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Anton Franzen

Anton Franzen

3 years ago

This is the driving force for my use of NFTs, which will completely transform the world.

More on NFTs & Art

nft now

nft now

3 years ago

Instagram NFTs Are Here… How does this affect artists?

Instagram (IG) is officially joining NFT. With the debut of new in-app NFT functionalities, influential producers can interact with blockchain tech on the social media platform.

Meta unveiled intentions for an Instagram NFT marketplace in March, but these latest capabilities focus more on content sharing than commerce. And why shouldn’t they? IG's entry into the NFT market is overdue, given that Twitter and Discord are NFT hotspots.

The NFT marketplace/Web3 social media race has continued to expand, with the expected Coinbase NFT Beta now live and blazing a trail through the NFT ecosystem.

IG's focus is on visual art. It's unlike any NFT marketplace or platform. IG NFTs and artists: what's the deal? Let’s take a look.

What are Instagram’s NFT features anyways?

As said, not everyone has Instagram's new features. 16 artists, NFT makers, and collectors can now post NFTs on IG by integrating third-party digital wallets (like Rainbow or MetaMask) in-app. IG doesn't charge to publish or share digital collectibles.

NFTs displayed on the app have a "shimmer" aesthetic effect. NFT posts also have a "digital collectable" badge that lists metadata such as the creator and/or owner, the platform it was created on, a brief description, and a blockchain identification.

Meta's social media NFTs have launched on Instagram, but the company is also preparing to roll out digital collectibles on Facebook, with more on the way for IG. Currently, only Ethereum and Polygon are supported, but Flow and Solana will be added soon.

How will artists use these new features?

Artists are publishing NFTs they developed or own on IG by linking third-party digital wallets. These features have no NFT trading aspects built-in, but are aimed to let authors share NFTs with IG audiences.

Creators, like IG-native aerial/street photographer Natalie Amrossi (@misshattan), are discovering novel uses for IG NFTs.

Amrossi chose to not only upload his own NFTs but also encourage other artists in the field. "That's the beauty of connecting your wallet and sharing NFTs. It's not just what you make, but also what you accumulate."

Amrossi has been producing and posting Instagram art for years. With IG's NFT features, she can understand Instagram's importance in supporting artists.

Web2 offered Amrossi the tools to become an artist and make a life. "Before 'influencer' existed, I was just making art. Instagram helped me reach so many individuals and brands, giving me a living.

Even artists without millions of viewers are encouraged to share NFTs on IG. Wilson, a relatively new name in the NFT space, seems to have already gone above and beyond the scope of these new IG features. By releasing "Losing My Mind" via IG NFT posts, she has evaded the lack of IG NFT commerce by using her network to market her multi-piece collection.

"'Losing My Mind' is a long-running photo series. Wilson was preparing to release it as NFTs before IG approached him, so it was a perfect match.

Wilson says the series is about Black feminine figures and media depiction. Respectable effort, given POC artists have been underrepresented in NFT so far.

“Over the past year, I've had mental health concerns that made my emotions so severe it was impossible to function in daily life, therefore that prompted this photo series. Every Wednesday and Friday for three weeks, I'll release a new Meta photo for sale.

Wilson hopes these new IG capabilities will help develop a connection between the NFT community and other internet subcultures that thrive on Instagram.

“NFTs can look scary as an outsider, but seeing them on your daily IG feed makes it less foreign,” adds Wilson. I think Instagram might become a hub for NFT aficionados, making them more accessible to artists and collectors.

What does it all mean for the NFT space?

Meta's NFT and metaverse activities will continue to impact Instagram's NFT ecosystem. Many think it will be for the better, as IG NFT frauds are another problem hurting the NFT industry.

IG's new NFT features seem similar to Twitter's PFP NFT verifications, but Instagram's tools should help cut down on scams as users can now verify the creation and ownership of whole NFT collections included in IG posts.

Given the number of visual artists and NFT creators on IG, it might become another hub for NFT fans, as Wilson noted. If this happens, it raises questions about Instagram success. Will artists be incentivized to distribute NFTs? Or will those with a large fanbase dominate?

Elise Swopes (@swopes) believes these new features should benefit smaller artists. Swopes was one of the first profiles placed to Instagram's original suggested user list in 2012.

Swopes says she wants IG to be a magnet for discovery and understands the value of NFT artists and producers.

"I'd love to see IG become a focus of discovery for everyone, not just the Beeples and Apes and PFPs. That's terrific for them, but [IG NFT features] are more about using new technology to promote emerging artists, Swopes added.

“Especially music artists. It's everywhere. Dancers, writers, painters, sculptors, musicians. My element isn't just for digital artists; it can be anything. I'm delighted to witness people's creativity."

Swopes, Wilson, and Amrossi all believe IG's new features can help smaller artists. It remains to be seen how these new features will effect the NFT ecosystem once unlocked for the rest of the IG NFT community, but we will likely see more social media NFT integrations in the months and years ahead.

Read the full article here

Adrien Book

Adrien Book

3 years ago

What is Vitalik Buterin's newest concept, the Soulbound NFT?

Decentralizing Web3's soul

Our tech must reflect our non-transactional connections. Web3 arose from a lack of social links. It must strengthen these linkages to get widespread adoption. Soulbound NFTs help.

This NFT creates digital proofs of our social ties. It embodies G. Simmel's idea of identity, in which individuality emerges from social groups, just as social groups evolve from people.

It's multipurpose. First, gather online our distinctive social features. Second, highlight and categorize social relationships between entities and people to create a spiderweb of networks.

1. 🌐 Reducing online manipulation: Only socially rich or respectable crypto wallets can participate in projects, ensuring that no one can create several wallets to influence decentralized project governance.

2. 🤝 Improving social links: Some sectors of society lack social context. Racism, sexism, and homophobia do that. Public wallets can help identify and connect distinct social groupings.

3. 👩‍❤️‍💋‍👨 Increasing pluralism: Soulbound tokens can ensure that socially connected wallets have less voting power online to increase pluralism. We can also overweight a minority of numerous voices.

4. 💰Making more informed decisions: Taking out an insurance policy requires a life review. Why not loans? Character isn't limited by income, and many people need a chance.

5. 🎶 Finding a community: Soulbound tokens are accessible to everyone. This means we can find people who are like us but also different. This is probably rare among your friends and family.

NFTs are dangerous, and I don't like them. Social credit score, privacy, lost wallet. We must stay informed and keep talking to innovators.

E. Glen Weyl, Puja Ohlhaver and Vitalik Buterin get all the credit for these ideas, having written the very accessible white paper “Decentralized Society: Finding Web3’s Soul”.

Sea Launch

Sea Launch

3 years ago

A guide to NFT pre-sales and whitelists

Before we dig through NFT whitelists and pre-sales, if you know absolutely nothing about NFTs, check our NFT Glossary.

What are pre-sales and whitelists on NFTs?

An NFT pre-sale, as the name implies, allows community members or early supporters of an NFT project to mint before the public, usually via a whitelist or mint pass.

Coin collectors can use mint passes to claim NFTs during the public sale. Because the mint pass is executed by “burning” an NFT into a specific crypto wallet, the collector is not concerned about gas price spikes.

A whitelist is used to approve a crypto wallet address for an NFT pre-sale. In a similar way to an early access list, it guarantees a certain number of crypto wallets can mint one (or more) NFT.

New NFT projects can do a pre-sale without a whitelist, but whitelists are good practice to avoid gas wars and a fair shot at minting an NFT before launching in competitive NFT marketplaces like Opensea, Magic Eden, or CNFT.

Should NFT projects do pre-sales or whitelists? 👇

The reasons to do pre-sales or a whitelist for NFT creators:

Time the market and gain traction.

Pre-sale or whitelists can help NFT projects gauge interest early on.

Whitelist spots filling up quickly is usually a sign of a successful launch, though it does not guarantee NFT longevity (more on that later). Also, full whitelists create FOMO and momentum for the public sale among non-whitelisted NFT collectors.

If whitelist signups are low or slow, projects may need to work on their vision, community, or product. Or the market is in a bear cycle. In either case, it aids NFT projects in market timing.

Reward the early NFT Community members.

Pre-sale and whitelists can help NFT creators reward early supporters.

First, by splitting the minting process into two phases, early adopters get a chance to mint one or more NFTs from their collection at a discounted or even free price.

Did you know that BAYC started at 0.08 eth each? A serum that allowed you to mint a Mutant Ape has become as valuable as the original BAYC.

(2) Whitelists encourage early supporters to help build a project's community in exchange for a slot or status. If you invite 10 people to the NFT Discord community, you get a better ranking or even a whitelist spot.

Pre-sale and whitelisting have become popular ways for new projects to grow their communities and secure future buyers.

Prevent gas wars.

Most new NFTs are created on the Ethereum blockchain, which has the highest transaction fees (also known as gas) (Solana, Cardano, Polygon, Binance Smart Chain, etc).

An NFT public sale is a gas war when a large number of NFT collectors (or bots) try to mint an NFT at the same time.

Competing collectors are willing to pay higher gas fees to prioritize their transaction and out-price others when upcoming NFT projects are hyped and very popular.

Pre-sales and whitelisting prevent gas wars by breaking the minting process into smaller batches of members or season launches.

The reasons to do pre-sales or a whitelists for NFT collectors:

How do I get on an NFT whitelist?

  1. Popular NFT collections act as a launchpad for other new or hyped NFT collections.

Example: Interfaces NFTs gives out 100 whitelist spots to Deadfellaz NFTs holders. Both NFT projects win. Interfaces benefit from Deadfellaz's success and brand equity.

In this case, to get whitelisted NFT collectors need to hold that specific NFT that is acting like a launchpad.

  1. A NFT studio or collection that launches a new NFT project and rewards previous NFT holders with whitelist spots or pre-sale access.

The whitelist requires previous NFT holders or community members.

NFT Alpha Groups are closed, small, tight-knit Discord servers where members share whitelist spots or giveaways from upcoming NFTs.

The benefit of being in an alpha group is getting information about new NFTs first and getting in on pre-sale/whitelist before everyone else.

There are some entry barriers to alpha groups, but if you're active in the NFT community, you'll eventually bump into, be invited to, or form one.

  1. A whitelist spot is awarded to members of an NFT community who are the most active and engaged.

This participation reward is the most democratic. To get a chance, collectors must work hard and play to their strengths.

Whitelisting participation examples:

  • Raffle, games and contest: NFT Community raffles, games, and contests. To get a whitelist spot, invite 10 people to X NFT Discord community.
  • Fan art: To reward those who add value and grow the community by whitelisting the best fan art and/or artists is only natural.
  • Giveaways: Lucky number crypto wallet giveaways promoted by an NFT community. To grow their communities and for lucky collectors, NFT projects often offer free NFT.
  • Activate your voice in the NFT Discord Community. Use voice channels to get NFT teams' attention and possibly get whitelisted.

The advantage of whitelists or NFT pre-sales.

Chainalysis's NFT stats quote is the best answer:

“Whitelisting isn’t just some nominal reward — it translates to dramatically better investing results. OpenSea data shows that users who make the whitelist and later sell their newly-minted NFT gain a profit 75.7% of the time, versus just 20.8% for users who do so without being whitelisted. Not only that, but the data suggests it’s nearly impossible to achieve outsized returns on minting purchases without being whitelisted.” Full report here.

Sure, it's not all about cash. However, any NFT collector should feel secure in their investment by owning a piece of a valuable and thriving NFT project. These stats help collectors understand that getting in early on an NFT project (via whitelist or pre-sale) will yield a better and larger return.

The downsides of pre-sales & whitelists for NFT creators.

Pre-sales and whitelist can cause issues for NFT creators and collectors.

NFT flippers

NFT collectors who only want to profit from early minting (pre-sale) or low mint cost (via whitelist). To sell the NFT in a secondary market like Opensea or Solanart, flippers go after the discounted price.

For example, a 1000 Solana NFT collection allows 100 people to mint 1 Solana NFT at 0.25 SOL. The public sale price for the remaining 900 NFTs is 1 SOL. If an NFT collector sells their discounted NFT for 0.5 SOL, the secondary market floor price is below the public mint.

This may deter potential NFT collectors. Furthermore, without a cap in the pre-sale minting phase, flippers can get as many NFTs as possible to sell for a profit, dumping them in secondary markets and driving down the floor price.

Hijacking NFT sites, communities, and pre-sales phase

People try to scam the NFT team and their community by creating oddly similar but fake websites, whitelist links, or NFT's Discord channel.

Established and new NFT projects must be vigilant to always make sure their communities know which are the official links, how a whitelist or pre-sale rules and how the team will contact (or not) community members.

Another way to avoid the scams around the pre-sale phase, NFT projects opt to create a separate mint contract for the whitelisted crypto wallets and then another for the public sale phase.

Scam NFT projects

We've seen a lot of mid-mint or post-launch rug pulls, indicating that some bad NFT projects are trying to scam NFT communities and marketplaces for quick profit. What happened to Magic Eden's launchpad recently will help you understand the scam.

We discussed the benefits and drawbacks of NFT pre-sales and whitelists for both projects and collectors. 

Finally, some practical tools and tips for finding new NFTs 👇

Tools & resources to find new NFT on pre-sale or to get on a whitelist:

In order to never miss an update, important pre-sale dates, or a giveaway, create a Tweetdeck or Tweeten Twitter dashboard with hyped NFT project pages, hashtags ( #NFTGiveaways , #NFTCommunity), or big NFT influencers.

Search for upcoming NFT launches that have been vetted by the marketplace and try to get whitelisted before the public launch.

Save-timing discovery platforms like sealaunch.xyz for NFT pre-sales and upcoming launches. How can we help 100x NFT collectors get projects? A project's official social media links, description, pre-sale or public sale dates, price and supply. We're also working with Dune on NFT data analysis to help NFT collectors make better decisions.

Don't invest what you can't afford to lose because a) the project may fail or become rugged. Find NFTs projects that you want to be a part of and support.

Read original post here

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Daniel Clery

3 years ago

Twisted device investigates fusion alternatives

German stellarator revamped to run longer, hotter, compete with tokamaks

Wendelstein 7-X’s complex geometry was a nightmare to build but, when fired up, worked from the start.

Tokamaks have dominated the search for fusion energy for decades. Just as ITER, the world's largest and most expensive tokamak, nears completion in southern France, a smaller, twistier testbed will start up in Germany.

If the 16-meter-wide stellarator can match or outperform similar-size tokamaks, fusion experts may rethink their future. Stellarators can keep their superhot gases stable enough to fuse nuclei and produce energy. They can theoretically run forever, but tokamaks must pause to reset their magnet coils.

The €1 billion German machine, Wendelstein 7-X (W7-X), is already getting "tokamak-like performance" in short runs, claims plasma physicist David Gates, preventing particles and heat from escaping the superhot gas. If W7-X can go long, "it will be ahead," he says. "Stellarators excel" Eindhoven University of Technology theorist Josefine Proll says, "Stellarators are back in the game." A few of startup companies, including one that Gates is leaving Princeton Plasma Physics Laboratory, are developing their own stellarators.

W7-X has been running at the Max Planck Institute for Plasma Physics (IPP) in Greifswald, Germany, since 2015, albeit only at low power and for brief runs. W7-X's developers took it down and replaced all inner walls and fittings with water-cooled equivalents, allowing for longer, hotter runs. The team reported at a W7-X board meeting last week that the revised plasma vessel has no leaks. It's expected to restart later this month to show if it can get plasma to fusion-igniting conditions.

Wendelstein 7-X’s twisting inner surface is now water cooled, enabling longer runs

Wendelstein 7-X's water-cooled inner surface allows for longer runs.

HOSAN/IPP

Both stellarators and tokamaks create magnetic gas cages hot enough to melt metal. Microwaves or particle beams heat. Extreme temperatures create a plasma, a seething mix of separated nuclei and electrons, and cause the nuclei to fuse, releasing energy. A fusion power plant would use deuterium and tritium, which react quickly. Non-energy-generating research machines like W7-X avoid tritium and use hydrogen or deuterium instead.

Tokamaks and stellarators use electromagnetic coils to create plasma-confining magnetic fields. A greater field near the hole causes plasma to drift to the reactor's wall.

Tokamaks control drift by circulating plasma around a ring. Streaming creates a magnetic field that twists and stabilizes ionized plasma. Stellarators employ magnetic coils to twist, not plasma. Once plasma physicists got powerful enough supercomputers, they could optimize stellarator magnets to improve plasma confinement.

W7-X is the first large, optimized stellarator with 50 6- ton superconducting coils. Its construction began in the mid-1990s and cost roughly twice the €550 million originally budgeted.

The wait hasn't disappointed researchers. W7-X director Thomas Klinger: "The machine operated immediately." "It's a friendly machine." It did everything we asked." Tokamaks are prone to "instabilities" (plasma bulging or wobbling) or strong "disruptions," sometimes associated to halted plasma flow. IPP theorist Sophia Henneberg believes stellarators don't employ plasma current, which "removes an entire branch" of instabilities.

In early stellarators, the magnetic field geometry drove slower particles to follow banana-shaped orbits until they collided with other particles and leaked energy. Gates believes W7-X's ability to suppress this effect implies its optimization works.

W7-X loses heat through different forms of turbulence, which push particles toward the wall. Theorists have only lately mastered simulating turbulence. W7-X's forthcoming campaign will test simulations and turbulence-fighting techniques.

A stellarator can run constantly, unlike a tokamak, which pulses. W7-X has run 100 seconds—long by tokamak standards—at low power. The device's uncooled microwave and particle heating systems only produced 11.5 megawatts. The update doubles heating power. High temperature, high plasma density, and extensive runs will test stellarators' fusion power potential. Klinger wants to heat ions to 50 million degrees Celsius for 100 seconds. That would make W7-X "a world-class machine," he argues. The team will push for 30 minutes. "We'll move step-by-step," he says.

W7-X's success has inspired VCs to finance entrepreneurs creating commercial stellarators. Startups must simplify magnet production.

Princeton Stellarators, created by Gates and colleagues this year, has $3 million to build a prototype reactor without W7-X's twisted magnet coils. Instead, it will use a mosaic of 1000 HTS square coils on the plasma vessel's outside. By adjusting each coil's magnetic field, operators can change the applied field's form. Gates: "It moves coil complexity to the control system." The company intends to construct a reactor that can fuse cheap, abundant deuterium to produce neutrons for radioisotopes. If successful, the company will build a reactor.

Renaissance Fusion, situated in Grenoble, France, raised €16 million and wants to coat plasma vessel segments in HTS. Using a laser, engineers will burn off superconductor tracks to carve magnet coils. They want to build a meter-long test segment in 2 years and a full prototype by 2027.

Type One Energy in Madison, Wisconsin, won DOE money to bend HTS cables for stellarator magnets. The business carved twisting grooves in metal with computer-controlled etching equipment to coil cables. David Anderson of the University of Wisconsin, Madison, claims advanced manufacturing technology enables the stellarator.

Anderson said W7-X's next phase will boost stellarator work. “Half-hour discharges are steady-state,” he says. “This is a big deal.”

Raad Ahmed

Raad Ahmed

3 years ago

How We Just Raised $6M At An $80M Valuation From 100+ Investors Using A Link (Without Pitching)

Lawtrades nearly failed three years ago.

We couldn't raise Series A or enthusiasm from VCs.

We raised $6M (at a $80M valuation) from 100 customers and investors using a link and no pitching.

Step-by-step:

We refocused our business first.

Lawtrades raised $3.7M while Atrium raised $75M. By comparison, we seemed unimportant.

We had to close the company or try something new.

As I've written previously, a pivot saved us. Our initial focus on SMBs attracted many unprofitable customers. SMBs needed one-off legal services, meaning low fees and high turnover.

Tech startups were different. Their General Councels (GCs) needed near-daily support, resulting in higher fees and lower churn than SMBs.

We stopped unprofitable customers and focused on power users. To avoid dilution, we borrowed against receivables. We scaled our revenue 10x, from $70k/mo to $700k/mo.

Then, we reconsidered fundraising (and do it differently)
This time was different. Lawtrades was cash flow positive for most of last year, so we could dictate our own terms. VCs were still wary of legaltech after Atrium's shutdown (though they were thinking about the space).

We neither wanted to rely on VCs nor dilute more than 10% equity. So we didn't compete for in-person pitch meetings.

AngelList Roll-Up Vehicle (RUV). Up to 250 accredited investors can invest in a single RUV. First, we emailed customers the RUV. Why? Because I wanted to help the platform's users.

Imagine if Uber or Airbnb let all drivers or Superhosts invest in an RUV. Humans make the platform, theirs and ours. Giving people a chance to invest increases their loyalty.

We expanded after initial interest.

We created a Journey link, containing everything that would normally go in an investor pitch:

  • Slides
  • Trailer (from me)
  • Testimonials
  • Product demo
  • Financials

We could also link to our AngelList RUV and send the pitch to an unlimited number of people. Instead of 1:1, we had 1:10,000 pitches-to-investors.

We posted Journey's link in RUV Alliance Discord. 600 accredited investors noticed it immediately. Within days, we raised $250,000 from customers-turned-investors.

Stonks, which live-streamed our pitch to thousands of viewers, was interested in our grassroots enthusiasm. We got $1.4M from people I've never met.

These updates on Pump generated more interest. Facebook, Uber, Netflix, and Robinhood executives all wanted to invest. Sahil Lavingia, who had rejected us, gave us $100k.

We closed the round with public support.

Without a single pitch meeting, we'd raised $2.3M. It was a result of natural enthusiasm: taking care of the people who made us who we are, letting them move first, and leveraging their enthusiasm with VCs, who were interested.

We used network effects to raise $3.7M from a founder-turned-VC, bringing the total to $6M at a $80M valuation (which, by the way, I set myself).

What flipping the fundraising script allowed us to do:

We started with private investors instead of 2–3 VCs to show VCs what we were worth. This gave Lawtrades the ability to:

  • Without meetings, share our vision. Many people saw our Journey link. I ended up taking meetings with people who planned to contribute $50k+, but still, the ratio of views-to-meetings was outrageously good for us.
  • Leverage ourselves. Instead of us selling ourselves to VCs, they did. Some people with large checks or late arrivals were turned away.
  • Maintain voting power. No board seats were lost.
  • Utilize viral network effects. People-powered.
  • Preemptively halt churn by turning our users into owners. People are more loyal and respectful to things they own. Our users make us who we are — no matter how good our tech is, we need human beings to use it. They deserve to be owners.

I don't blame founders for being hesitant about this approach. Pump and RUVs are new and scary. But it won’t be that way for long. Our approach redistributed some of the power that normally lies entirely with VCs, putting it into our hands and our network’s hands.

This is the future — another way power is shifting from centralized to decentralized.

Vitalik

Vitalik

4 years ago

An approximate introduction to how zk-SNARKs are possible (part 2)

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.

see part 3