An approximate introduction to how zk-SNARKs are possible (part 1)
You can make a proof for the statement "I know a secret number such that if you take the word ‘cow', add the number to the end, and SHA256 hash it 100 million times, the output starts with 0x57d00485aa". The verifier can verify the proof far more quickly than it would take for them to run 100 million hashes themselves, and the proof would also not reveal what the secret number is.
In the context of blockchains, this has 2 very powerful applications: Perhaps the most powerful cryptographic technology to come out of the last decade is general-purpose succinct zero knowledge proofs, usually called zk-SNARKs ("zero knowledge succinct arguments of knowledge"). A zk-SNARK allows you to generate a proof that some computation has some particular output, in such a way that the proof can be verified extremely quickly even if the underlying computation takes a very long time to run. The "ZK" part adds an additional feature: the proof can keep some of the inputs to the computation hidden.
You can make a proof for the statement "I know a secret number such that if you take the word ‘cow', add the number to the end, and SHA256 hash it 100 million times, the output starts with 0x57d00485aa". The verifier can verify the proof far more quickly than it would take for them to run 100 million hashes themselves, and the proof would also not reveal what the secret number is.
In the context of blockchains, this has two very powerful applications:
- Scalability: if a block takes a long time to verify, one person can verify it and generate a proof, and everyone else can just quickly verify the proof instead
- Privacy: you can prove that you have the right to transfer some asset (you received it, and you didn't already transfer it) without revealing the link to which asset you received. This ensures security without unduly leaking information about who is transacting with whom to the public.
But zk-SNARKs are quite complex; indeed, as recently as in 2014-17 they were still frequently called "moon math". The good news is that since then, the protocols have become simpler and our understanding of them has become much better. This post will try to explain how ZK-SNARKs work, in a way that should be understandable to someone with a medium level of understanding of mathematics.
Why ZK-SNARKs "should" be hard
Let us take the example that we started with: we have a number (we can encode "cow" followed by the secret input as an integer), we take the SHA256 hash of that number, then we do that again another 99,999,999 times, we get the output, and we check what its starting digits are. This is a huge computation.
A "succinct" proof is one where both the size of the proof and the time required to verify it grow much more slowly than the computation to be verified. If we want a "succinct" proof, we cannot require the verifier to do some work per round of hashing (because then the verification time would be proportional to the computation). Instead, the verifier must somehow check the whole computation without peeking into each individual piece of the computation.
One natural technique is random sampling: how about we just have the verifier peek into the computation in 500 different places, check that those parts are correct, and if all 500 checks pass then assume that the rest of the computation must with high probability be fine, too?
Such a procedure could even be turned into a non-interactive proof using the Fiat-Shamir heuristic: the prover computes a Merkle root of the computation, uses the Merkle root to pseudorandomly choose 500 indices, and provides the 500 corresponding Merkle branches of the data. The key idea is that the prover does not know which branches they will need to reveal until they have already "committed to" the data. If a malicious prover tries to fudge the data after learning which indices are going to be checked, that would change the Merkle root, which would result in a new set of random indices, which would require fudging the data again... trapping the malicious prover in an endless cycle.
But unfortunately there is a fatal flaw in naively applying random sampling to spot-check a computation in this way: computation is inherently fragile. If a malicious prover flips one bit somewhere in the middle of a computation, they can make it give a completely different result, and a random sampling verifier would almost never find out.
It only takes one deliberately inserted error, that a random check would almost never catch, to make a computation give a completely incorrect result.
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? There is a clever solution.
see part 2
(Edited)
More on Web3 & Crypto

Chris
2 years ago
What the World's Most Intelligent Investor Recently Said About Crypto
Cryptoshit. This thing is crazy to buy.
Charlie Munger is revered and powerful in finance.
Munger, vice chairman of Berkshire Hathaway, is noted for his wit, no-nonsense attitude to investment, and ability to spot promising firms and markets.
Munger's crypto views have upset some despite his reputation as a straight shooter.
“There’s only one correct answer for intelligent people, just totally avoid all the people that are promoting it.” — Charlie Munger
The Munger Interview on CNBC (4:48 secs)
This Monday, CNBC co-anchor Rebecca Quick interviewed Munger and brought up his 2007 statement, "I'm not allowed to have an opinion on this subject until I can present the arguments against my viewpoint better than the folks who are supporting it."
Great investing and life advice!
If you can't explain the opposing reasons, you're not informed enough to have an opinion.
In today's world, it's important to grasp both sides of a debate before supporting one.
Rebecca inquired:
Does your Wall Street Journal article on banning cryptocurrency apply? If so, would you like to present the counterarguments?
Mungers reply:
I don't see any viable counterarguments. I think my opponents are idiots, hence there is no sensible argument against my position.
Consider his words.
Do you believe Munger has studied both sides?
He said, "I assume my opponents are idiots, thus there is no sensible argument against my position."
This is worrisome, especially from a guy who once encouraged studying both sides before forming an opinion.
Munger said:
National currencies have benefitted humanity more than almost anything else.
Hang on, I think we located the perpetrator.
Munger thinks crypto will replace currencies.
False.
I doubt he studied cryptocurrencies because the name is deceptive.
He misread a headline as a Dollar destroyer.
Cryptocurrencies are speculations.
Like Tesla, Amazon, Apple, Google, Microsoft, etc.
Crypto won't replace dollars.
In the interview with CNBC, Munger continued:
“I’m not proud of my country for allowing this crap, what I call the cryptoshit. It’s worthless, it’s no good, it’s crazy, it’ll do nothing but harm, it’s anti-social to allow it.” — Charlie Munger
Not entirely inaccurate.
Daily cryptos are established solely to pump and dump regular investors.
Let's get into Munger's crypto aversion.
Rat poison is bitcoin.
Munger famously dubbed Bitcoin rat poison and a speculative bubble that would implode.
Partially.
But the bubble broke. Since 2021, the market has fallen.
Scam currencies and NFTs are being eliminated, which I like.
Whoa.
Why does Munger doubt crypto?
Mungers thinks cryptocurrencies has no intrinsic value.
He worries about crypto fraud and money laundering.
Both are valid issues.
Yet grouping crypto is intellectually dishonest.
Ethereum, Bitcoin, Solana, Chainlink, Flow, and Dogecoin have different purposes and values (not saying they’re all good investments).
Fraudsters who hurt innocents will be punished.
Therefore, complaining is useless.
Why not stop it? Repair rather than complain.
Regrettably, individuals today don't offer solutions.
Blind Areas for Mungers
As with everyone, Mungers' bitcoin views may be impacted by his biases and experiences.
OK.
But Munger has always advocated classic value investing and may be wary of investing in an asset outside his expertise.
Mungers' banking and insurance investments may influence his bitcoin views.
Could a coworker or acquaintance have told him crypto is bad and goes against traditional finance?
Right?
Takeaways
Do you respect Charlie Mungers?
Yes and no, like any investor or individual.
To understand Mungers' bitcoin beliefs, you must be critical.
Mungers is a successful investor, but his views about bitcoin should be considered alongside other viewpoints.
Munger’s success as an investor has made him an influencer in the space.
Influence gives power.
He controls people's thoughts.
Munger's ok. He will always be heard.
I'll do so cautiously.

Yogesh Rawal
3 years ago
Blockchain to solve growing privacy challenges
Most online activity is now public. Businesses collect, store, and use our personal data to improve sales and services.
In 2014, Uber executives and employees were accused of spying on customers using tools like maps. Another incident raised concerns about the use of ‘FaceApp'. The app was created by a small Russian company, and the photos can be used in unexpected ways. The Cambridge Analytica scandal exposed serious privacy issues. The whole incident raised questions about how governments and businesses should handle data. Modern technologies and practices also make it easier to link data to people.
As a result, governments and regulators have taken steps to protect user data. The General Data Protection Regulation (GDPR) was introduced by the EU to address data privacy issues. The law governs how businesses collect and process user data. The Data Protection Bill in India and the General Data Protection Law in Brazil are similar.
Despite the impact these regulations have made on data practices, a lot of distance is yet to cover.
Blockchain's solution
Blockchain may be able to address growing data privacy concerns. The technology protects our personal data by providing security and anonymity. The blockchain uses random strings of numbers called public and private keys to maintain privacy. These keys allow a person to be identified without revealing their identity. Blockchain may be able to ensure data privacy and security in this way. Let's dig deeper.
Financial transactions
Online payments require third-party services like PayPal or Google Pay. Using blockchain can eliminate the need to trust third parties. Users can send payments between peers using their public and private keys without providing personal information to a third-party application. Blockchain will also secure financial data.
Healthcare data
Blockchain technology can give patients more control over their data. There are benefits to doing so. Once the data is recorded on the ledger, patients can keep it secure and only allow authorized access. They can also only give the healthcare provider part of the information needed.
The major challenge
We tried to figure out how blockchain could help solve the growing data privacy issues. However, using blockchain to address privacy concerns has significant drawbacks. Blockchain is not designed for data privacy. A ‘distributed' ledger will be used to store the data. Another issue is the immutability of blockchain. Data entered into the ledger cannot be changed or deleted. It will be impossible to remove personal data from the ledger even if desired.
MIT's Enigma Project aims to solve this. Enigma's ‘Secret Network' allows nodes to process data without seeing it. Decentralized applications can use Secret Network to use encrypted data without revealing it.
Another startup, Oasis Labs, uses blockchain to address data privacy issues. They are working on a system that will allow businesses to protect their customers' data.
Conclusion
Blockchain technology is already being used. Several governments use blockchain to eliminate centralized servers and improve data security. In this information age, it is vital to safeguard our data. How blockchain can help us in this matter is still unknown as the world explores the technology.

Stephen Moore
3 years ago
Web 2 + Web 3 = Web 5.
Monkey jpegs and shitcoins have tarnished Web3's reputation. Let’s move on.
Web3 was called "the internet's future."
Well, 'crypto bros' shouted about it loudly.
As quickly as it arrived to be the next internet, it appears to be dead. It's had scandals, turbulence, and crashes galore:
Web 3.0's cryptocurrencies have crashed. Bitcoin's all-time high was $66,935. This month, Ethereum fell from $2130 to $1117. Six months ago, the cryptocurrency market peaked at $3 trillion. Worst is likely ahead.
Gas fees make even the simplest Web3 blockchain transactions unsustainable.
Terra, Luna, and other dollar pegs collapsed, hurting crypto markets. Celsius, a crypto lender backed by VCs and Canada's second-largest pension fund, and Binance, a crypto marketplace, have withheld money and coins. They're near collapse.
NFT sales are falling rapidly and losing public interest.
Web3 has few real-world uses, like most crypto/blockchain technologies. Web3's image has been tarnished by monkey profile pictures and shitcoins while failing to become decentralized (the whole concept is controlled by VCs).
The damage seems irreparable, leaving Web3 in the gutter.
Step forward our new saviour — Web5
Fear not though, as hero awaits to drag us out of the Web3 hellscape. Jack Dorsey revealed his plan to save the internet quickly.
Dorsey has long criticized Web3, believing that VC capital and silicon valley insiders have created a centralized platform. In a tweet that upset believers and VCs (he was promptly blocked by Marc Andreessen), Dorsey argued, "You don't own "Web3." VCs and LPs do. Their incentives prevent it. It's a centralized organization with a new name.
Dorsey announced Web5 on June 10 in a very Elon-like manner. Block's TBD unit will work on the project (formerly Square).
Web5's pitch is that users will control their own data and identity. Bitcoin-based. Sound familiar? The presentation pack's official definition emphasizes decentralization. Web5 is a decentralized web platform that enables developers to write decentralized web apps using decentralized identifiers, verifiable credentials, and decentralized web nodes, returning ownership and control over identity and data to individuals.
Web5 would be permission-less, open, and token-less. What that means for Earth is anyone's guess. Identity. Ownership. Blockchains. Bitcoin. Different.
Web4 appears to have been skipped, forever destined to wish it could have shown the world what it could have been. (It was probably crap.) As this iteration combines Web2 and Web3, simple math and common sense add up to 5. Or something.
Dorsey and his team have had this idea simmering for a while. Daniel Buchner, a member of Block's Decentralized Identity team, said, "We're finishing up Web5's technical components."
Web5 could be the project that decentralizes the internet. It must be useful to users and convince everyone to drop the countless Web3 projects, products, services, coins, blockchains, and websites being developed as I write this.
Web5 may be too late for Dorsey and the incoming flood of creators.
Web6 is planned!
The next months and years will be hectic and less stable than the transition from Web 1.0 to Web 2.0.
Web1 was around 1991-2004.
Web2 ran from 2004 to 2021. (though the Web3 term was first used in 2014, it only really gained traction years later.)
Web3 lasted a year.
Web4 is dead.
Silicon Valley billionaires are turning it into a startup-style race, each disrupting the next iteration until they crack it. Or destroy it completely.
Web5 won't last either.
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Charlie Brown
3 years ago
What Happens When You Sell Your House, Never Buying It Again, Reverse the American Dream
Homeownership isn't the only life pattern.
Want to irritate people?
My party trick is to say I used to own a house but no longer do.
I no longer wish to own a home, not because I lost it or because I'm moving.
It was a long-term plan. It was more deliberate than buying a home. Many people are committed for this reason.
Poppycock.
Anyone who told me that owning a house (or striving to do so) is a must is wrong.
Because, URGH.
One pattern for life is to own a home, but there are millions of others.
You can afford to buy a home? Go, buddy.
You think you need 1,000 square feet (or more)? You think it's non-negotiable in life?
Nope.
It's insane that society forces everyone to own real estate, regardless of income, wants, requirements, or situation. As if this trade brings happiness, stability, and contentment.
Take it from someone who thought this for years: drywall isn't happy. Living your way brings contentment.
That's in real estate. It may also be renting a small apartment in a city that makes your soul sing, but you can't afford the downpayment or mortgage payments.
Living or traveling abroad is difficult when your life savings are connected to something that eats your money the moment you sign.
#vanlife, which seems like torment to me, makes some people feel alive.
I've seen co-living, vacation rental after holiday rental, living with family, and more work.
Insisting that home ownership is the only path in life is foolish and reduces alternative options.
How little we question homeownership is a disgrace.
No one challenges a homebuyer's motives. We congratulate them, then that's it.
When you offload one, you must answer every question, even if you have a loose screw.
Why do you want to sell?
Do you have any concerns about leaving the market?
Why would you want to renounce what everyone strives for?
Why would you want to abandon a beautiful place like that?
Why would you mismanage your cash in such a way?
But surely it's only temporary? RIGHT??
Incorrect questions. Buying a property requires several inquiries.
The typical American has $4500 saved up. When something goes wrong with the house (not if, it’s never if), can you actually afford the repairs?
Are you certain that you can examine a home in less than 15 minutes before committing to buying it outright and promising to pay more than twice the asking price on a 30-year 7% mortgage?
Are you certain you're ready to leave behind friends, family, and the services you depend on in order to acquire something?
Have you thought about the connotation that moving to a suburb, which more than half of Americans do, means you will be dependent on a car for the rest of your life?
Plus:
Are you sure you want to prioritize home ownership over debt, employment, travel, raising kids, and daily routines?
Homeownership entails that. This ex-homeowner says it will rule your life from the time you put the key in the door.
This isn't questioned. We don't question enough. The holy home-ownership grail was set long ago, and we don't challenge it.
Many people question after signing the deeds. 70% of homeowners had at least one regret about buying a property, including the expense.
Exactly. Tragic.
Homes are different from houses
We've been fooled into thinking home ownership will make us happy.
Some may agree. No one.
Bricks and brick hindered me from living the version of my life that made me most comfortable, happy, and steady.
I'm spending the next month in a modest apartment in southern Spain. Even though it's late November, today will be 68 degrees. My spouse and I will soon meet his visiting parents. We'll visit a Sherry store. We'll eat, nap, walk, and drink Sherry. Writing. Jerez means flamenco.
That's my home. This is such a privilege. Living a fulfilling life brings me the contentment that buying a home never did.
I'm happy and comfortable knowing I can make almost all of my days good. Rejecting home ownership is partly to blame.
I'm broke like most folks. I had to choose between home ownership and comfort. I said, I didn't find them together.
Feeling at home trumps owning brick-and-mortar every day.
The following is the reality of what it's like to turn the American Dream around.
Leaving the housing market.
Sometimes I wish I owned a home.
I miss having my own yard and bed. My kitchen, cookbooks, and pizza oven are missed.
But I rarely do.
Someone else's life plan pushed home ownership on me. I'm grateful I figured it out at 35. Many take much longer, and some never understand homeownership stinks (for them).
It's confusing. People will think you're dumb or suicidal.
If you read what I write, you'll know. You'll realize that all you've done is choose to live intentionally. Find a home beyond four walls and a picket fence.
Miss? As I said, they're not home. If it were, a pizza oven, a good mattress, and a well-stocked kitchen would bring happiness.
No.
If you can afford a house and desire one, more power to you.
There are other ways to discover home. Find calm and happiness. For fun.
For it, look deeper than your home's foundation.

Theresa W. Carey
3 years ago
How Payment for Order Flow (PFOF) Works
What is PFOF?
PFOF is a brokerage firm's compensation for directing orders to different parties for trade execution. The brokerage firm receives fractions of a penny per share for directing the order to a market maker.
Each optionable stock could have thousands of contracts, so market makers dominate options trades. Order flow payments average less than $0.50 per option contract.
Order Flow Payments (PFOF) Explained
The proliferation of exchanges and electronic communication networks has complicated equity and options trading (ECNs) Ironically, Bernard Madoff, the Ponzi schemer, pioneered pay-for-order-flow.
In a December 2000 study on PFOF, the SEC said, "Payment for order flow is a method of transferring trading profits from market making to brokers who route customer orders to specialists for execution."
Given the complexity of trading thousands of stocks on multiple exchanges, market making has grown. Market makers are large firms that specialize in a set of stocks and options, maintaining an inventory of shares and contracts for buyers and sellers. Market makers are paid the bid-ask spread. Spreads have narrowed since 2001, when exchanges switched to decimals. A market maker's ability to play both sides of trades is key to profitability.
Benefits, requirements
A broker receives fees from a third party for order flow, sometimes without a client's knowledge. This invites conflicts of interest and criticism. Regulation NMS from 2005 requires brokers to disclose their policies and financial relationships with market makers.
Your broker must tell you if it's paid to send your orders to specific parties. This must be done at account opening and annually. The firm must disclose whether it participates in payment-for-order-flow and, upon request, every paid order. Brokerage clients can request payment data on specific transactions, but the response takes weeks.
Order flow payments save money. Smaller brokerage firms can benefit from routing orders through market makers and getting paid. This allows brokerage firms to send their orders to another firm to be executed with other orders, reducing costs. The market maker or exchange benefits from additional share volume, so it pays brokerage firms to direct traffic.
Retail investors, who lack bargaining power, may benefit from order-filling competition. Arrangements to steer the business in one direction invite wrongdoing, which can erode investor confidence in financial markets and their players.
Pay-for-order-flow criticism
It has always been controversial. Several firms offering zero-commission trades in the late 1990s routed orders to untrustworthy market makers. During the end of fractional pricing, the smallest stock spread was $0.125. Options spreads widened. Traders found that some of their "free" trades cost them a lot because they weren't getting the best price.
The SEC then studied the issue, focusing on options trades, and nearly decided to ban PFOF. The proliferation of options exchanges narrowed spreads because there was more competition for executing orders. Options market makers said their services provided liquidity. In its conclusion, the report said, "While increased multiple-listing produced immediate economic benefits to investors in the form of narrower quotes and effective spreads, these improvements have been muted with the spread of payment for order flow and internalization."
The SEC allowed payment for order flow to continue to prevent exchanges from gaining monopoly power. What would happen to trades if the practice was outlawed was also unclear. SEC requires brokers to disclose financial arrangements with market makers. Since then, the SEC has watched closely.
2020 Order Flow Payment
Rule 605 and Rule 606 show execution quality and order flow payment statistics on a broker's website. Despite being required by the SEC, these reports can be hard to find. The SEC mandated these reports in 2005, but the format and reporting requirements have changed over the years, most recently in 2018.
Brokers and market makers formed a working group with the Financial Information Forum (FIF) to standardize order execution quality reporting. Only one retail brokerage (Fidelity) and one market maker remain (Two Sigma Securities). FIF notes that the 605/606 reports "do not provide the level of information that allows a retail investor to gauge how well a broker-dealer fills a retail order compared to the NBBO (national best bid or offer’) at the time the order was received by the executing broker-dealer."
In the first quarter of 2020, Rule 606 reporting changed to require brokers to report net payments from market makers for S&P 500 and non-S&P 500 equity trades and options trades. Brokers must disclose payment rates per 100 shares by order type (market orders, marketable limit orders, non-marketable limit orders, and other orders).
Richard Repetto, Managing Director of New York-based Piper Sandler & Co., publishes a report on Rule 606 broker reports. Repetto focused on Charles Schwab, TD Ameritrade, E-TRADE, and Robinhood in Q2 2020. Repetto reported that payment for order flow was higher in the second quarter than the first due to increased trading activity, and that options paid more than equities.
Repetto says PFOF contributions rose overall. Schwab has the lowest options rates, while TD Ameritrade and Robinhood have the highest. Robinhood had the highest equity rating. Repetto assumes Robinhood's ability to charge higher PFOF reflects their order flow profitability and that they receive a fixed rate per spread (vs. a fixed rate per share by the other brokers).
Robinhood's PFOF in equities and options grew the most quarter-over-quarter of the four brokers Piper Sandler analyzed, as did their implied volumes. All four brokers saw higher PFOF rates.
TD Ameritrade took the biggest income hit when cutting trading commissions in fall 2019, and this report shows they're trying to make up the shortfall by routing orders for additional PFOF. Robinhood refuses to disclose trading statistics using the same metrics as the rest of the industry, offering only a vague explanation on their website.
Summary
Payment for order flow has become a major source of revenue as brokers offer no-commission equity (stock and ETF) orders. For retail investors, payment for order flow poses a problem because the brokerage may route orders to a market maker for its own benefit, not the investor's.
Infrequent or small-volume traders may not notice their broker's PFOF practices. Frequent traders and those who trade larger quantities should learn about their broker's order routing system to ensure they're not losing out on price improvement due to a broker prioritizing payment for order flow.
This post is a summary. Read full article here

Rita McGrath
3 years ago
Flywheels and Funnels
Traditional sales organizations used the concept of a sales “funnel” to describe the process through which potential customers move, ending up with sales at the end. Winners today have abandoned that way of thinking in favor of building flywheels — business models in which every element reinforces every other.
Ah, the marketing funnel…
Prospective clients go through a predictable set of experiences, students learn in business school marketing classes. It looks like this:
Understanding the funnel helps evaluate sales success indicators. Gail Goodwin, former CEO of small business direct mail provider Constant Contact, said managing the pipeline was key to escaping the sluggish SaaS ramp of death.
Like the funnel concept. To predict how well your business will do, measure how many potential clients are aware of it (awareness) and how many take the next step. If 1,000 people heard about your offering and 10% showed interest, you'd have 100 at that point. If 50% of these people made buyer-like noises, you'd know how many were, etc. It helped model buying trends.
TV, magazine, and radio advertising are pricey for B2C enterprises. Traditional B2B marketing involved armies of sales reps, which was expensive and a barrier to entry.
Cracks in the funnel model
Digital has exposed the funnel's limitations. Hubspot was born at a time when buyers and sellers had huge knowledge asymmetries, according to co-founder Brian Halligan. Those selling a product could use the buyer's lack of information to become a trusted partner.
As the world went digital, getting information and comparing offerings became faster, easier, and cheaper. Buyers didn't need a seller to move through a funnel. Interactions replaced transactions, and the relationship didn't end with a sale.
Instead, buyers and sellers interacted in a constant flow. In many modern models, the sale is midway through the process (particularly true with subscription and software-as-a-service models). Example:
You're creating a winding journey with many touch points, not a funnel (and lots of opportunities for customers to get lost).
From winding journey to flywheel
Beyond this revised view of an interactive customer journey, a company can create what Jim Collins famously called a flywheel. Imagine rolling a heavy disc on its axis. The first few times you roll it, you put in a lot of effort for a small response. The same effort yields faster turns as it gains speed. Over time, the flywheel gains momentum and turns without your help.
Modern digital organizations have created flywheel business models, in which any additional force multiplies throughout the business. The flywheel becomes a force multiplier, according to Collins.
Amazon is a famous flywheel example. Collins explained the concept to Amazon CEO Jeff Bezos at a corporate retreat in 2001. In The Everything Store, Brad Stone describes in his book The Everything Store how he immediately understood Amazon's levers.
The result (drawn on a napkin):
Low prices and a large selection of products attracted customers, while a focus on customer service kept them coming back, increasing traffic. Third-party sellers then increased selection. Low-cost structure supports low-price commitment. It's brilliant! Every wheel turn creates acceleration.
Where from here?
Flywheel over sales funnel! Consider these business terms.
