[{"data":1,"prerenderedAt":1195},["ShallowReactive",2],{"content-query-Vyb8apfUZH":3},{"_path":4,"_dir":5,"_draft":6,"_partial":6,"_locale":7,"title":8,"description":7,"body":9,"_type":1189,"_id":1190,"_source":1191,"_file":1192,"_stem":1193,"_extension":1194},"/writings/sigma","writings",false,"","Sigma:  a general model for digital token distribution and liquidity management through a singular, continuously accessible global market.",{"type":10,"children":11,"toc":1165},"root",[12,27,34,40,53,59,72,77,82,114,117,120,126,133,152,170,201,207,212,217,223,254,259,265,270,296,301,312,317,335,340,345,359,364,369,387,399,417,422,428,434,439,444,449,461,466,474,480,485,490,495,507,512,520,526,531,536,546,551,556,561,573,578,588,598,608,618,636,641,646,658,663,675,680,685,691,696,701,706,718,723,728,740,745,751,756,761,767,785,803,809,814,819,831,836,848,853,859,876,881,886,891,896],{"type":13,"tag":14,"props":15,"children":17},"element","h1",{"id":16},"sigma-a-general-model-for-digital-token-distribution-and-liquidity-management-through-a-singular-continuously-accessible-global-market",[18,21,25],{"type":19,"value":20},"text","Sigma: ",{"type":13,"tag":22,"props":23,"children":24},"br",{},[],{"type":19,"value":26}," a general model for digital token distribution and liquidity management through a singular, continuously accessible global market.",{"type":13,"tag":28,"props":29,"children":31},"h2",{"id":30},"abstract",[32],{"type":19,"value":33},"Abstract",{"type":13,"tag":35,"props":36,"children":37},"p",{},[38],{"type":19,"value":39},"We present a novel system for monetizing a product/service with a blockchain-enabled digital token. The proposed system allows the product or service it underpins to achieve optimal value capture, predictable pricing and perpetual accessibility resistant to censorship. Sigma is a smart contract consisting of a digital token and its dedicated liquidity pool with bonding curve pricing mechanism - an automated market maker. The accomplished arrangement allows independence from external sources of liquidity (traditional market makers) and, in certain cases, venture funding for both going to market and keeping the underlying product/service self-sustainable under varying conditions. The parameters of the system can be adjusted to best meet each project type and desired outcomes. In this paper we present an illustrative set of parameters and release them in conjunction with a reference implementation. We expect to release more variations following this publication. ",{"type":13,"tag":35,"props":41,"children":42},{},[43,45],{"type":19,"value":44},"To review the code, please visit: ",{"type":13,"tag":46,"props":47,"children":51},"a",{"href":48,"rel":49},"https://github.com/gagravc/sigma",[50],"nofollow",[52],{"type":19,"value":48},{"type":13,"tag":28,"props":54,"children":56},{"id":55},"_1-introduction",[57],{"type":19,"value":58},"1. INTRODUCTION ",{"type":13,"tag":35,"props":60,"children":61},{},[62,64,70],{"type":19,"value":63},"The advent of Bitcoin ",{"type":13,"tag":65,"props":66,"children":67},"span",{},[68],{"type":19,"value":69},"1",{"type":19,"value":71}," has spawned tens of thousands, if not more, private digital currencies and assets that leverage blockchain technology for censorship resistant global distribution. However the cottage industry that has sprung around digital assets since 2009, has so far abused its privilege of unrestricted token creation, which results in >90% of these instruments fading into irrelevance over short time, often pulling down otherwise worthy projects.",{"type":13,"tag":35,"props":73,"children":74},{},[75],{"type":19,"value":76},"Absent further innovation in economic design, some issuers are now forced to revert back to originally paper-based (and thus functionally limited) equity and credit asset mechanisms - such as cash flow distributions and buy-backs - to sustain their tokens’ market value. This approach diminishes digital tokens' ability to provide unstoppable access to underlying products at global scale, given regulatory restrictions around cash flow assets, and also undermines value capture given most blockchain applications get only a fracture of generated revenues, usually split with a decentralized set of service providers. In this paper we aim to propose, first and foremost, a novel approach to value capture without resorting to mechanics of securities and similar financial (paper) instruments.",{"type":13,"tag":35,"props":78,"children":79},{},[80],{"type":19,"value":81},"Before we discuss Sigma in detail, we would like to dedicate some attention to key motivating factors behind our design:",{"type":13,"tag":83,"props":84,"children":85},"ul",{},[86,98,106],{"type":13,"tag":87,"props":88,"children":89},"li",{},[90,96],{"type":13,"tag":91,"props":92,"children":93},"strong",{},[94],{"type":19,"value":95},"Network effects",{"type":19,"value":97}," (as a proxy for value)",{"type":13,"tag":87,"props":99,"children":100},{},[101],{"type":13,"tag":91,"props":102,"children":103},{},[104],{"type":19,"value":105},"Stable product/service pricing",{"type":13,"tag":87,"props":107,"children":108},{},[109],{"type":13,"tag":91,"props":110,"children":111},{},[112],{"type":19,"value":113},"Global access",{"type":13,"tag":22,"props":115,"children":116},{},[],{"type":13,"tag":22,"props":118,"children":119},{},[],{"type":13,"tag":28,"props":121,"children":123},{"id":122},"_2-key-motivations",[124],{"type":19,"value":125},"2. KEY MOTIVATIONS",{"type":13,"tag":127,"props":128,"children":130},"h3",{"id":129},"_21-network-effects",[131],{"type":19,"value":132},"2.1. NETWORK EFFECTS",{"type":13,"tag":35,"props":134,"children":135},{},[136,138,150],{"type":19,"value":137},"As researched by economists in the recent decades ",{"type":13,"tag":139,"props":140,"children":141},"sup",{},[142],{"type":13,"tag":46,"props":143,"children":148},{"href":144,"ariaDescribedBy":145,"dataFootnoteRef":7,"id":147},"#user-content-fn-2",[146],"footnote-label","user-content-fnref-2",[149],{"type":19,"value":69},{"type":19,"value":151},", the so-called “network effects” of a technology contribute heavily to user lock-in that is occurring as its adoption grows - which allows the product to improve over time and results in users converging on a standard on which other technologies can be built. The real network effect, according to this perspective, is not just in the number of users or providers (for social networks or two-sided platforms, respectively), but the overall adoption of a technology within its vertical, which in turn helps it get even more entrenched as a component to further technological development elsewhere. Thus, network effects naturally bring extensively utilized tech products and services to the forefront of a category and protect them from competition by making them fundamental to subsequent developments in their and adjacent domains.",{"type":13,"tag":35,"props":153,"children":154},{},[155,157,168],{"type":19,"value":156},"These properties fit nicely with blockchain applications’ inherent composability and a broader framework of the so-called Web 3.0, which describes internet applications and software protocols as a stack of interconnected token-powered networks ",{"type":13,"tag":139,"props":158,"children":159},{},[160],{"type":13,"tag":46,"props":161,"children":165},{"href":162,"ariaDescribedBy":163,"dataFootnoteRef":7,"id":164},"#user-content-fn-3",[146],"user-content-fnref-3",[166],{"type":19,"value":167},"2",{"type":19,"value":169},". ",{"type":13,"tag":35,"props":171,"children":172},{},[173,175,186,188,199],{"type":19,"value":174},"We do not intend to provide a methodology to evaluate network effects in investment terms, which have been many since the first attempt by Metcalfe ",{"type":13,"tag":139,"props":176,"children":177},{},[178],{"type":13,"tag":46,"props":179,"children":183},{"href":180,"ariaDescribedBy":181,"dataFootnoteRef":7,"id":182},"#user-content-fn-4",[146],"user-content-fnref-4",[184],{"type":19,"value":185},"3",{"type":19,"value":187},", and none really robust. But we do allow for the network effects to be implicitly accounted for in our flow-based value accrual mechanism through a bonding curve ",{"type":13,"tag":139,"props":189,"children":190},{},[191],{"type":13,"tag":46,"props":192,"children":196},{"href":193,"ariaDescribedBy":194,"dataFootnoteRef":7,"id":195},"#user-content-fn-5",[146],"user-content-fnref-5",[197],{"type":19,"value":198},"4",{"type":19,"value":200}," that prices wider distributed tokens higher.",{"type":13,"tag":127,"props":202,"children":204},{"id":203},"_22-stable-pricing",[205],{"type":19,"value":206},"2.2. STABLE PRICING",{"type":13,"tag":35,"props":208,"children":209},{},[210],{"type":19,"value":211},"Given the nascent and speculative nature of digital assets, price volatility is a major blocker to adoption if the underlying product or service is priced with or accessed through a token. Unpredictability of service pricing also creates issues for its providers/contributors, which often represent a decentralized set of actors coordinated by nothing more than the token itself. But even if a single team is the primary operator behind such a service, volatility in $ terms of token-denominated revenue forces them to continuously maximize token sales, which creates unnecessary overhead and misaligns long- and short-term goals of the project.",{"type":13,"tag":35,"props":213,"children":214},{},[215],{"type":19,"value":216},"We present a solution that allows for a token-powered “app” or software protocol to experience significant token price appreciation (given adoption), while keeping the underlying product/service price predictable and avoiding any external dependencies. ",{"type":13,"tag":127,"props":218,"children":220},{"id":219},"_23-global-access",[221],{"type":19,"value":222},"2.3. GLOBAL ACCESS",{"type":13,"tag":35,"props":224,"children":225},{},[226,228,239,241,252],{"type":19,"value":227},"The original promise of blockchains-as-computers introduced by Ethereum in 2014 ",{"type":13,"tag":139,"props":229,"children":230},{},[231],{"type":13,"tag":46,"props":232,"children":236},{"href":233,"ariaDescribedBy":234,"dataFootnoteRef":7,"id":235},"#user-content-fn-6",[146],"user-content-fnref-6",[237],{"type":19,"value":238},"5",{"type":19,"value":240},", extends the decentralized and censorship resistant properties of Bitcoin to other assets and products/services. It is achieved through the use of smart contracts ",{"type":13,"tag":139,"props":242,"children":243},{},[244],{"type":13,"tag":46,"props":245,"children":249},{"href":246,"ariaDescribedBy":247,"dataFootnoteRef":7,"id":248},"#user-content-fn-7",[146],"user-content-fnref-7",[250],{"type":19,"value":251},"6",{"type":19,"value":253}," - deterministic software programs that act like “digital vending machines”, autonomously offering pre-defined functions to economic agents that interact with them. A set of smart contracts that represents an application or agentic program can encompass a digital business in its entirety.\n \nPaired with public blockchains' censorship resistance, smart contracts open possibilities for perpetual services on the internet that are unstoppable. This is an extremely useful property when paired with global distribution that blockchains also allow for - creating enormous economic incentives for programmers while lifting extra operational weight off their shoulders. Unstoppable, globally accessible smart contracts thus represent an opportunity to create a perfect market for digital services.",{"type":13,"tag":35,"props":255,"children":256},{},[257],{"type":19,"value":258},"The token system proposed in this paper allows for any team or community of contributors to generate economic rent from their code without having to directly deal with revenue streams, which entails taking on operational and legal liabilities. This, in turn, allows the product/service they may program to maintain global and unrestricted accessibility - as regulatory compliance and operational burdens are significantly lowered and offloaded to an individual level.",{"type":13,"tag":28,"props":260,"children":262},{"id":261},"_3-overview",[263],{"type":19,"value":264},"3. OVERVIEW",{"type":13,"tag":35,"props":266,"children":267},{},[268],{"type":19,"value":269},"The Sigma system is a single smart contract with two interconnected modules, deployed on a public blockchain: ",{"type":13,"tag":83,"props":271,"children":272},{},[273,278],{"type":13,"tag":87,"props":274,"children":275},{},[276],{"type":19,"value":277}," a digital token, with mechanics determined by the administrator of the contract (“admin”, for short): “subscription/access token, “in-platform currency\", “governance token”, “asset-backed token”, etc. ",{"type":13,"tag":87,"props":279,"children":280},{},[281,283,294],{"type":19,"value":282}," a token liquidity pool, functioning as an automated market maker (AMM) ",{"type":13,"tag":139,"props":284,"children":285},{},[286],{"type":13,"tag":46,"props":287,"children":291},{"href":288,"ariaDescribedBy":289,"dataFootnoteRef":7,"id":290},"#user-content-fn-8",[146],"user-content-fnref-8",[292],{"type":19,"value":293},"7",{"type":19,"value":295},". The AMM is used for standard market operations as well as token distributions outside of market sales: user incentives, partnership/grant allocations, public pre-sales, etc. Thus, the liquidity pool is both the source of primary token distribution and the main trading venue.",{"type":13,"tag":35,"props":297,"children":298},{},[299],{"type":19,"value":300},"“The admin” here can mean a single programmer, a team or a decentralized community.",{"type":13,"tag":35,"props":302,"children":303},{},[304,306,311],{"type":19,"value":305},"When employing Sigma, the token contract is created by the admin along with a dedicated liquidity pool/AMM. The cap on the supply of tokens or rules governing further issuance are set in advance and are clearly stated in the contract with the admin minting tokens within those pre-defined rules. But instead of the issuer transferring them out post-mint, the way most tokens hit circulation is through the liquidity pool’s bonding curve (except for e.g. admin’s own allocation which shouldn't count as value-accretive distribution). Thus, ",{"type":13,"tag":91,"props":307,"children":308},{},[309],{"type":19,"value":310},"the amount of tokens distributed through or sold back into the AMM - the net circulating supply - determines the token price at any given time",{"type":19,"value":169},{"type":13,"tag":35,"props":313,"children":314},{},[315],{"type":19,"value":316},"The token price is set according to a bonding curve with a sigmoid-shaped curvature. Its shape reflects product lifecycle phases: ",{"type":13,"tag":83,"props":318,"children":319},{},[320,325,330],{"type":13,"tag":87,"props":321,"children":322},{},[323],{"type":19,"value":324},"starting with early adoption which is expressed by a more gradual curve; ",{"type":13,"tag":87,"props":326,"children":327},{},[328],{"type":19,"value":329},"followed by a growth/expansion phase with a steeper slope; ",{"type":13,"tag":87,"props":331,"children":332},{},[333],{"type":19,"value":334},"and maturity stage, with more stable price, asymptotically reaching towards the upper boundary.",{"type":13,"tag":35,"props":336,"children":337},{},[338],{"type":19,"value":339},"The shape of the bonding curve is illustrated in Figure 1 below. ",{"type":13,"tag":35,"props":341,"children":342},{},[343],{"type":19,"value":344},"The admin sets a starting price and its terminal target, as well as trigger points on the bonding curve - A and B in Fig.1 - that change the pricing formula in a bi-directional way. The switch points are determined based on project stage-specific considerations (e.g. growth phase vs maturity phase) according to admin’s expectations. All of these inputs can be transparently recalibrated if needed - to better reflect actual economics of the service post-launch.",{"type":13,"tag":35,"props":346,"children":347},{},[348,353],{"type":13,"tag":349,"props":350,"children":352},"img",{"alt":7,"src":351},"/images/writings/bonding-curve.jpg",[],{"type":13,"tag":354,"props":355,"children":356},"em",{},[357],{"type":19,"value":358},"Figure 1. The piecewise-defined bonding curve of Sigma (not-to-scale)",{"type":13,"tag":35,"props":360,"children":361},{},[362],{"type":19,"value":363},"For economic flexibility, as well as analytical and computational feasibility, the Sigma AMM is actually combining three separate logistic functions that make up the sigmoid shape of the curve, as depicted in Fig.1. The functions are piecewise-defined, with the negative subdomain corresponding to the net negative token demand. The two positive subdomains, termed \"lower\" and \"upper” branches, are also set up separately. The trigger points A and B essentially denote when the price function switches from one branch to another.",{"type":13,"tag":35,"props":365,"children":366},{},[367],{"type":19,"value":368},"As mentioned earlier, since Sigma is the only source of primary token distribution, the token amount in circulation - not e.g. the liquidity ratio between the token and its trading pair - is the driver of the marginal price on the bonding curve. Thus, the AMM does not require initial liquidity to set a price for a token, solving for a “cold start” problem. It can launch with 0 pair asset units (e.g. $ETH, $SOL or $USD) and accumulate them as users buy the token for product/service use. The only important note here is that Sigma presumes that the token launch follows the product launch and the token is closely tied to product usage or other sources of organic inbound liquidity. But it also allows for free token distributions, such as “airdrops\", to affect the price on the curve positively without requiring any pair asset liquidity to match them in the pool - accounting for the network effects such distributions generate. ",{"type":13,"tag":35,"props":370,"children":371},{},[372,374,385],{"type":19,"value":373},"To absorb all of the token supply sold back into the AMM, Sigma accumulates more liquidity and significantly improves price resistance to any selling volume compared to common bonding curve functions, like e.g. the Constant Product ",{"type":13,"tag":139,"props":375,"children":376},{},[377],{"type":13,"tag":46,"props":378,"children":382},{"href":379,"ariaDescribedBy":380,"dataFootnoteRef":7,"id":381},"#user-content-fn-9",[146],"user-content-fnref-9",[383],{"type":19,"value":384},"8",{"type":19,"value":386},". One can see in Figure 2 that when reaching the same price (Y axis) in Point A, Sigma accumulates more than twice as much of the pair asset (the area between the curve and the X axis) than a constant-product-based curve, while also allowing for bigger price appreciation earlier. ",{"type":13,"tag":35,"props":388,"children":389},{},[390,394],{"type":13,"tag":349,"props":391,"children":393},{"alt":7,"src":392},"/images/writings/pricing-and-liquidity.jpg",[],{"type":13,"tag":354,"props":395,"children":396},{},[397],{"type":19,"value":398},"Figure 2. Pricing and liquidity: sigmoid function vs constant product function",{"type":13,"tag":35,"props":400,"children":401},{},[402,404,415],{"type":19,"value":403},"The Sigma liquidity pool not only becomes the primary source of token pricing, but through that - also of product/service pricing. The service pricing is described in Section 4.2 below and is an important achievement, alleviating the need for any external value anchor (e.g. $USD) and dependency on its sources like oracle services ",{"type":13,"tag":139,"props":405,"children":406},{},[407],{"type":13,"tag":46,"props":408,"children":412},{"href":409,"ariaDescribedBy":410,"dataFootnoteRef":7,"id":411},"#user-content-fn-10",[146],"user-content-fnref-10",[413],{"type":19,"value":414},"9",{"type":19,"value":416},", which are often points of failure or manipulation. This property strengthens the autonomy of the service implementing Sigma.",{"type":13,"tag":35,"props":418,"children":419},{},[420],{"type":19,"value":421},"Another Sigma achievement is allowing the contributors (whether a single team or a community) to monetize their tokens without having to engage market makers or go through centralized exchange listings, both of which involve significant financial undertakings and often adversary agent-principal dynamics.",{"type":13,"tag":28,"props":423,"children":425},{"id":424},"_4-pricing-mechanism",[426],{"type":19,"value":427},"4. PRICING MECHANISM ",{"type":13,"tag":127,"props":429,"children":431},{"id":430},"_41-token-pricing",[432],{"type":19,"value":433},"4.1 TOKEN PRICING",{"type":13,"tag":35,"props":435,"children":436},{},[437],{"type":19,"value":438},"As described in the previous section, the exchange rate of the token is decided by net accumulated token buyout, i.e. the net volume of tokens distributed out of or sold back into the AMM. The value representing it at any given time determines the point on the bonding curve at which the price will clear at that time. The terminal target for the token price should be identified in advance when setting Sigma parameters, but can be updated in the contract for better precision as the project gathers more usage data. Thus, the contract admin directly defines only the starting and the target price. The sigmoid slope, on the other hand, is established via off-chain numerical solutions and is therefore controlled indirectly (except for the branch-switching trigger points). ",{"type":13,"tag":35,"props":440,"children":441},{},[442],{"type":19,"value":443},"To illustrate Sigma in concrete terms we modeled it for a token-gated consumer application with a subscription-style monetization: users need to buy and hold a certain amount of tokens to access the service. For the sake of simplicity the amount is a one-time purchase for lifetime access. This token mechanism may not cover all potential applications, but is most optimal for correlating demand with buy pressure, and thus very straightforward for our modeling purposes. Sigma can be applied to any other token functionality just as easily.",{"type":13,"tag":35,"props":445,"children":446},{},[447],{"type":19,"value":448},"We assume consistent growth of monthly active users in multiple scenarios (from hundreds to single-digit millions at terminal state), with admin costs consisting of user acquisition (one-time) and servicing (ongoing), the latter rising as the product grows. The costs translate into the monthly selling pressure coming from the admin. There’s also additional selling pressure assumed in our models that comes from the users, as their subscription price drops in token terms (while maintaining relative stability in $USD), prompting users to sell all of their surplus.  The key model inputs, based on company surveys and market research, are covered in Section 5, with a median token price modeling result reported below.",{"type":13,"tag":35,"props":450,"children":451},{},[452,456],{"type":13,"tag":349,"props":453,"children":455},{"alt":7,"src":454},"/images/writings/token-log-price.jpg",[],{"type":13,"tag":354,"props":457,"children":458},{},[459],{"type":19,"value":460},"Figure 3. Simple average token log price across three growth scenarios for a hypothetical token-gated consumer application: Conservative, Moderate and Homerun; monthly intervals",{"type":13,"tag":35,"props":462,"children":463},{},[464],{"type":19,"value":465},"In Figure 3 above, the token price is modeled on the number of monthly active users (only utility-based demand), reflected in the aggregate token buy pressure (one-time purchase per user) and offset by the selling pressure coming from application developers covering their $-denominated costs, and users who no longer need to keep as many tokens to gain access to the application. We can see that the price trend is firmly up and to the right even under expectation of consistent selling pressure. Specifically, the median of the modeled scenarios gives us a 565x appreciation over a course of 3 years following launch! ",{"type":13,"tag":35,"props":467,"children":468},{},[469],{"type":13,"tag":91,"props":470,"children":471},{},[472],{"type":19,"value":473},"Any other business logic/token mechanics, including but not limited to: transaction fee collection, direct sales to users, staking mechanics, in-platform currency, etc. - can all be implemented in Sigma with varying degrees of adjustments to the base model.",{"type":13,"tag":127,"props":475,"children":477},{"id":476},"_42-service-pricing",[478],{"type":19,"value":479},"4.2 SERVICE PRICING",{"type":13,"tag":35,"props":481,"children":482},{},[483],{"type":19,"value":484},"The amount of tokens required to hold or stake (i.e. lock in the designated smart contract) for application access in our example model, is closely related to the token price, but not directly correlated. It may follow the project growth trajectory and rise in pair asset terms (e.g. $USD), but at a different, much slower pace than the token exchange rate. In our example models we start with a conservative 55$ lifetime subscription price, which under different scenarios gradually rises to a maximum value of ~$150 over ~6 years and then stabilizes with project maturity. It is orders of magnitude less volatile than the token price in the same period.",{"type":13,"tag":35,"props":486,"children":487},{},[488],{"type":19,"value":489},"The service price curve is expressed in a logistic function similar to the token price curve, and similarly starts at the admin-defined value but is further set by the market dynamics. The service price may respond to the market in either direction - including towards depreciation over time in e.g. $USD while the token itself appreciates against it. So, the admin determines not only the starting value but also the overall direction (inflationary or deflationary) of service pricing. Yet, its actual value at each point in time is a function of its response to the token price dynamics.",{"type":13,"tag":35,"props":491,"children":492},{},[493],{"type":19,"value":494},"We assumed cost inflation and growing service offering in our example models, which should drive the subscription price up. It increases in $USD terms over the first 5-6 years of the product's lifecycle - corresponding to the exponential product adoption and token price growth. However, even in the case of extreme surplus to the token price, the product pricing remained relatively stable. In our most aggressive scenarios the token price rose 14 800% over ~6 years, with the service price jumping only 175% - even with our bold annual inflation input of 30%. The jump in service price could have been more muted if we had set more modest targets.",{"type":13,"tag":35,"props":496,"children":497},{},[498,502],{"type":13,"tag":349,"props":499,"children":501},{"alt":7,"src":500},"/images/writings/example-economic-model.jpg",[],{"type":13,"tag":354,"props":503,"children":504},{},[505],{"type":19,"value":506},"Figure 4. Service pricing, token exchange rate, and token holding requirement (subscription amount in tokens) in the example economic model",{"type":13,"tag":35,"props":508,"children":509},{},[510],{"type":19,"value":511},"Example of a service price function dynamics within a single scenario-based simulation is reported above. Figure 4 depicts the relation between the service price in $USD, token exchange rate, and the service price denominated in tokens - all driven by the aggregate token buyout from the Sigma pool over time (X axis).",{"type":13,"tag":35,"props":513,"children":514},{},[515],{"type":13,"tag":91,"props":516,"children":517},{},[518],{"type":19,"value":519},"One can similarly model e.g.: transaction fee dynamics in response to volume; direct sale price adjustments in response to demand; network staking requirements in relation to the aggregate stake - and other product/service pricing curves for differing token mechanics to the one presented here.",{"type":13,"tag":28,"props":521,"children":523},{"id":522},"_5-liquidity-management",[524],{"type":19,"value":525},"5. LIQUIDITY MANAGEMENT",{"type":13,"tag":35,"props":527,"children":528},{},[529],{"type":19,"value":530},"The distribution of supply and token monetization is the main concern of this section. Balancing selling pressure with inbound liquidity, especially in the early stages of the project often marked by heavier distribution, is at the core of solving for good token economics. The key prerequisite is actual utility demand, which is up for token creators to solve for, but the aim is for Sigma to simplify everything else.",{"type":13,"tag":35,"props":532,"children":533},{},[534],{"type":19,"value":535},"An important property of this proposed system is that it allows for complete disconnect between product revenues and admin-controlled account inflows while maintaining value capture. It is key for keeping the coders behind a digital service shielded from burdens imposed on revenue-generating businesses and yield-generating financial assets (i.e. securities) - as applicable in most jurisdictions. This approach lowers innovation barriers while keeping economic incentives intact. ",{"type":13,"tag":35,"props":537,"children":538},{},[539,541],{"type":19,"value":540},"The token becomes the primary vessel for capturing in- and outbound value flows instead: users buy into the token to use the product, admin then sells some tokens into the pool to monetize those gains. Under conditions of growing demand this should result in a healthy token appreciation. ",{"type":13,"tag":91,"props":542,"children":543},{},[544],{"type":19,"value":545},"All the value inflow into the product - regardless of the underlying mechanics, which may differ according to project specifics - should be captured directly by the token and monetized via token sales back into the pool, which is the core principle underlying Sigma.",{"type":13,"tag":35,"props":547,"children":548},{},[549],{"type":19,"value":550},"However, a financial strategy is necessary to safeguard token value and monetize it effectively. In addition to admin’s initial token allocation, we added a mechanism to let them mint and monetize extra tokens as the product/service grows, without diluting the supply (fixed supply is our basis, but isn’t mandatory). The source of those additional tokens corresponds to the fees imposed on users. A mechanism more tailored to a specific product can be chosen, but for our “access token” example we chose levying a fee on users that leave early - i.e. take a small cut from the tokens they sell/unstake (which constitutes leaving) - to balance with user churn and heavy incentives early in the project’s lifecycle. Those fees are then “burned”, while a corresponding amount is added to the admin’s unminted token allocation. The admin can issue and monetize additional tokens up to the aggregate value of accumulated “burns” in the period.",{"type":13,"tag":35,"props":552,"children":553},{},[554],{"type":19,"value":555},"The scenario analysis reported below assumes reliance on fees ranging between 0.6%-6%, imposed on users for the 6 years following launch. The token selling volume on behalf of the admin is assumed to be made up of monthly costs, including user acquisition, operational expenses and a 10% profit margin (reflecting the lean nature of blockchain businesses). Presuming a positive adoption trend, this strategy is more than enough to provide funding for growth and operations under our scenario-based modeling. Additionally, this approach allows the token admin to allocate more of the initial supply towards incentives and other distributions instead of themselves - as they can expect to accumulate more tokens with product growth.",{"type":13,"tag":35,"props":557,"children":558},{},[559],{"type":19,"value":560},"Within the outlined framework, three operational scenarios (denoted Conservative, Moderate and Homerun) and a negative scenario (denoted Pessimistic) were developed. Respective assumptions for adoption dynamics are summarized in Table 1 below.",{"type":13,"tag":35,"props":562,"children":563},{},[564,568],{"type":13,"tag":349,"props":565,"children":567},{"alt":7,"src":566},"/images/writings/scenario-assumtions.jpg",[],{"type":13,"tag":354,"props":569,"children":570},{},[571],{"type":19,"value":572},"Table 1. Scenario assumptions",{"type":13,"tag":35,"props":574,"children":575},{},[576],{"type":19,"value":577},"For the simulations we also assumed the following parameters:",{"type":13,"tag":35,"props":579,"children":580},{},[581,586],{"type":13,"tag":91,"props":582,"children":583},{},[584],{"type":19,"value":585},"Cost Structure",{"type":19,"value":587},": $3 per-user onboarding cost (one-time), $1.8 per-user servicing (ongoing) cost",{"type":13,"tag":35,"props":589,"children":590},{},[591,596],{"type":13,"tag":91,"props":592,"children":593},{},[594],{"type":19,"value":595},"Profit Margin",{"type":19,"value":597},": 10%",{"type":13,"tag":35,"props":599,"children":600},{},[601,606],{"type":13,"tag":91,"props":602,"children":603},{},[604],{"type":19,"value":605},"Starting Service Price",{"type":19,"value":607},": $55",{"type":13,"tag":35,"props":609,"children":610},{},[611,616],{"type":13,"tag":91,"props":612,"children":613},{},[614],{"type":19,"value":615},"Service Price Inflation in $USD",{"type":19,"value":617}," (~6-year period): ",{"type":13,"tag":83,"props":619,"children":620},{},[621,626,631],{"type":13,"tag":87,"props":622,"children":623},{},[624],{"type":19,"value":625},"175% (Moderate, Homerun)",{"type":13,"tag":87,"props":627,"children":628},{},[629],{"type":19,"value":630},"125% (Conservative)",{"type":13,"tag":87,"props":632,"children":633},{},[634],{"type":19,"value":635},"23% (Pessimistic)",{"type":13,"tag":35,"props":637,"children":638},{},[639],{"type":19,"value":640},"The service price (per-user revenue) reaches a plateau in our simulations as the project approaches maturity and token price volatility drops. However, the admin may modify the service pricing function to keep it growing (or lowering) instead, even while the token price is stabilized.",{"type":13,"tag":35,"props":642,"children":643},{},[644],{"type":19,"value":645},"Figure 5 below shows token price plots under the four scenarios. The extreme volatility of months 11-25 on the graphs is an artifact of low time resolution and intense within-period token turnover. To approximate the equilibrium within-period rate, smoothed moving average (7-day) values were used for Moderate and Homerun scenarios. ",{"type":13,"tag":35,"props":647,"children":648},{},[649,653],{"type":13,"tag":349,"props":650,"children":652},{"alt":7,"src":651},"/images/writings/scenario-analysis.jpg",[],{"type":13,"tag":354,"props":654,"children":655},{},[656],{"type":19,"value":657},"Figure 5. Scenario analysis of the token price dynamics, monthly intervals",{"type":13,"tag":35,"props":659,"children":660},{},[661],{"type":19,"value":662},"The quantitative simulation results from our model also describe periodic cash deficit depths, aggregate buyout volumes and minimum admin reserve requirements. These results are summarized numerically in Table 2 below.",{"type":13,"tag":35,"props":664,"children":665},{},[666,670],{"type":13,"tag":349,"props":667,"children":669},{"alt":7,"src":668},"/images/writings/simulation-results.jpg",[],{"type":13,"tag":354,"props":671,"children":672},{},[673],{"type":19,"value":674},"Table 2. Simulation results",{"type":13,"tag":35,"props":676,"children":677},{},[678],{"type":19,"value":679},"In the long run, the period preceding maturity should be strategically dedicated to token reserve accumulation, while net reserve depletion is the behavioral mode for the mature state of the project. However, the admin may implement whichever strategy most fits their needs. Thus, Sigma allows for continuous monetization of the token by letting the token admin maintain a healthy stash for perpetual funding as opposed to established market practice of drawing out initial team/community token reserves over time.",{"type":13,"tag":35,"props":681,"children":682},{},[683],{"type":19,"value":684},"As noted earlier, for illustrative purposes we chose token-gated access mechanics, which are well-suited for the majority of application-level blockchain use cases. But other mechanisms for both the token utility and the source of admin’s additional mint may be explored using Sigma.",{"type":13,"tag":28,"props":686,"children":688},{"id":687},"_6-arbitrage-with-external-sources-of-liquidity",[689],{"type":19,"value":690},"6. ARBITRAGE WITH EXTERNAL SOURCES OF LIQUIDITY ",{"type":13,"tag":35,"props":692,"children":693},{},[694],{"type":19,"value":695},"The scenario analysis reported in Sections 5 suggests robustness of the token and service pricing mechanisms under a simple financial management strategy in a range of scenarios. However, the exclusiveness of Sigma as the trading venue for the token, at least during early phases of the project, seems to be necessary for its success.",{"type":13,"tag":35,"props":697,"children":698},{},[699],{"type":19,"value":700},"For an arbitrage to be effective against Sigma’s synthetic pricing one needs to be able to buy the token elsewhere with less upside volatility and sell it back into the Sigma AMM for a higher price. For a utility-maximizing agent, an optimal behaviour is to split every token transaction between the two trading floors - Sigma and a constant product AMM - in order to minimize the average purchase price or maximize the average sale price. A constant product pool of sufficient depth is capable of keeping the marginal price practically stable up to a certain transaction size. Any synthetic pricing curve (including Sigma) does not hold this property by definition and will always change the price with each transaction. ",{"type":13,"tag":35,"props":702,"children":703},{},[704],{"type":19,"value":705},"However, a natural economic protection against arbitrage exists. Sigma’s overall liquidity-optimizing property provides a practical barrier, as illustrated in Figure 6 below. The axes of the diagram represent respective volumes of the two assets within a pool: X axis denotes the token, (capped at 1bn supply) and Y axis shows corresponding amount of pair asset ($USD in our example). The constant-product curve has a hyperbolic convex shape, shown in dark blue. The curve’s distance from the origin corresponds to the total accumulated buyout of one asset versus the other. A hypothetical constant price function - i.e. a pool that maintains the same exchange rate despite changes in each of the assets’ supply - is shown in light blue. The Sigma function is shown in purple. ",{"type":13,"tag":35,"props":707,"children":708},{},[709,713],{"type":13,"tag":349,"props":710,"children":712},{"alt":7,"src":711},"/images/writings/liquidity-requirements.jpg",[],{"type":13,"tag":354,"props":714,"children":715},{},[716],{"type":19,"value":717},"Figure 6. Liquidity requirements for comparative price moves in Sigma vs Constant-Product vs Constant-Price",{"type":13,"tag":35,"props":719,"children":720},{},[721],{"type":19,"value":722},"Accumulation of a considerable token volume is only possible when the purchase price is low enough. Thus, a Sigma token may not be readily available in quantities sufficient to create deep external pools with low enough volatility to incentivize arbitrage. To get to the same price level, marked by points A and B in Fig.6 , Sigma needs to sell ~9x less tokens than the constant product pool. The Sigma price accelerates sharply during the “growth phase” (bottom right corner of the graph), accumulating $USD liquidity up to the volume equivalent to almost complete sell-out of the constant product pool. Constant product has to sell ~950m tokens (95% of supply) to accumulate the same amount of $USD as accrued by a 20% sell-out from Sigma - as shown by points C and D. After reaching maturity, further liquidity accumulation in Sigma is equivalent to the constant-price function (light blue line). This liquidity depth can preclude formation of competing third-party AMM pools long after the initial growth phase as well.",{"type":13,"tag":35,"props":724,"children":725},{},[726],{"type":19,"value":727},"Despite the economic barrier outlined above, any large enough external source of liquidity in theory still provides a persistent arbitrage opportunity, negatively affecting Sigma’s pricing power. Figure 7 below depicts the results of a simplified analytic simulation for a market system consisting of a linear synthetic price curve and a constant product curve. We used the same set of assumptions and timeline as in Sigma simulations, just a more straightforward synthetic pricing function for illustrative simplicity. The closed market scenario (dark blue line) refers to an absence of third-party liquidity pools, while the open market scenario (light blue line) shows the arbitrage equilibrium price in both AMMs. As one can see, the existence of an arbitrage depresses the price (Y axis) until the synthetic curve changes its slope to a more gradual one (maturity phase), where arbitrage actually slightly pulls the price upward instead.",{"type":13,"tag":35,"props":729,"children":730},{},[731,735],{"type":13,"tag":349,"props":732,"children":734},{"alt":7,"src":733},"/images/writings/price-action-scenario.jpg",[],{"type":13,"tag":354,"props":736,"children":737},{},[738],{"type":19,"value":739},"Figure 7. Price action scenario analysis under a condition of “deep-enough” external liquidity pool, monthly intervals",{"type":13,"tag":35,"props":741,"children":742},{},[743],{"type":19,"value":744},"To mitigate the negative effects of arbitrage, Sigma token issuers may consider 3 naive solutions, with varying degrees of limitations imposed on market turnover of the token - to be considered for implementation up to a certain stage of project maturity: ",{"type":13,"tag":127,"props":746,"children":748},{"id":747},"_1-distribution-only-use-of-the-sigma-bonding-curve",[749],{"type":19,"value":750},"1. Distribution-only use of the Sigma bonding curve.",{"type":13,"tag":35,"props":752,"children":753},{},[754],{"type":19,"value":755},"The pool is used only for primary distribution where the bonding curve determines the marginal price of the next sold token. The accumulated liquidity can be used by the admin to monetize their holdings - also affecting price as in the original design. But the tokens cannot be sold back into the curve by third-parties, who are also tasked with establishing secondary markets for themselves. ",{"type":13,"tag":35,"props":757,"children":758},{},[759],{"type":19,"value":760},"While simple and thus attractive, this approach ignores that there may not be enough demand for issuance of new tokens once external markets allow access to already distributed tokens - essentially creating the same arbitrage dynamics. To partially mitigate it, the admin may route inbound users through Sigma using their platform’s frontend. However, such a “patch” solution is at the very least risking their ability to fully monetize token holdings since utility-maximizing buyers are still free to use external pools. ",{"type":13,"tag":127,"props":762,"children":764},{"id":763},"_2-sales-into-the-bonding-curve-allowed-only-for-wallets-that-never-transfer-their-tokens-further",[765],{"type":19,"value":766},"2. Sales into the bonding curve allowed only for wallets that never transfer their tokens further.",{"type":13,"tag":35,"props":768,"children":769},{},[770,772,783],{"type":19,"value":771},"This approach allows for Sigma to be used for both primary distribution and secondary market but only to a limited set of token holders - utility-driven buyers or non-arbitrage-driven speculators. Any transfer out of the wallet that originally bought the tokens blocks its access to the Sigma AMM for sales. It should essentially kill any direct arbitrage, while leaving room for derivative-based external trading floors: for wrapped assets, backed by held tokens; or synthetic derivatives (e.g. perpetual futures ",{"type":13,"tag":139,"props":773,"children":774},{},[775],{"type":13,"tag":46,"props":776,"children":780},{"href":777,"ariaDescribedBy":778,"dataFootnoteRef":7,"id":779},"#user-content-fn-11",[146],"user-content-fnref-11",[781],{"type":19,"value":782},"10",{"type":19,"value":784},").",{"type":13,"tag":35,"props":786,"children":787},{},[788,790,801],{"type":19,"value":789},"Alternatively, all secondary transactions might be directly taxed on the spot token level, without explicit transfer limitations. Historically, token designs that experimented with taxes on transfers or other undesirable actions haven’t done well in the market ",{"type":13,"tag":139,"props":791,"children":792},{},[793],{"type":13,"tag":46,"props":794,"children":798},{"href":795,"ariaDescribedBy":796,"dataFootnoteRef":7,"id":797},"#user-content-fn-12",[146],"user-content-fnref-12",[799],{"type":19,"value":800},"11",{"type":19,"value":802},", but those were predominantly speculative instruments. One also has to note that a token with additional functions may not always be compatible with existent blockchain applications tailored for standard token smart contracts. ",{"type":13,"tag":127,"props":804,"children":806},{"id":805},"_3-the-bonding-curve-contract-has-two-identical-but-separate-price-functions-one-for-purchase-and-one-for-sale",[807],{"type":19,"value":808},"3. The bonding curve contract has two identical, but separate price functions - one for purchase and one for sale.",{"type":13,"tag":35,"props":810,"children":811},{},[812],{"type":19,"value":813},"The sale price here is determined by tokens that are staked for utility demand. So, if someone buys a token for speculative use and doesn’t stake them to gain access to the service in our example model, the marginal price on the “sell price curve” does not rise. When all of the tokens bought out are staked for product access, the purchase and the sale price factors are equal. ",{"type":13,"tag":35,"props":815,"children":816},{},[817],{"type":19,"value":818},"The scenario modeling for this option, presented in Figure 8 below, suggests its lower robustness compared to the single price arrangement described in Section 5.  The purchase (red line) and sale (blue line) price dynamics clearly illustrate the diminishing effect of this arrangement on the admin’s ability to monetize their holdings.",{"type":13,"tag":35,"props":820,"children":821},{},[822,826],{"type":13,"tag":349,"props":823,"children":825},{"alt":7,"src":824},"/images/writings/homerun-scenario.jpg",[],{"type":13,"tag":354,"props":827,"children":828},{},[829],{"type":19,"value":830},"Figure 8. Token price dynamics for the Homerun scenario under the double price curve",{"type":13,"tag":35,"props":832,"children":833},{},[834],{"type":19,"value":835},"The simulation results for this option based on two of the market scenarios described in Section 5 are summarized in Table 3 below. The Homerun scenario is shown to represent an extreme case in this double price arrangement - subject to deep cash deficits and requiring total supply to exceed the 1B token cap we assumed. In the Moderate scenario, the admin’s solvency is preserved.  ",{"type":13,"tag":35,"props":837,"children":838},{},[839,843],{"type":13,"tag":349,"props":840,"children":842},{"alt":7,"src":841},"/images/writings/scenario-simulations.jpg",[],{"type":13,"tag":354,"props":844,"children":845},{},[846],{"type":19,"value":847},"Table 3. Scenario simulations for anti-arbitrage double pricing on the bonding curve",{"type":13,"tag":35,"props":849,"children":850},{},[851],{"type":19,"value":852},"The solutions presented above may not be easily translatable to token functionality involving more complex interactions than the “access token” mechanics used in our examples. For each specific case - especially tokens used as in-platform currencies that require wider distribution and higher turnover - more tailored anti-arbitrage solutions must be considered.",{"type":13,"tag":28,"props":854,"children":856},{"id":855},"_7-implementation-notes-and-closing-thoughts",[857],{"type":19,"value":858},"7. IMPLEMENTATION NOTES AND CLOSING THOUGHTS",{"type":13,"tag":35,"props":860,"children":861},{},[862,864,875],{"type":19,"value":863},"Our base implementation follows the example mechanics described throughout this paper and is presented at this time as an Ethereum Virtual Machine smart contract. There are some challenges to math precision when implementing the bonding curve in this environment. One can review how we address those minor challenges in the dedicated repository ",{"type":13,"tag":139,"props":865,"children":866},{},[867],{"type":13,"tag":46,"props":868,"children":872},{"href":869,"ariaDescribedBy":870,"dataFootnoteRef":7,"id":871},"#user-content-fn-13",[146],"user-content-fnref-13",[873],{"type":19,"value":874},"12",{"type":19,"value":169},{"type":13,"tag":35,"props":877,"children":878},{},[879],{"type":19,"value":880},"As a following step we plan to release a Solana Virtual Machine implementation, which may also form the basis for other Rust-flavored smart contract language implementations. But to ensure our system fits the needs of as wide of a set of projects as possible, the real goal is to achieve a solution that allows for Sigma contracts to be deployed on any major blockchain and accessed from anywhere else without compromising on any of its properties.",{"type":13,"tag":35,"props":882,"children":883},{},[884],{"type":19,"value":885},"But technical implementation aside, there are a few important economic considerations we expect to explore in future research. Primarily, the maturity phase service and token pricing mechanisms of Sigma may need to be updated to reflect the more complex economic reality of product growth and market competition in the long run. It is too early to distinguish specific directions, but naive intuition suggests that Sigma is most optimal in the first years of product growth. At a certain stage of maturity multiple liquidity venues for the token may be more beneficial for further token appreciation as suggested by simulation in Fig.7, without disrupting the stable service pricing provided by Sigma. Expanding the liquidity profile of the token is also more beneficial for the contract admin (team or community) as it allows them to monetize their holdings with lesser price impact while preserving the cushion of the main Sigma liquidity pool, which can serve as the fallback censorship-resistant trading venue.",{"type":13,"tag":35,"props":887,"children":888},{},[889],{"type":19,"value":890},"We will also, most likely, consider project-specific arbitrage mitigation solutions. Imposing blanket restrictions on a token in the environment of radically open and unconstrained blockchain markets is a risky strategy if one strives for a broad adoption, so we would like to address our concerns with a more elegant set of adjustments. As for the root cause driving the arbitrage - price calibration on the bonding curve, we expect certain patterns to reveal themselves, so that we could generalize them into practical standards, like e.g. per-token-distributed multiples for different kinds of applications. ",{"type":13,"tag":35,"props":892,"children":893},{},[894],{"type":19,"value":895},"In general, we are planning to tweak both the baseline and project-specific parameters through practice, while collecting data as more Sigma tokens are used in real economic context. We hope to report results in future research.",{"type":13,"tag":897,"props":898,"children":901},"section",{"className":899,"dataFootnotes":7},[900],"footnotes",[902,909],{"type":13,"tag":28,"props":903,"children":906},{"className":904,"id":146},[905],"sr-only",[907],{"type":19,"value":908},"Footnotes",{"type":13,"tag":910,"props":911,"children":912},"ol",{},[913,936,964,985,1005,1025,1045,1065,1085,1105,1125,1146],{"type":13,"tag":87,"props":914,"children":916},{"id":915},"user-content-fn-2",[917,919,925,927],{"type":19,"value":918},"W.B. Arthur, “Competing Technologies, Increasing Returns, And Lock-In by Historical Events”, ",{"type":13,"tag":46,"props":920,"children":923},{"href":921,"rel":922},"https://sites.santafe.edu/~wbarthur/Papers/Arthur_1989.pdf",[50],[924],{"type":19,"value":921},{"type":19,"value":926},"   ",{"type":13,"tag":46,"props":928,"children":933},{"href":929,"ariaLabel":930,"className":931,"dataFootnoteBackref":7},"#user-content-fnref-2","Back to reference 1",[932],"data-footnote-backref",[934],{"type":19,"value":935},"↩",{"type":13,"tag":87,"props":937,"children":939},{"id":938},"user-content-fn-3",[940,942,947,949,955,957],{"type":19,"value":941},"Gagra Ventures, “The New ",{"type":13,"tag":65,"props":943,"children":944},{},[945],{"type":19,"value":946},"Internet",{"type":19,"value":948}," Value Stack”, ",{"type":13,"tag":46,"props":950,"children":953},{"href":951,"rel":952},"https://gagra.vc/writings/the-new-value-stack",[50],[954],{"type":19,"value":951},{"type":19,"value":956}," ",{"type":13,"tag":46,"props":958,"children":962},{"href":959,"ariaLabel":960,"className":961,"dataFootnoteBackref":7},"#user-content-fnref-3","Back to reference 2",[932],[963],{"type":19,"value":935},{"type":13,"tag":87,"props":965,"children":967},{"id":966},"user-content-fn-4",[968,970,976,978],{"type":19,"value":969},"B. Metcalfe, \"Metcalfe's Law after 40 Years of Ethernet”, ",{"type":13,"tag":46,"props":971,"children":974},{"href":972,"rel":973},"https://ieeexplore.ieee.org/document/6636305",[50],[975],{"type":19,"value":972},{"type":19,"value":977},"  ",{"type":13,"tag":46,"props":979,"children":983},{"href":980,"ariaLabel":981,"className":982,"dataFootnoteBackref":7},"#user-content-fnref-4","Back to reference 3",[932],[984],{"type":19,"value":935},{"type":13,"tag":87,"props":986,"children":988},{"id":987},"user-content-fn-5",[989,991,997,998],{"type":19,"value":990},"A. Sergeenkov, “Bonding curves in DeFi, explained\", ",{"type":13,"tag":46,"props":992,"children":995},{"href":993,"rel":994},"https://cointelegraph.com/explained/bonding-curves-in-defi-explained",[50],[996],{"type":19,"value":993},{"type":19,"value":956},{"type":13,"tag":46,"props":999,"children":1003},{"href":1000,"ariaLabel":1001,"className":1002,"dataFootnoteBackref":7},"#user-content-fnref-5","Back to reference 4",[932],[1004],{"type":19,"value":935},{"type":13,"tag":87,"props":1006,"children":1008},{"id":1007},"user-content-fn-6",[1009,1011,1017,1018],{"type":19,"value":1010},"V. Buterin, \"Ethereum: A Next-Generation Smart Contract and Decentralized Application Platform”, ",{"type":13,"tag":46,"props":1012,"children":1015},{"href":1013,"rel":1014},"https://ethereum.org/content/whitepaper/whitepaper-pdf/Ethereum_Whitepaper_-_Buterin_2014.pdf",[50],[1016],{"type":19,"value":1013},{"type":19,"value":956},{"type":13,"tag":46,"props":1019,"children":1023},{"href":1020,"ariaLabel":1021,"className":1022,"dataFootnoteBackref":7},"#user-content-fnref-6","Back to reference 5",[932],[1024],{"type":19,"value":935},{"type":13,"tag":87,"props":1026,"children":1028},{"id":1027},"user-content-fn-7",[1029,1031,1037,1038],{"type":19,"value":1030},"N. Szabo, “Smart Contracts”, ",{"type":13,"tag":46,"props":1032,"children":1035},{"href":1033,"rel":1034},"https://www.fon.hum.uva.nl/rob/Courses/InformationInSpeech/CDROM/Literature/LOTwinterschool2006/szabo.best.vwh.net/smart.contracts.html",[50],[1036],{"type":19,"value":1033},{"type":19,"value":956},{"type":13,"tag":46,"props":1039,"children":1043},{"href":1040,"ariaLabel":1041,"className":1042,"dataFootnoteBackref":7},"#user-content-fnref-7","Back to reference 6",[932],[1044],{"type":19,"value":935},{"type":13,"tag":87,"props":1046,"children":1048},{"id":1047},"user-content-fn-8",[1049,1051,1057,1058],{"type":19,"value":1050},"J. Xu, et al., \"SoK: Decentralized exchanges (DEX) with automated market maker (AMM) protocols\", ",{"type":13,"tag":46,"props":1052,"children":1055},{"href":1053,"rel":1054},"https://arxiv.org/pdf/2103.12732",[50],[1056],{"type":19,"value":1053},{"type":19,"value":956},{"type":13,"tag":46,"props":1059,"children":1063},{"href":1060,"ariaLabel":1061,"className":1062,"dataFootnoteBackref":7},"#user-content-fnref-8","Back to reference 7",[932],[1064],{"type":19,"value":935},{"type":13,"tag":87,"props":1066,"children":1068},{"id":1067},"user-content-fn-9",[1069,1071,1077,1078],{"type":19,"value":1070},"Y. Zhang, et al., “Formal Specification of Constant Product (x × y = k) Market Maker Model and Implementation\",  ",{"type":13,"tag":46,"props":1072,"children":1075},{"href":1073,"rel":1074},"https://safefiles.defiyield.info/safe/files/audit/pdf/Uniswap_V1.pdf",[50],[1076],{"type":19,"value":1073},{"type":19,"value":977},{"type":13,"tag":46,"props":1079,"children":1083},{"href":1080,"ariaLabel":1081,"className":1082,"dataFootnoteBackref":7},"#user-content-fnref-9","Back to reference 8",[932],[1084],{"type":19,"value":935},{"type":13,"tag":87,"props":1086,"children":1088},{"id":1087},"user-content-fn-10",[1089,1091,1097,1098],{"type":19,"value":1090},"F. Zhang, et al., \"Town Crier: An Authenticated Data Feed for Smart Contracts”, ",{"type":13,"tag":46,"props":1092,"children":1095},{"href":1093,"rel":1094},"https://eprint.iacr.org/2016/168.pdf",[50],[1096],{"type":19,"value":1093},{"type":19,"value":977},{"type":13,"tag":46,"props":1099,"children":1103},{"href":1100,"ariaLabel":1101,"className":1102,"dataFootnoteBackref":7},"#user-content-fnref-10","Back to reference 9",[932],[1104],{"type":19,"value":935},{"type":13,"tag":87,"props":1106,"children":1108},{"id":1107},"user-content-fn-11",[1109,1111,1117,1118],{"type":19,"value":1110},"S. 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