[06/20/2022 update] We have now implemented a powerful text editor, but you can still use markdown.

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> Human beings face ever more complex and urgent problems, and their effectiveness in dealing with these problems is a matter that is critical to the stability and continued progress of society. \- Doug Engelbart, 1961

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We support LaTex to typeset math. We recommend reading the full documentation on the official website

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By Surojit Chatterjee, Chief Product Officer

2021 proved to be a breakout year for crypto with BTC price gaining almost 70% yoy, Defi hitting $150B in value locked, and NFTs emerging as a new category. Here’s my view through the crystal ball into 2022 and what it holds for our industry:

1. Eth scalability will improve, but newer L1 chains will see substantial growth — As we welcome the next hundred million users to crypto and Web3, scalability challenges for Eth are likely to grow. I am optimistic about improvements in Eth scalability with the emergence of Eth2 and many L2 rollups. Traction of Solana, Avalanche and other L1 chains shows that we’ll live in a multi-chain world in the future. We’re also going to see newer L1 chains emerge that focus on specific use cases such as gaming or social media.

2. There will be significant usability improvements in L1-L2 bridges — As more L1 networks gain traction and L2s become bigger, our industry will desperately seek improvements in speed and usability of cross-L1 and L1-L2 bridges. We’re likely to see interesting developments in usability of bridges in the coming year.

3. Zero knowledge proof technology will get increased traction — 2021 saw protocols like ZkSync and Starknet beginning to get traction. As L1 chains get clogged with increased usage, ZK-rollup technology will attract both investor and user attention. We’ll see new privacy-centric use cases emerge, including privacy-safe applications, and gaming models that have privacy built into the core. This may also bring in more regulator attention to crypto as KYC/AML could be a real challenge in privacy centric networks.

4. Regulated Defi and emergence of on-chain KYC attestation — Many Defi protocols will embrace regulation and will create separate KYC user pools. Decentralized identity and on-chain KYC attestation services will play key roles in connecting users’ real identity with Defi wallet endpoints. We’ll see more acceptance of ENS type addresses, and new systems from cross chain name resolution will emerge.

5. Institutions will play a much bigger role in Defi participation — Institutions are increasingly interested in participating in Defi. For starters, institutions are attracted to higher than average interest-based returns compared to traditional financial products. Also, cost reduction in providing financial services using Defi opens up interesting opportunities for institutions. However, they are still hesitant to participate in Defi. Institutions want to confirm that they are only transacting with known counterparties that have completed a KYC process. Growth of regulated Defi and on-chain KYC attestation will help institutions gain confidence in Defi.

6. Defi insurance will emerge — As Defi proliferates, it also becomes the target of security hacks. According to London-based firm Elliptic, total value lost by Defi exploits in 2021 totaled over $10B. To protect users from hacks, viable insurance protocols guaranteeing users’ funds against security breaches will emerge in 2022.

7. NFT Based Communities will give material competition to Web 2.0 social networks — NFTs will continue to expand in how they are perceived. We’ll see creator tokens or fan tokens take more of a first class seat. NFTs will become the next evolution of users’ digital identity and passport to the metaverse. Users will come together in small and diverse communities based on types of NFTs they own. User created metaverses will be the future of social networks and will start threatening the advertising driven centralized versions of social networks of today.

8. Brands will start actively participating in the metaverse and NFTs — Many brands are realizing that NFTs are great vehicles for brand marketing and establishing brand loyalty. Coca-Cola, Campbell’s, Dolce & Gabbana and Charmin released NFT collectibles in 2021. Adidas recently launched a new metaverse project with Bored Ape Yacht Club. We’re likely to see more interesting brand marketing initiatives using NFTs. NFTs and the metaverse will become the new Instagram for brands. And just like on Instagram, many brands may start as NFT native. We’ll also see many more celebrities jumping in the bandwagon and using NFTs to enhance their personal brand.

9. Web2 companies will wake up and will try to get into Web3 — We’re already seeing this with Facebook trying to recast itself as a Web3 company. We’re likely to see other big Web2 companies dipping their toes into Web3 and metaverse in 2022. However, many of them are likely to create centralized and closed network versions of the metaverse.

10. Time for DAO 2.0 — We’ll see DAOs become more mature and mainstream. More people will join DAOs, prompting a change in definition of employment — never receiving a formal offer letter, accepting tokens instead of or along with fixed salaries, and working in multiple DAO projects at the same time. DAOs will also confront new challenges in terms of figuring out how to do M&A, run payroll and benefits, and coordinate activities in larger and larger organizations. We’ll see a plethora of tools emerge to help DAOs execute with efficiency. Many DAOs will also figure out how to interact with traditional Web2 companies. We’re likely to see regulators taking more interest in DAOs and make an attempt to educate themselves on how DAOs work.

Thanks to our customers and the ecosystem for an incredible 2021. Looking forward to another year of building the foundations for Web3. Wagmi.

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.

On Saturday, Moonbird #2642, one of the collection's rarest NFTs, sold for a record 350 ETH (over $1 million) on OpenSea.

The Sandbox, a blockchain-based gaming company based in Hong Kong, bought the piece. The seller, "oscuranft" on OpenSea, made around $600,000 after buying the NFT for 100 ETH a week ago.

Owl avatars

Moonbirds is a 10,000 owl NFT collection. It is one of the quickest collections to achieve bluechip status. Proof, a media startup founded by renowned VC Kevin Rose, launched Moonbirds on April 16.

Rose is currently a partner at True Ventures, a technology-focused VC firm. He was a Google Ventures general partner and has 1.5 million Twitter followers.

Rose has an NFT podcast on Proof. It follows Proof Collective, a group of 1,000 NFT collectors and artists, including Beeple, who hold a Proof Collective NFT and receive special benefits.

These include early access to the Proof podcast and in-person events.

According to the Moonbirds website, they are "the official Proof PFP" (picture for proof).

Moonbirds NFTs sold nearly $360 million in just over a week, according to The Block Research and Dune Analytics. Its top ten sales range from $397,000 to $1 million.

In the current market, Moonbirds are worth 33.3 ETH. Each NFT is 2.5 ETH. Holders have gained over 12 times in just over a week.

Why was it so popular?

The Block Research's NFT analyst, Thomas Bialek, attributes Moonbirds' rapid rise to Rose's backing, the success of his previous Proof Collective project, and collectors' preference for proven NFT projects.

Proof Collective NFT holders have made huge gains. These NFTs were sold in a Dutch auction last December for 5 ETH each. According to OpenSea, the current floor price is 109 ETH.

According to The Block Research, citing Dune Analytics, Proof Collective NFTs have sold over $39 million to date.

Rose has bigger plans for Moonbirds. Moonbirds is introducing "nesting," a non-custodial way for holders to stake NFTs and earn rewards.

Holders of NFTs can earn different levels of status based on how long they keep their NFTs locked up.

Rose went on to say that Proof is just the start of "a multi-decade journey to build a new media company."

With the help of Virgil Abloh and Union LA‘s Chris Gibbs, it's now clear that Jordan Brand intended to bring the Air Jordan 2 back in 2022.
The “Future Is Now” collection includes two colorways of MJ's second signature as well as an extensive range of apparel and accessories.

The classic co-branding appears on short-sleeve tees, hoodies, and sweat shorts/sweat pants, all lightly distressed at the hems and seams.
Also, a filtered black-and-white photo of MJ graces the adjacent long sleeves, labels stitch into the socks, and the Jumpman logo adorns the four caps.
Liner jackets and flight pants will also be available, adding reimagined militaria to a civilian ensemble.
The Union LA x Air Jordan 2 (Grey Fog and Rattan) shares many of the same beats. Vintage suedes show age, while perforations and detailing reimagine Bruce Kilgore's design for the future.
The “UN/LA” tag across the modified eye stays, the leather patch across the tongue, and the label that wraps over the lateral side of the collar complete the look.
The footwear will also include a Crater Slide in the “Grey Fog” color scheme.

BUYING

On 4/9 and 4/10 from 9am-3pm, Union LA will be giving away a pair of Air Jordan 2s at their La Brea storefront (110 S. LA BREA AVE. LA, CA 90036). The raffle is only open to LA County residents with a valid CA ID. You must enter by 11:59pm on 4/10 to win. Winners will be notified via email.