requires no assembly and simply unfolds.\n\n\n![1_0vsWGWSbcA4nPxH5CCb4JQ.jpg](https://cdn.steemitimages.com/DQmZ8giuDLrc8wcd4XzP3kqnGVsS7u5onwWY7HACdMAw8nC/1_0vsWGWSbcA4nPxH5CCb4JQ.jpg)\n\nAdjusting the tripod’s mast mount fittings:\nYou can fine-tune the tripod and mast’s level with the six screws pictured here (the two not-visible fittings are on the opposite side). Mine came with a bubble-level that fits on the top of the mast. A smartphone app might also work.\n\n![1_Q2jt9PfBh5OuQnmOyxDUnw.png](https://cdn.steemitimages.com/DQmeBQZ1itEzE9m1f7YCyvvfBjJbSfCbGytYZttmFT9VRW9/1_Q2jt9PfBh5OuQnmOyxDUnw.png)\n\n\nFit the dish assembly to the tripod mast:\nThere are two bolts used to secure the dish assembly to the tripod mast, and two bolts (one shown, one on other side) used to secure the dish assembly’s elevation. Tighten all of the bolts enough to hold their position, but be able to be adjusted with a fair amount of physical effort in order for you to fine-tune the dish assembly’s azimuth and elevation.\n\nMounting the LNB bracket to the LNB support arm:\nMount the bracket on the top of the support arm and make sure it is center-aligned and not skewed left or right. Mount the LNB onto the LNB bracket as shown, but keep the screws semi-loose to allow you to adjust the LNB’s polarity while aligning. You can go ahead and connect the coax cable to the LNB at this point if you want.\n\n\n![1_lr1M_rh5qy1zFa2FqEgnRw.jpg](https://cdn.steemitimages.com/DQmWUQsfDJUESSmS83AzKLzn1iTCg94femG2bsT7gEh8KYx/1_lr1M_rh5qy1zFa2FqEgnRw.jpg)\n\n\nConnecting the cabling:\nRefer to my attempt at a simple cabling chart to help you connect the SDR to the LNB power supply using the SMA to F adapter cable, and the LNB to the LNB power supply with the coaxial cable. Your power supply may have different labeling for the connections. If you attach the SDR to the wrong connection, you may damage the SDR. Make sure to research your own LNB power supply to know for sure where to connect everything.\n\n![1_ckjJ2LstRfnoWTlu2DYTZw.png](https://cdn.steemitimages.com/DQmYTKLxTDLv4hbZsovJuocdujEXLLhxVyPpdQKrP6jB6a7/1_ckjJ2LstRfnoWTlu2DYTZw.png)\n\n\nThis concludes Part 1 — Hardware Assembly. Part 2 will focus on installing the necessary software to receive blocks from Blockstream Satellites. Part 3 will consist of using Gnuradio to align your dish and start receiving blocks!\n\nA special thanks to Chris Cook at Blockstream for walking me through setting my sat node up, and also to Greg Maxwell for informing me of such a cool and exciting application of technology.\n\nFor a more in-depth guide visit: https://github.com/Blockstream/satellite",
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      "body": "Hi! I am a robot. I just upvoted you! I found similar content that readers might be interested in:\nhttps://en.wikipedia.org/wiki/Fractal_dimension",
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      "title": "Fractal dimension",
      "body": "In mathematics, more specifically in fractal geometry, a fractal dimension is a ratio providing a statistical index of complexity comparing how detail in a pattern (strictly speaking, a fractal pattern) changes with the scale at which it is measured. It has also been characterized as a measure of the space-filling capacity of a pattern that tells how a fractal scales differently from the space it is embedded in; a fractal dimension does not have to be an integer.[1][2][3]\n\nThe essential idea of \"fractured\" dimensions has a long history in mathematics, but the term itself was brought to the fore by Benoit Mandelbrot based on his 1967 paper on self-similarity in which he discussed fractional dimensions.[4] In that paper, Mandelbrot cited previous work by Lewis Fry Richardson describing the counter-intuitive notion that a coastline's measured length changes with the length of the measuring stick used (see Fig. 1). In terms of that notion, the fractal dimension of a coastline quantifies how the number of scaled measuring sticks required to measure the coastline changes with the scale applied to the stick.[5] There are several formal mathematical definitions of fractal dimension that build on this basic concept of change in detail with change in scale.\n\nUltimately, the term fractal dimension became the phrase with which Mandelbrot himself became most comfortable with respect to encapsulating the meaning of the word fractal, a term he created. After several iterations over years, Mandelbrot settled on this use of the language: \"...to use fractal without a pedantic definition, to use fractal dimension as a generic term applicable to all the variants.\"[6]\n\nOne non-trivial example is the fractal dimension of a Koch snowflake. It has a topological dimension of 1, but it is by no means a rectifiable curve: the length of the curve between any two points on the Koch snowflake is infinite. No small piece of it is line-like, but rather it is composed of an infinite number of segments joined at different angles. The fractal dimension of a curve can be explained intuitively thinking of a fractal line as an object too detailed to be one-dimensional, but too simple to be two-dimensional.[7] Therefore its dimension might best be described not by its usual topological dimension of 1 but by its fractal dimension, which is often a number between one and two; in the case of the Koch snowflake, it is about 1.262.\n\nIntroduction\n\n\nFigure 2. A 32-segment quadric fractal scaled and viewed through boxes of different sizes. The pattern illustrates self similarity. The theoretical fractal dimension for this fractal is log32/log8 = 1.67; its empirical fractal dimension from box counting analysis is ±1%[8] using fractal analysis software.\nA fractal dimension is an index for characterizing fractal patterns or sets by quantifying their complexity as a ratio of the change in detail to the change in scale.[5]:1 Several types of fractal dimension can be measured theoretically and empirically (see Fig. 2).[3][9] Fractal dimensions are used to characterize a broad spectrum of objects ranging from the abstract[1][3] to practical phenomena, including turbulence,[5]:97–104 river networks,:246–247 urban growth,[10][11] human physiology,[12][13] medicine,[9] and market trends.[14] The essential idea of fractional or fractal dimensions has a long history in mathematics that can be traced back to the 1600s,[5]:19[15] but the terms fractal and fractal dimension were coined by mathematician Benoit Mandelbrot in 1975.[1][2][5][9][14][16]\n\nFractal dimensions were first applied as an index characterizing complicated geometric forms for which the details seemed more important than the gross picture.[16] For sets describing ordinary geometric shapes, the theoretical fractal dimension equals the set's familiar Euclidean or topological dimension. Thus, it is 0 for sets describing points (0-dimensional sets); 1 for sets describing lines (1-dimensional sets having length only); 2 for sets describing surfaces (2-dimensional sets having length and width); and 3 for sets describing volumes (3-dimensional sets having length, width, and height). But this changes for fractal sets. If the theoretical fractal dimension of a set exceeds its topological dimension, the set is considered to have fractal geometry.[17]\n\nUnlike topological dimensions, the fractal index can take non-integer values,[18] indicating that a set fills its space qualitatively and quantitatively differently from how an ordinary geometrical set does.[1][2][3] For instance, a curve with a fractal dimension very near to 1, say 1.10, behaves quite like an ordinary line, but a curve with fractal dimension 1.9 winds convolutedly through space very nearly like a surface. Similarly, a surface with fractal dimension of 2.1 fills space very much like an ordinary surface, but one with a fractal dimension of 2.9 folds and flows to fill space rather nearly like a volume.[17]:48[notes 1] This general relationship can be seen in the two images of fractal curves in Fig.2 and Fig. 3 – the 32-segment contour in Fig. 2, convoluted and space filling, has a fractal dimension of 1.67, compared to the perceptibly less complex Koch curve in Fig. 3, which has a fractal dimension of 1.26.\n\n\na Koch curve animation\nFigure 3. The Koch curve is a classic iterated fractal curve. It is a theoretical construct that is made by iteratively scaling a starting segment. As shown, each new segment is scaled by 1/3 into 4 new pieces laid end to end with 2 middle pieces leaning toward each other between the other two pieces, so that if they were a triangle its base would be the length of the middle piece, so that the whole new segment fits across the traditionally measured length between the endpoints of the previous segment. Whereas the animation only shows a few iterations, the theoretical curve is scaled in this way infinitely. Beyond about 6 iterations on an image this small, the detail is lost.\nThe relationship of an increasing fractal dimension with space-filling might be taken to mean fractal dimensions measure density, but that is not so; the two are not strictly correlated.[8] Instead, a fractal dimension measures complexity, a concept related to certain key features of fractals: self-similarity and detail or irregularity.[notes 2] These features are evident in the two examples of fractal curves. Both are curves with topological dimension of 1, so one might hope to be able to measure their length or slope, as with ordinary lines. But we cannot do either of these things, because fractal curves have complexity in the form of self-similarity and detail that ordinary lines lack.[5] The self-similarity lies in the infinite scaling, and the detail in the defining elements of each set. The length between any two points on these curves is undefined because the curves are theoretical constructs that never stop repeating themselves.[19] Every smaller piece is composed of an infinite number of scaled segments that look exactly like the first iteration. These are not rectifiable curves, meaning they cannot be measured by being broken down into many segments approximating their respective lengths. They cannot be characterized by finding their lengths or slopes. However, their fractal dimensions can be determined, which shows that both fill space more than ordinary lines but less than surfaces, and allows them to be compared in this regard.\n\nThe two fractal curves described above show a type of self-similarity that is exact with a repeating unit of detail that is readily visualized. This sort of structure can be extended to other spaces (e.g., a fractal that extends the Koch curve into 3-d space has a theoretical D=2.5849). However, such neatly countable complexity is only one example of the self-similarity and detail that are present in fractals.[3][14] The example of the coast line of Britain, for instance, exhibits self-similarity of an approximate pattern with approximate scaling.[5]:26 Overall, fractals show several types and degrees of self-similarity and detail that may not be easily visualized. These include, as examples, strange attractors for which the detail has been described as in essence, smooth portions piling up,[17]:49 the Julia set, which can be seen to be complex swirls upon swirls, and heart rates, which are patterns of rough spikes repeated and scaled in time.[20] Fractal complexity may not always be resolvable into easily grasped units of detail and scale without complex analytic methods but it is still quantifiable through fractal dimensions.[5]:197; 262\n\nHistory\nThe terms fractal dimension and fractal were coined by Mandelbrot in 1975,[16] about a decade after he published his paper on self-similarity in the coastline of Britain. Various historical authorities credit him with also synthesizing centuries of complicated theoretical mathematics and engineering work and applying them in a new way to study complex geometries that defied description in usual linear terms.[15][21][22] The earliest roots of what Mandelbrot synthesized as the fractal dimension have been traced clearly back to writings about undifferentiable, infinitely self-similar functions, which are important in the mathematical definition of fractals, around the time that calculus was discovered in the mid-1600s.[5]:405 There was a lull in the published work on such functions for a time after that, then a renewal starting in the late 1800s with the publishing of mathematical functions and sets that are today called canonical fractals (such as the eponymous works of von Koch,[19] Sierpiński, and Julia), but at the time of their formulation were often considered antithetical mathematical \"monsters\".[15][22] These works were accompanied by perhaps the most pivotal point in the development of the concept of a fractal dimension through the work of Hausdorff in the early 1900s who defined a \"fractional\" dimension that has come to be named after him and is frequently invoked in defining modern fractals.[4][5]:44[17][21]\n\nSee Fractal history for more information\n\n\nRole of scaling\n\nLines, squares, and cubes.\nFigure 4. Traditional notions of geometry for defining scaling and dimension.\nThe concept of a fractal dimension rests in unconventional views of scaling and dimension.[23] As Fig. 4 illustrates, traditional notions of geometry dictate that shapes scale predictably according to intuitive and familiar ideas about the space they are contained within, such that, for instance, measuring a line using first one measuring stick then another 1/3 its size, will give for the second stick a total length 3 times as many sticks long as with the first. This holds in 2 dimensions, as well. If one measures the area of a square then measures again with a box of side length 1/3 the size of the original, one will find 9 times as many squares as with the first measure. Such familiar scaling relationships can be defined mathematically by the general scaling rule in Equation 1, where the variable {\\displaystyle N}N stands for the number of sticks, {\\displaystyle \\varepsilon }\\varepsilon  for the scaling factor, and {\\displaystyle D}D for the fractal dimension:\n\n{\\displaystyle {N\\propto \\varepsilon ^{-D}},}{\\displaystyle {N\\propto \\varepsilon ^{-D}},}\n\n \n\n \n\n \n\n \n\n(1)\n\nwhere {\\displaystyle \\propto }\\propto  denotes proportionality. This scaling rule typifies conventional rules about geometry and dimension – for lines, it quantifies that, because {\\displaystyle N=3}N=3 when {\\displaystyle \\varepsilon ={\\tfrac {1}{3}}}{\\displaystyle \\varepsilon ={\\tfrac {1}{3}}} as in the example above, {\\displaystyle D=1,}{\\displaystyle D=1,} and for squares, because {\\displaystyle N=9}{\\displaystyle N=9} when {\\displaystyle \\varepsilon ={\\tfrac {1}{3}},D=2.}{\\displaystyle \\varepsilon ={\\tfrac {1}{3}},D=2.}\n\n\nA fractal contour of a koch snowflake\nFigure 5. The first four iterations of the Koch snowflake, which has an approximate Hausdorff dimension of 1.2619.\nThe same rule applies to fractal geometry but less intuitively. To elaborate, a fractal line measured at first to be one length, when remeasured using a new stick scaled by 1/3 of the old may not be the expected 3 but instead 4 times as many scaled sticks long. In this case, {\\displaystyle N=4}N=4 when {\\displaystyle \\varepsilon ={\\tfrac {1}{3}},}{\\displaystyle \\varepsilon ={\\tfrac {1}{3}},} and the value of {\\displaystyle D}D can be found by rearranging Equation 1:\n\n{\\displaystyle {\\log _{\\varepsilon }{N}={-D}={\\frac {\\log {N}}{\\log {\\varepsilon }}}}}{\\displaystyle {\\log _{\\varepsilon }{N}={-D}={\\frac {\\log {N}}{\\log {\\varepsilon }}}}}\n\n \n\n \n\n \n\n \n\n(2)\n\nThat is, for a fractal described by {\\displaystyle N=4}N=4 when {\\displaystyle \\varepsilon ={\\tfrac {1}{3}},D=1.2619,}{\\displaystyle \\varepsilon ={\\tfrac {1}{3}},D=1.2619,} a non-integer dimension that suggests the fractal has a dimension not equal to the space it resides in.[3] The scaling used in this example is the same scaling of the Koch curve and snowflake. Of note, the images shown are not true fractals because the scaling described by the value of {\\displaystyle D}D cannot continue infinitely for the simple reason that the images only exist to the point of their smallest component, a pixel. The theoretical pattern that the digital images represent, however, has no discrete pixel-like pieces, but rather is composed of an infinite number of infinitely scaled segments joined at different angles and does indeed have a fractal dimension of 1.2619.[5][23]\n\nD is not a unique descriptor\n\n\nFigure 6. Two L-systems branching fractals that are made by producing 4 new parts for every 1/3 scaling so have the same theoretical {\\displaystyle D}D as the Koch curve and for which the empirical box counting {\\displaystyle D}D has been demonstrated with 2% accuracy.[8]\nAs is the case with dimensions determined for lines, squares, and cubes, fractal dimensions are general descriptors that do not uniquely define patterns.[23][24] The value of D for the Koch fractal discussed above, for instance, quantifies the pattern's inherent scaling, but does not uniquely describe nor provide enough information to reconstruct it. Many fractal structures or patterns could be constructed that have the same scaling relationship but are dramatically different from the Koch curve, as is illustrated in Figure 6.\n\nFor examples of how fractal patterns can be constructed, see Fractal, Sierpinski triangle, Mandelbrot set, Diffusion limited aggregation, L-System.\n\n\nFractal surface structures\nThe concept of fractality is applied increasingly in the field of surface science, providing a bridge between surface characteristics and functional properties.[25] Numerous surface descriptors are used to interpret the structure of nominally flat surfaces, which often exhibit self-affine features across multiple length-scales. Mean surface roughness, usually denoted RA, is the most commonly applied surface descriptor, however numerous other descriptors including mean slope, root mean square roughness (RRMS) and others are regularly applied. It is found however that many physical surface phenomena cannot readily be interpreted with reference to such descriptors, thus fractal dimension is increasingly applied to establish correlations between surface structure in terms of scaling behavior and performance.[26] The fractal dimensions of surfaces have been employed to explain and better understand phenomena in areas of contact mechanics,[27] frictional behavior,[28] electrical contact resistance[29] and transparent conducting oxides.[30]\n\n\nFigure 7: Illustration of increasing surface fractality. Self-affine surfaces (left) and corresponding surface profiles (right) showing increasing fractal dimension Df\nExamples\nThe concept of fractal dimension described in this article is a basic view of a complicated construct. The examples discussed here were chosen for clarity, and the scaling unit and ratios were known ahead of time. In practice, however, fractal dimensions can be determined using techniques that approximate scaling and detail from limits estimated from regression lines over log vs log plots of size vs scale. Several formal mathematical definitions of different types of fractal dimension are listed below. Although for some classic fractals all these dimensions coincide, in general they are not equivalent:\n\nBox counting dimension: D is estimated as the exponent of a power law.\n{\\displaystyle D_{0}=\\lim _{\\varepsilon \\to 0}{\\frac {\\log N(\\varepsilon )}{\\log {\\frac {1}{\\varepsilon }}}}.}{\\displaystyle D_{0}=\\lim _{\\varepsilon \\to 0}{\\frac {\\log N(\\varepsilon )}{\\log {\\frac {1}{\\varepsilon }}}}.}\nInformation dimension: D considers how the average information needed to identify an occupied box scales with box size; {\\displaystyle p}p is a probability.\n{\\displaystyle D_{1}=\\lim _{\\varepsilon \\to 0}{\\frac {-\\langle \\log p_{\\varepsilon }\\rangle }{\\log {\\frac {1}{\\varepsilon }}}}}{\\displaystyle D_{1}=\\lim _{\\varepsilon \\to 0}{\\frac {-\\langle \\log p_{\\varepsilon }\\rangle }{\\log {\\frac {1}{\\varepsilon }}}}}\nCorrelation dimension: D is based on {\\displaystyle M}M as the number of points used to generate a representation of a fractal and gε, the number of pairs of points closer than ε to each other.\n{\\displaystyle D_{2}=\\lim _{M\\to \\infty }\\lim _{\\varepsilon \\to 0}{\\frac {\\log(g_{\\varepsilon }/M^{2})}{\\log \\varepsilon }}}{\\displaystyle D_{2}=\\lim _{M\\to \\infty }\\lim _{\\varepsilon \\to 0}{\\frac {\\log(g_{\\varepsilon }/M^{2})}{\\log \\varepsilon }}}[citation needed]\nGeneralized or Rényi dimensions: The box-counting, information, and correlation dimensions can be seen as special cases of a continuous spectrum of generalized dimensions of order α, defined by:\n{\\displaystyle D_{\\alpha }=\\lim _{\\varepsilon \\to 0}{\\frac {{\\frac {1}{\\alpha -1}}\\log(\\sum _{i}p_{i}^{\\alpha })}{\\log \\varepsilon }}}{\\displaystyle D_{\\alpha }=\\lim _{\\varepsilon \\to 0}{\\frac {{\\frac {1}{\\alpha -1}}\\log(\\sum _{i}p_{i}^{\\alpha })}{\\log \\varepsilon }}}\nHiguchi dimension[31]\n{\\displaystyle D={\\frac {d\\ \\log(L(k))}{d\\ \\log(k)}}}D={\\frac {d\\ \\log(L(k))}{d\\ \\log(k)}}\nLyapunov dimension\nMultifractal dimensions: a special case of Rényi dimensions where scaling behaviour varies in different parts of the pattern.\nUncertainty exponent\nHausdorff dimension: For any subset {\\displaystyle S}S of a metric space {\\displaystyle X}X and {\\displaystyle d\\geq 0}{\\displaystyle d\\geq 0}, the d-dimensional Hausdorff content of S is defined by\n{\\displaystyle C_{H}^{d}(S):=\\inf {\\Bigl \\{}\\sum _{i}r_{i}^{d}:{\\text{ there is a cover of }}S{\\text{ by balls with radii }}r_{i}>0{\\Bigr \\}}.}C_H^d(S):=\\inf\\Bigl\\{\\sum_i r_i^d:\\text{ there is a cover of } S\\text{ by balls with radii }r_i>0\\Bigr\\}.\nThe Hausdorff dimension of S is defined by\n{\\displaystyle \\dim _{\\operatorname {H} }(X):=\\inf\\{d\\geq 0:C_{H}^{d}(X)=0\\}.}\\dim _{{\\operatorname {H}}}(X):=\\inf\\{d\\geq 0:C_{H}^{d}(X)=0\\}.",
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      "body": "welcome to future lol",
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      "body": "That is interesting for sure. Ofc someone will find a way to exploit it. If its possible, people will try.",
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      "permlink": "a-new-bike-that-mining-cryptocurrencies-for-everyone-who-leads-them-and-ensures-you-a-profit-according-to-the-distance-you",
      "title": "A new bike that mining cryptocurrencies for everyone who leads them and ensures you a profit according to the distance you traveled",
      "body": "The UK bicycle manufacturer has manufactured 50 bikes, the world's first electronic bike capable of generating digital coins.\nThe company has developed 50 motorcycles, a bicycle manufacturer in the UK, and is the world's first electronic bike capable of earning cryptocurrency. Although it is, the idea itself is very innovative.\n\n\n![ggg.png](https://cdn.steemitimages.com/DQmYfTxz2mr3vYfoMcDu2uSdAfhkVZrT38Ho1w8gVNvhUY8/ggg.png)\n\n\nThe bike called the Toba will be able to generate LoyalCoin at a rate of approximately £ 20 per 1,000 miles. Once you have enough Toba coins, you can either trade them in Bitcoin, Zen, Litecoin or Digibytes, or exchange them at any store that accepts cryptocurrency. Cyclists will be able to monitor tokens generated using a smartphone app.\nEach turnover will earn you a Toba wheel, tokens that can be used to buy products from 50 motorcycles at a discount. It's mainly stimulating cycling.\n Toba bikes will have their own digital currency which will become one of thousands of coins in the future, and Toba will allow passengers to become an integral part of the growth you know.\n\n![image1.jpg](https://cdn.steemitimages.com/DQmT5sSBqyFc5GaPb8DeibwgNVhueBRhG3Dnx2RQuhHswmi/image1.jpg)\n\n\n\nThere is one issue to think about, people will find ways to trick the game. I can imagine someone disassembling the bike and turning it in a car, for example, or finding a way to make the wheels spin constantly. Someone will inevitably find a way to exploit the system, so it is clear that security measures must be put in place.\nThe Toba will be launched in the UK in September.",
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      "body": "<center><a href='https://d.tube/#!/v/alwaysnew/fkapptzr3d8'><img src='https://snap1.d.tube/ipfs/QmdBzLHtM7TnoaZhXDRNiaxQxdLSvB9dnJCF8ah8Fb1Nou'></a></center><hr>\n\nBitcoin giveaway rules here ► http://bit.ly/coinrul\nWe're giving away 1 BITCOIN, split between 2 winners:\n• ½ BTC to a commenter on this video, just tell us who won and why\n• ½ BTC to a contestant who enters using the alternate entry form http://bit.ly/coinrul\n\nAlexander Hamilton and Satoshi Nakamoto engage in a battle rap debate on the merits of centralized and decentralized currencies. What do you think? Let us know in the comments below for a chance to win bitcoin. (Yes, we’re serious.)\n\nWatch the behind the scenes to see how this was made ► \nhttp://bit.ly/2m0qLJp\n\n\n\n<hr><a href='https://d.tube/#!/v/alwaysnew/fkapptzr3d8'> ▶️ DTube</a><br /><a href='https://ipfs.io/ipfs/QmP3zwB9HHSeB9aZAX7L571ePvURE7R3yrU7f4roicjeFq'> ▶️ IPFS</a>",
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