# Automated Market Maker Invariants ⎊ Area ⎊ Resource 1 --- ## What is the Algorithm of Automated Market Maker Invariants? Automated Market Maker Invariants, fundamentally, represent the mathematical relationships that govern the pricing and liquidity provision within AMMs. These invariants, often expressed as equations, ensure that the pool's total value remains constant, or adheres to a predictable curve, despite trading activity. A common example is the x y = k invariant in constant product AMMs, where x and y represent the quantities of two assets and k is a constant. Deviations from these invariants can signal arbitrage opportunities or inefficiencies within the market, prompting traders to rebalance the pool and restore equilibrium. ## What is the Price of Automated Market Maker Invariants? The price discovery mechanism within an AMM is directly dictated by its invariant. As traders swap assets, the relative quantities within the pool shift, altering the ratio and consequently, the observed price. This dynamic pricing reflects supply and demand pressures, albeit within the constraints imposed by the invariant function. Options pricing, when integrated into AMMs, introduces additional complexity, requiring adjustments to the invariant to account for factors like strike price, time to expiration, and volatility, thereby influencing the observed price of the derivative. ## What is the Risk of Automated Market Maker Invariants? Invariants, while providing a theoretical framework for price stability, do not eliminate risk. Impermanent loss, a significant concern in AMMs, arises from the divergence of asset prices outside the pool compared to holding them individually. Furthermore, the reliance on a specific invariant can create vulnerabilities if the underlying assumptions of that invariant are violated, such as significant shifts in market conditions or the introduction of novel trading strategies. Effective risk management necessitates a thorough understanding of the invariant's limitations and potential failure modes. --- ## [Automated Market Makers](https://term.greeks.live/definition/automated-market-makers/) Decentralized exchange protocols using math formulas to enable automatic, pool-based liquidity and asset pricing. ⎊ Definition ## [Automated Market Maker](https://term.greeks.live/definition/automated-market-maker/) A decentralized exchange mechanism using algorithms and liquidity pools to facilitate trades without a traditional order book. ⎊ Definition ## [Options Automated Market Makers](https://term.greeks.live/term/options-automated-market-makers/) Meaning ⎊ Options AMMs automate the pricing and liquidity provision for derivatives by managing complex non-linear risks, primarily Delta and Vega exposure, within decentralized pools. ⎊ Definition ## [Market Maker Strategies](https://term.greeks.live/definition/market-maker-strategies/) Algorithms and techniques used by liquidity providers to capture spreads while managing inventory and market risk. ⎊ Definition ## [Market Maker Incentives](https://term.greeks.live/definition/market-maker-incentives/) Economic mechanisms and rewards used to attract and retain liquidity providers to ensure narrow spreads and deep markets. ⎊ Definition ## [Automated Market Maker Options](https://term.greeks.live/term/automated-market-maker-options/) Meaning ⎊ Automated Market Maker Options utilize algorithmic pricing and pooled liquidity to facilitate decentralized options trading, transforming risk management and capital efficiency in derivatives markets. ⎊ Definition ## [Automated Market Making](https://term.greeks.live/definition/automated-market-making/) A decentralized liquidity provision model using mathematical formulas to set prices in automated pools. ⎊ Definition ## [Market Maker Risk](https://term.greeks.live/definition/market-maker-risk/) The multifaceted risks faced by liquidity providers, including inventory exposure, adverse selection, and price volatility. ⎊ Definition ## [Market Maker Risk Management](https://term.greeks.live/term/market-maker-risk-management/) Meaning ⎊ Market maker risk management is the continuous process of adjusting a portfolio's exposure to price, volatility, and time decay to maintain solvency while providing liquidity. ⎊ Definition ## [Automated Market Maker Risk](https://term.greeks.live/term/automated-market-maker-risk/) Meaning ⎊ Automated Market Maker Risk in options protocols arises from the mispricing of non-linear risk, primarily gamma and vega, which exposes liquidity providers to systemic arbitrage. ⎊ Definition ## [Market Maker Capital Efficiency](https://term.greeks.live/definition/market-maker-capital-efficiency/) Optimizing the ratio of active liquidity to deployed collateral to maximize trading volume and reduce idle capital waste. ⎊ Definition ## [Market Maker Hedging](https://term.greeks.live/definition/market-maker-hedging/) The active management of risks by liquidity providers to maintain a neutral position against their client-facing trades. ⎊ Definition ## [Market Maker Strategy](https://term.greeks.live/term/market-maker-strategy/) Meaning ⎊ Market maker strategy in crypto options provides essential liquidity by managing complex risk exposures derived from volatility and protocol design, collecting profit from the bid-ask spread. ⎊ Definition ## [Market Maker Data Feeds](https://term.greeks.live/term/market-maker-data-feeds/) Meaning ⎊ Market Maker Data Feeds are high-frequency information channels providing real-time options pricing and risk data, crucial for managing implied volatility and liquidity across decentralized markets. ⎊ Definition ## [Market Maker Dynamics](https://term.greeks.live/definition/market-maker-dynamics/) The strategies and risk management behaviors used by liquidity providers to maintain quotes and capture the bid-ask spread. ⎊ Definition ## [Automated Market Makers Options](https://term.greeks.live/term/automated-market-makers-options/) Meaning ⎊ AMM options are decentralized derivative protocols that utilize liquidity pools and automated pricing algorithms to facilitate options trading without a traditional order book. ⎊ Definition ## [Automated Market Maker Slippage](https://term.greeks.live/definition/automated-market-maker-slippage/) The adverse price change experienced during a trade on a decentralized exchange caused by the trade size relative to depth. ⎊ Definition ## [Market Maker Profitability](https://term.greeks.live/definition/market-maker-profitability/) The ability of liquidity providers to earn revenue from spreads and fees while managing inventory risk. ⎊ Definition ## [Automated Market Maker Design](https://term.greeks.live/definition/automated-market-maker-design/) The mathematical and logical frameworks that enable decentralized trading and price discovery without order books. ⎊ Definition ## [Automated Market Maker Pricing](https://term.greeks.live/definition/automated-market-maker-pricing/) The algorithmic determination of asset prices based on liquidity pool ratios rather than traditional order books. ⎊ Definition ## [Virtual Automated Market Makers](https://term.greeks.live/term/virtual-automated-market-makers/) Meaning ⎊ Virtual Automated Market Makers facilitate capital-efficient decentralized derivatives trading by simulating liquidity and managing risk through funding rates and insurance funds. ⎊ Definition ## [Automated Market Maker Fees](https://term.greeks.live/definition/automated-market-maker-fees/) Transaction costs paid by traders to liquidity providers, acting as a core incentive and revenue source in decentralized markets. ⎊ Definition ## [Financial Systems Theory](https://term.greeks.live/term/financial-systems-theory/) Meaning ⎊ The Decentralized Volatility Surface is the on-chain, auditable representation of market-implied risk, integrating smart contract physics and liquidity dynamics to define the systemic health of decentralized derivatives. ⎊ Definition ## [AMMs](https://term.greeks.live/term/amms/) Meaning ⎊ Crypto options AMMs utilize volatility-adjusted constant function market makers and discrete vault models to provide passive liquidity for non-linear derivative instruments. ⎊ Definition ## [Automated Market Maker Hybrid](https://term.greeks.live/term/automated-market-maker-hybrid/) Meaning ⎊ The Dynamic Volatility Surface AMM is a hybrid protocol that uses options pricing models to dynamically shape the liquidity invariant for capital-efficient, risk-managed derivatives trading. ⎊ Definition ## [Maker-Taker Models](https://term.greeks.live/term/maker-taker-models/) Meaning ⎊ The Maker-Taker Model is a critical market microstructure design that uses differentiated transaction fees to subsidize passive liquidity provision and minimize the effective trading spread for crypto options. ⎊ Definition ## [Order Book Data Visualization Tools and Techniques](https://term.greeks.live/term/order-book-data-visualization-tools-and-techniques/) Meaning ⎊ Order Book Data Visualization translates options market microstructure into actionable risk telemetry, quantifying liquidity foundation resilience and systemic load for precise financial strategy. ⎊ Definition ## [Real-Time Formal Verification](https://term.greeks.live/term/real-time-formal-verification/) Meaning ⎊ Real-Time Formal Verification provides continuous mathematical proofs of smart contract invariants to ensure systemic solvency in derivative markets. ⎊ Definition ## [Blockchain Based Marketplaces Data](https://term.greeks.live/term/blockchain-based-marketplaces-data/) Meaning ⎊ Blockchain Based Marketplaces Data provides the verifiable and immutable record of on-chain economic activity required for decentralized risk modeling. ⎊ Definition ## [Economic Invariant Stress Testing](https://term.greeks.live/term/economic-invariant-stress-testing/) Meaning ⎊ Economic Invariant Stress Testing quantifies the mathematical boundaries of protocol solvency to prevent systemic failure in volatile markets. ⎊ Definition --- ## 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A common example is the x y = k invariant in constant product AMMs, where x and y represent the quantities of two assets and k is a constant. Deviations from these invariants can signal arbitrage opportunities or inefficiencies within the market, prompting traders to rebalance the pool and restore equilibrium." } }, { "@type": "Question", "name": "What is the Price of Automated Market Maker Invariants?", "acceptedAnswer": { "@type": "Answer", "text": "The price discovery mechanism within an AMM is directly dictated by its invariant. As traders swap assets, the relative quantities within the pool shift, altering the ratio and consequently, the observed price. This dynamic pricing reflects supply and demand pressures, albeit within the constraints imposed by the invariant function. 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The layered structure creates a sense of dynamic motion and complex integration between components." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/automated-market-makers-options/", "url": "https://term.greeks.live/term/automated-market-makers-options/", "headline": "Automated Market Makers Options", "description": "Meaning ⎊ AMM options are decentralized derivative protocols that utilize liquidity pools and automated pricing algorithms to facilitate options trading without a traditional order book. ⎊ Definition", "datePublished": "2025-12-19T09:12:54+00:00", "dateModified": "2026-01-04T17:54:38+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/real-time-automated-market-making-algorithm-execution-flow-and-layered-collateralized-debt-obligation-structuring.jpg", "width": 3850, "height": 2166, "caption": "An abstract digital rendering showcases a segmented object with alternating dark blue, light blue, and off-white components, culminating in a bright green glowing core at the end. The object's layered structure and fluid design create a sense of advanced technological processes and data flow." } }, { "@type": "Article", "@id": "https://term.greeks.live/definition/automated-market-maker-slippage/", "url": "https://term.greeks.live/definition/automated-market-maker-slippage/", "headline": "Automated Market Maker Slippage", "description": "The adverse price change experienced during a trade on a decentralized exchange caused by the trade size relative to depth. ⎊ Definition", "datePublished": "2025-12-19T09:20:45+00:00", "dateModified": "2026-04-07T14:34:18+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/multi-layered-market-structure-analysis-focusing-on-systemic-liquidity-risk-and-automated-market-maker-interactions.jpg", "width": 3850, "height": 2166, "caption": "An abstract digital rendering shows a spiral structure composed of multiple thick, ribbon-like bands in different colors, including navy blue, light blue, cream, green, and white, intertwining in a complex vortex. The bands create layers of depth as they wind inward towards a central, tightly bound knot." } }, { "@type": "Article", "@id": "https://term.greeks.live/definition/market-maker-profitability/", "url": "https://term.greeks.live/definition/market-maker-profitability/", "headline": "Market Maker Profitability", "description": "The ability of liquidity providers to earn revenue from spreads and fees while managing inventory risk. ⎊ Definition", "datePublished": "2025-12-19T09:25:30+00:00", "dateModified": "2026-04-05T09:09:25+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/decentralized-finance-architecture-visualizing-automated-market-maker-interoperability-and-derivative-pricing-mechanisms.jpg", "width": 3850, "height": 2166, "caption": "An abstract 3D render displays a complex, stylized object composed of interconnected geometric forms. The structure transitions from sharp, layered blue elements to a prominent, glossy green ring, with off-white components integrated into the blue section." } }, { "@type": "Article", "@id": "https://term.greeks.live/definition/automated-market-maker-design/", "url": "https://term.greeks.live/definition/automated-market-maker-design/", "headline": "Automated Market Maker Design", "description": "The mathematical and logical frameworks that enable decentralized trading and price discovery without order books. ⎊ Definition", "datePublished": "2025-12-19T10:03:37+00:00", "dateModified": "2026-04-07T02:19:12+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/decentralized-automated-market-maker-protocol-structure-and-liquidity-provision-dynamics-modeling.jpg", "width": 3850, "height": 2166, "caption": "A close-up view presents an articulated joint structure featuring smooth curves and a striking color gradient shifting from dark blue to bright green. The design suggests a complex mechanical system, visually representing the underlying architecture of a decentralized finance DeFi derivatives platform." } }, { "@type": "Article", "@id": "https://term.greeks.live/definition/automated-market-maker-pricing/", "url": "https://term.greeks.live/definition/automated-market-maker-pricing/", "headline": "Automated Market Maker Pricing", "description": "The algorithmic determination of asset prices based on liquidity pool ratios rather than traditional order books. ⎊ Definition", "datePublished": "2025-12-21T09:08:37+00:00", "dateModified": "2026-04-04T07:57:40+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/collateralized-debt-positions-and-automated-market-maker-architecture-in-decentralized-finance-risk-modeling.jpg", "width": 3850, "height": 2166, "caption": "An abstract digital rendering showcases smooth, highly reflective bands in dark blue, cream, and vibrant green. The bands form intricate loops and intertwine, with a central cream band acting as a focal point for the other colored strands." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/virtual-automated-market-makers/", "url": "https://term.greeks.live/term/virtual-automated-market-makers/", "headline": "Virtual Automated Market Makers", "description": "Meaning ⎊ Virtual Automated Market Makers facilitate capital-efficient decentralized derivatives trading by simulating liquidity and managing risk through funding rates and insurance funds. ⎊ Definition", "datePublished": "2025-12-21T10:06:27+00:00", "dateModified": "2025-12-21T10:06:27+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/layered-collateralization-structures-for-options-trading-and-defi-automated-market-maker-liquidity.jpg", "width": 3850, "height": 2166, "caption": "A close-up view shows coiled lines of varying colors, including bright green, white, and blue, wound around a central structure. The prominent green line stands out against the darker blue background, which contains the lighter blue and white strands." } }, { "@type": "Article", "@id": "https://term.greeks.live/definition/automated-market-maker-fees/", "url": "https://term.greeks.live/definition/automated-market-maker-fees/", "headline": "Automated Market Maker Fees", "description": "Transaction costs paid by traders to liquidity providers, acting as a core incentive and revenue source in decentralized markets. ⎊ Definition", "datePublished": "2025-12-22T11:12:56+00:00", "dateModified": "2026-03-13T16:49:31+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/decentralized-automated-market-maker-protocol-structure-and-liquidity-provision-dynamics-modeling.jpg", "width": 3850, "height": 2166, "caption": "A close-up view presents an articulated joint structure featuring smooth curves and a striking color gradient shifting from dark blue to bright green. The design suggests a complex mechanical system, visually representing the underlying architecture of a decentralized finance DeFi derivatives platform." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/financial-systems-theory/", "url": "https://term.greeks.live/term/financial-systems-theory/", "headline": "Financial Systems Theory", "description": "Meaning ⎊ The Decentralized Volatility Surface is the on-chain, auditable representation of market-implied risk, integrating smart contract physics and liquidity dynamics to define the systemic health of decentralized derivatives. ⎊ Definition", "datePublished": "2026-01-05T09:36:33+00:00", "dateModified": "2026-01-05T09:36:52+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/synthetic-structured-derivatives-risk-tranche-chain-visualization-underlying-asset-collateralization.jpg", "width": 3850, "height": 2166, "caption": "A series of smooth, interconnected, torus-shaped rings are shown in a close-up, diagonal view. The colors transition sequentially from a light beige to deep blue, then to vibrant green and teal." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/amms/", "url": "https://term.greeks.live/term/amms/", "headline": "AMMs", "description": "Meaning ⎊ Crypto options AMMs utilize volatility-adjusted constant function market makers and discrete vault models to provide passive liquidity for non-linear derivative instruments. ⎊ Definition", "datePublished": "2026-01-05T09:57:12+00:00", "dateModified": "2026-01-05T09:57:40+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/decentralized-options-protocol-mechanism-for-advanced-structured-crypto-derivatives-and-automated-algorithmic-arbitrage.jpg", "width": 3850, "height": 2166, "caption": "A futuristic, stylized mechanical component features a dark blue body, a prominent beige tube-like element, and white moving parts. The tip of the mechanism includes glowing green translucent sections." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/automated-market-maker-hybrid/", "url": "https://term.greeks.live/term/automated-market-maker-hybrid/", "headline": "Automated Market Maker Hybrid", "description": "Meaning ⎊ The Dynamic Volatility Surface AMM is a hybrid protocol that uses options pricing models to dynamically shape the liquidity invariant for capital-efficient, risk-managed derivatives trading. ⎊ Definition", "datePublished": "2026-02-04T22:45:33+00:00", "dateModified": "2026-02-04T22:46:43+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/synthetic-asset-collateralization-framework-illustrating-automated-market-maker-mechanisms-and-dynamic-risk-adjustment-protocol.jpg", "width": 3850, "height": 2166, "caption": "A detailed view shows a high-tech mechanical linkage, composed of interlocking parts in dark blue, off-white, and teal. A bright green circular component is visible on the right side." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/maker-taker-models/", "url": "https://term.greeks.live/term/maker-taker-models/", "headline": "Maker-Taker Models", "description": "Meaning ⎊ The Maker-Taker Model is a critical market microstructure design that uses differentiated transaction fees to subsidize passive liquidity provision and minimize the effective trading spread for crypto options. ⎊ Definition", "datePublished": "2026-02-07T11:10:42+00:00", "dateModified": "2026-02-07T11:23:34+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/decentralized-finance-infrastructure-automated-market-maker-protocol-execution-visualization-of-derivatives-pricing-models-and-risk-management.jpg", "width": 3850, "height": 2166, "caption": "The visualization presents smooth, brightly colored, rounded elements set within a sleek, dark blue molded structure. The close-up shot emphasizes the smooth contours and precision of the components." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/order-book-data-visualization-tools-and-techniques/", "url": "https://term.greeks.live/term/order-book-data-visualization-tools-and-techniques/", "headline": "Order Book Data Visualization Tools and Techniques", "description": "Meaning ⎊ Order Book Data Visualization translates options market microstructure into actionable risk telemetry, quantifying liquidity foundation resilience and systemic load for precise financial strategy. ⎊ Definition", "datePublished": "2026-02-08T11:20:38+00:00", "dateModified": "2026-02-08T11:21:59+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/high-precision-financial-engineering-mechanism-for-collateralized-derivatives-and-automated-market-maker-protocols.jpg", "width": 3850, "height": 2166, "caption": "A high-tech mechanical component features a curved white and dark blue structure, highlighting a glowing green and layered inner wheel mechanism. 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The core of the mechanism is highlighted by a bright green glowing data-like structure, partially covered by a matching blue shield element." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/blockchain-based-marketplaces-data/", "url": "https://term.greeks.live/term/blockchain-based-marketplaces-data/", "headline": "Blockchain Based Marketplaces Data", "description": "Meaning ⎊ Blockchain Based Marketplaces Data provides the verifiable and immutable record of on-chain economic activity required for decentralized risk modeling. ⎊ Definition", "datePublished": "2026-02-23T13:52:53+00:00", "dateModified": "2026-02-23T13:53:01+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/algorithmic-leverage-mechanism-conceptualization-for-decentralized-options-trading-and-automated-risk-management-protocols.jpg", "width": 3850, "height": 2166, "caption": "A futuristic mechanical component featuring a dark structural frame and a light blue body is presented against a dark, minimalist background. A pair of off-white levers pivot within the frame, connecting the main body and highlighted by a glowing green circle on the end piece." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/economic-invariant-stress-testing/", "url": "https://term.greeks.live/term/economic-invariant-stress-testing/", "headline": "Economic Invariant Stress Testing", "description": "Meaning ⎊ Economic Invariant Stress Testing quantifies the mathematical boundaries of protocol solvency to prevent systemic failure in volatile markets. ⎊ Definition", "datePublished": "2026-03-10T17:54:51+00:00", "dateModified": "2026-03-10T17:55:15+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/decentralized-finance-protocol-algorithmic-volatility-dampening-mechanism-for-derivative-settlement-optimization.jpg", "width": 3850, "height": 2166, "caption": "The image displays a cutaway view of a precision technical mechanism, revealing internal components including a bright green dampening element, metallic blue structures on a threaded rod, and an outer dark blue casing. The assembly illustrates a mechanical system designed for precise movement control and impact absorption." } } ], "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/advanced-decentralized-finance-derivative-architecture-illustrating-dynamic-margin-collateralization-and-automated-risk-calculation.jpg" } } ``` --- **Original URL:** https://term.greeks.live/area/automated-market-maker-invariants/resource/1/