If tasked with the problem of coming up with a zk-SNARK protocol, many people would make their way to this point and then get stuck and give up. How can a verifier possibly check every single piece of the computation, without looking at each piece of the computation individually? But it turns out that there is a clever solution.

Polynomials

Polynomials are a special class of algebraic expressions of the form:

• x+5
• x^4
• x^3+3x^2+3x+1
• 628x^{271}+318x^{270}+530x^{269}+…+69x+381

i.e. they are a sum of any (finite!) number of terms of the form cx^k

There are many things that are fascinating about polynomials. But here we are going to zoom in on a particular one: polynomials are a single mathematical object that can contain an unbounded amount of information (think of them as a list of integers and this is obvious). The fourth example above contained 816 digits of tau, and one can easily imagine a polynomial that contains far more.

Furthermore, a single equation between polynomials can represent an unbounded number of equations between numbers. For example, consider the equation A(x)+ B(x) = C(x). If this equation is true, then it's also true that:

• A(0)+B(0)=C(0)
• A(1)+B(1)=C(1)
• A(2)+B(2)=C(2)
• A(3)+B(3)=C(3)

And so on for every possible coordinate. You can even construct polynomials to deliberately represent sets of numbers so you can check many equations all at once. For example, suppose that you wanted to check:

• 12+1=13
• 10+8=18
• 15+8=23
• 15+13=28

You can use a procedure called Lagrange interpolation to construct polynomials A(x) that give (12,10,15,15) as outputs at some specific set of coordinates (eg. (0,1,2,3)), B(x) the outputs (1,8,8,13) on thos same coordinates, and so forth. In fact, here are the polynomials:

• A(x)=-2x^3+\frac{19}{2}x^2-\frac{19}{2}x+12
• B(x)=2x^3-\frac{19}{2}x^2+\frac{29}{2}x+1
• C(x)=5x+13

Checking the equation A(x)+B(x)=C(x) with these polynomials checks all four above equations at the same time.

Comparing a polynomial to itself

You can even check relationships between a large number of adjacent evaluations of the same polynomial using a simple polynomial equation. This is slightly more advanced. Suppose that you want to check that, for a given polynomial F, F(x+2)=F(x)+F(x+1) with the integer range {0,1…89} (so if you also check F(0)=F(1)=1, then F(100) would be the 100th Fibonacci number)

As polynomials, F(x+2)-F(x+1)-F(x) would not be exactly zero, as it could give arbitrary answers outside the range x={0,1…98}. But we can do something clever. In general, there is a rule that if a polynomial P is zero across some set S=\{x_1,x_2…x_n\} then it can be expressed as P(x)=Z(x)*H(x), where Z(x)=(x-x_1)*(x-x_2)*…*(x-x_n) and H(x) is also a polynomial. In other words, any polynomial that equals zero across some set is a (polynomial) multiple of the simplest (lowest-degree) polynomial that equals zero across that same set.

Why is this the case? It is a nice corollary of polynomial long division: the factor theorem. We know that, when dividing P(x) by Z(x), we will get a quotient Q(x) and a remainder R(x) is strictly less than that of Z(x). Since we know that P is zero on all of S, it means that R has to be zero on all of S as well. So we can simply compute R(x) via polynomial interpolation, since it's a polynomial of degree at most n-1 and we know n values (the zeros at S). Interpolating a polynomial with all zeroes gives the zero polynomial, thus R(x)=0 and H(x)=Q(x).

Going back to our example, if we have a polynomial F that encodes Fibonacci numbers (so F(x+2)=F(x)+F(x+1) across x=\{0,1…98\}), then I can convince you that F actually satisfies this condition by proving that the polynomial P(x)=F(x+2)-F(x+1)-F(x) is zero over that range, by giving you the quotient:
H(x)=\frac{F(x+2)-F(x+1)-F(x)}{Z(x)}
Where Z(x) = (x-0)*(x-1)*…*(x-98).
You can calculate Z(x) yourself (ideally you would have it precomputed), check the equation, and if the check passes then F(x) satisfies the condition!

Now, step back and notice what we did here. We converted a 100-step-long computation into a single equation with polynomials. Of course, proving the N'th Fibonacci number is not an especially useful task, especially since Fibonacci numbers have a closed form. But you can use exactly the same basic technique, just with some extra polynomials and some more complicated equations, to encode arbitrary computations with an arbitrarily large number of steps.

Creating 10,000 auto-generated artworks, deploying a smart contract to the Ethereum / Polygon blockchain, setting up some tools, etc.

There is so much to do from launching to running an NFT project. Creating parts for artworks, generating 10,000 unique artworks and metadata, creating a smart contract and deploying it to a blockchain network, creating a website, creating a Twitter account, setting up a Discord server, setting up an OpenSea collection. In addition, you need to have MetaMask installed in your browser and have some ETH / MATIC. Did you get tired of doing all this? Don’t worry, once you know what you need to do, all you have to do is do it one by one.

To be honest, it’s best to run an NFT project in a team of three or more, including artists, developers, and marketers. However, depending on your motivation, you can do it by yourself. Some people might come later to offer help with your project. The most important thing is to take a step as soon as possible.

Creating Parts for Artworks

There are lots of free/paid software for drawing, but after all, I think Adobe Illustrator or Photoshop is the best. The images of Skulls In Love are a composite of 48x48 pixel parts created using Photoshop.

How Many Parts Should You Create?

Are you wondering how many parts you should create to avoid duplication as much as possible when generating your artworks? My friend Stephane, a developer, has created a great tool to help with that.

Generating 10,000 Unique Artworks and Metadata

I highly recommend using the HashLips Art Engine to generate your artworks and metadata. Perhaps there is no better artworks generation tool at the moment.

GitHub: https://github.com/HashLips/hashlips_art_engine
YouTube:

Storing Artworks and Metadata

Ideally, the generated artworks and metadata should be stored on-chain, but if you want to store them off-chain, you should use IPFS. Do not store in centralized storage. This is because data will be lost if the server goes down or if the company goes down. On the other hand, IPFS is a more secure way to find data because it utilizes a distributed, decentralized system.

Storing to IPFS is easy with Pinata, NFT.Storage, and so on. The Skulls In Love uses Pinata. It’s very easy to use, just upload the folder containing your artworks.

Creating and Deploying a Smart Contract

You don’t have to create a smart contract from scratch. There are many great NFT projects, many of which publish their contract source code on Etherscan / PolygonScan. You can choose the contract you like and reuse it. Of course, that requires some knowledge of Solidity, but it depends on your efforts. If you don’t know which contract to choose, use the HashLips smart contract. It’s very simple, but it has almost all the functions you need.

GitHub: https://github.com/HashLips/hashlips_nft_contract

Creating a Website

The website here is not just a static site to showcase your project, it’s a so-called dApp that allows you to access your smart contract and mint NFTs. In fact, this level of dApp is not too difficult for anyone who has ever created a website. Because the ethers.js / web3.js libraries make it easy to interact with your smart contract. There’s also no problem connecting wallets, as MetaMask has great documentation.

The Skulls In Love uses a simple, fast, and modern dApp that I built from scratch using Next.js. It is published on GitHub, so feel free to use it.

Why do people mint NFTs on a website?

Ethereum’s gas fees are high, so if you mint all your NFTs, there will be a huge initial cost. So it makes sense to get the buyers to help with the gas fees for minting.
What about Polygon? Polygon’s gas fees are super cheap, so even if you mint 10,000 NFTs, it’s not a big deal. But we don’t do that. Since NFT projects are a kind of game, it involves the fun of not knowing what will come out after minting.

Creating a Twitter Account

I highly recommend creating a Twitter account. Twitter is an indispensable tool for announcing giveaways and reaching more people. It’s better to announce your project and your artworks little by little, 1–2 weeks before launching your project.

Creating and Setting Up a Discord Server

I highly recommend creating a Discord server as well as a Twitter account. The Discord server is a community and its home. Fans of your NFT project will want to join your community and interact with many other members. So, carefully create each channel on your Discord server to make it a cozy place for your community members.

If you are unfamiliar with Discord, you may be particularly confused by the following:
What bots should I use?
How should I set roles and permissions?
But don’t worry. There are lots of great YouTube videos and blog posts about these.
It’s also a good idea to join the Discord servers of some NFT projects and see how they’re made. Our Discord server is so simple that even beginners will find it easy to understand. Please join us and see it!

UPDATED: As your Discord server grows, you cannot manage it on your own. In this case, you will be hiring several moderators, but choose carefully before hiring. And don’t give them important role permissions right after hiring. Initially, the same permissions as other members are sufficient. After a while, you can add permissions as needed, such as kicking/banning, using the “@every” tag, and adding roles. Again, don’t immediately give significant permissions to your Mod role. Your server can be messed up by fake moderators.

Setting Up Your OpenSea Collection

Before you start selling your NFTs, you need to reserve some for airdrops, giveaways, staff, and more. It’s up to you whether it’s 100, 500, or how many.

After minting some of your NFTs, your account and collection should have been created in OpenSea. Go to OpenSea, connect to your wallet, and set up your collection. Just set your logo, banner image, description, links, royalties, and more. It’s not that difficult.

Promoting Your Project

After all, promotion is the most important thing. In fact, almost every successful NFT project spends a lot of time and effort on it.

In addition to Twitter and Discord, it’s even better to use Instagram, Reddit, and Medium. Also, register your project in NFTCalendar and DISBOARD

About Promoters

You’ll probably get lots of contacts from promoters on your Discord, Twitter, Instagram, and more. But most of them are scams, so don’t pay right away. If you have a promoter that looks attractive to you, be sure to check the promoter’s social media accounts or website to see who he/she is. They basically charge in dollars. The amount they charge isn’t cheap, but promoters with lots of followers may have some temporary effect on your project. Some promoters accept 50% prepaid and 50% postpaid. If you can afford it, it might be worth a try. I never ask them, though.

When Should the Promotion Activities Start?

You may be worried that if you promote your project before it starts, someone will copy your project (artworks). It is true that some projects have actually suffered such damage. I don’t have a clear answer to this question right now, but:

• Do not publish all the information about your project too early
• The information should be released little by little
• Creating artworks that no one can easily copy
  I think these are important.
  If anyone has a good idea, please share it!

About Giveaways

When hosting giveaways, you’ll probably use multiple social media platforms. You may want to grow your Discord server faster. But if joining the Discord server is included in the giveaway requirements, some people hate it. I recommend holding giveaways for each platform. On Twitter and Reddit, you should just add the words “Discord members-only giveaway is being held now! Please join us if you like!”.

If you want to easily pick a giveaway winner in your browser, I recommend Twitter Picker.

Precautions for Distributing Free NFTs

If you want to increase your Twitter followers and Discord members, you can actually get a lot of people by holding events such as giveaways and invite contests. However, distributing many free NFTs at once can be dangerous. Some people who want free NFTs, as soon as they get a free one, sell it at a very low price on marketplaces such as OpenSea. They don’t care about your project and are only thinking about replacing their own “free” NFTs with Ethereum. The lower the floor price of your NFTs, the lower the value of your NFTs (project). Try to think of ways to get people to “buy” your NFTs as much as possible.

Ethereum vs. Polygon

Even though Ethereum has high gas fees, NFT projects on the Ethereum network are still mainstream and popular. On the other hand, Polygon has very low gas fees and fast transaction processing, but NFT projects on the Polygon network are not very popular.

Why? There are several reasons, but the biggest one is that it’s a lot of work to get MATIC (on Polygon blockchain, use MATIC instead of ETH) ready to use. Simply put, you need to bridge your tokens to the Polygon chain. So people need to do this first before minting your NFTs on your website. It may not be a big deal for those who are familiar with crypto and blockchain, but it may be complicated for those who are not. I hope that the tedious work will be simplified in the near future.

If you are confident that your NFTs will be purchased even if they are expensive, or if the total supply of your NFTs is low, you may choose Ethereum. If you just want to save money, you should choose Polygon. Keep in mind that gas fees are incurred not only when minting, but also when performing some of your smart contract functions and when transferring your NFTs.
If I were to launch a new NFT project, I would probably choose Ethereum or Solana.

Conclusion

Some people may want to start an NFT project to make money, but don’t forget to enjoy your own project. Several months ago, I was playing with creating generative art by imitating the CryptoPunks. I found out that auto-generated artworks would be more interesting than I had imagined, and since then I’ve been completely absorbed in generative art.

This is one of the Skulls In Love artworks:

This character wears a cowboy hat, black slim sunglasses, and a kimono. If anyone looks like this, I can’t help laughing!

The Skulls In Love NFTs can be minted for a small amount of MATIC on the official website. Please give it a try to see what kind of unique characters will appear 💀💖

Thank you for reading to the end. I hope this article will be helpful to those who want to launch an NFT project in the future ✨

We asked Mercedes to clarify whether "customers" refers to people who have expressed interest in buying the AMG ONE but haven't made a down payment or paid in full for a production slot, and a company spokesperson told that it's the latter – "Actual customers for AMG ONE in the United States and Canada." 

The Mercedes-AMG ONE has finally arrived in manufacturing form after numerous delays. This may be the most complicated and magnificent hypercar ever created, but according to Mercedes, those roads will not be found in the United States or Canada.

Despite all of the well-deserved excitement around the gorgeous AMG ONE, there was no word on when US customers could expect their cars. Our Editor-in-Chief became aware of this and contacted Mercedes to clarify the matter. Mercedes-hypercar AMG's with the F1-derived 1,049 HP 1.6-liter V6 engine will not be homologated for the US market, they've confirmed.

Mercedes has informed its customers in the United States and Canada that the ONE will not be arriving to North America after all, as of today, June 1, 2022. The whole text of the letter is included below, so sit back and wait for Mercedes to explain why we (or they) won't be getting (or seeing) the hypercar. Mercedes claims that all 275 cars it wants to produce have already been reserved, with net pricing in Europe starting at €2.75 million (about US$2.93 million at today's exchange rates), before country-specific taxes.

"The AMG-ONE was created with one purpose in mind: to provide a straight technology transfer of the World Championship-winning Mercedes-AMG Petronas Formula 1 E PERFORMANCE drive unit to the road." It's the first time a complete Formula 1 drive unit has been integrated into a road car.

Every component of the AMG ONE has been engineered to redefine high performance, with 1,000+ horsepower, four electric motors, and a blazing top speed of more than 217 mph. While the engine's beginnings are in competition, continuous research and refinement has left us with a difficult choice for the US market.

We determined that following US road requirements would considerably damage its performance and overall driving character in order to preserve the distinctive nature of its F1 powerplant. We've made the strategic choice to make the automobile available for road use in Europe, where it complies with all necessary rules."

If this is the first time US customers have heard about it, which it shouldn't be, we understand if it's a bit off-putting. The AMG ONE could very probably be Mercedes' final internal combustion hypercar of this type.

Nonetheless, we wouldn't be surprised if a few make their way to the United States via the federal government's "Show and Display" exemption provision. This legislation permits the importation of automobiles such as the AMG ONE, but only for a total of 2,500 miles per year.

The McLaren Speedtail, the Koenigsegg One:1, and the Bugatti EB110 are among the automobiles that have been imported under this special rule. We just hope we don't have to wait too long to see the ONE in the United States.