# Constant Product Invariant ⎊ Area ⎊ Resource 1 --- ## What is the Formula of Constant Product Invariant? The constant product invariant is a fundamental mathematical formula, typically expressed as x y = k, where x and y represent the quantities of two different assets in a liquidity pool, and k is a constant product. This invariant ensures that as one asset is traded for another, the product of their reserves remains unchanged, assuming no fees or external additions. It forms the core pricing mechanism for many automated market makers (AMMs) in decentralized finance. ## What is the Application of Constant Product Invariant? This invariant finds its primary application in decentralized exchanges (DEXs) that utilize AMMs to facilitate permissionless and continuous trading. Liquidity providers deposit pairs of assets into these pools, and the constant product formula algorithmically determines the exchange rate based on the relative quantities of assets available. Traders interact directly with the smart contract, swapping tokens without needing a traditional order book. This mechanism underpins a significant portion of the crypto derivatives landscape. ## What is the Implication of Constant Product Invariant? The constant product invariant has profound implications for liquidity provision, pricing, and impermanent loss. It ensures that liquidity is always available, albeit at potentially unfavorable prices for large trades due to slippage. The continuous adjustment of asset ratios inherently exposes liquidity providers to impermanent loss, where the value of their pooled assets diverges from simply holding the individual assets. Understanding this formula is essential for participants engaging with AMM-based derivatives and liquidity strategies. --- ## [Non-Linear Invariant Curve](https://term.greeks.live/term/non-linear-invariant-curve/) Meaning ⎊ The Non-Linear Invariant Curve is the core mathematical function enabling automated options market making by managing risk and pricing based on liquidity ratios. ⎊ Term ## [Capital Cost of Manipulation](https://term.greeks.live/term/capital-cost-of-manipulation/) Meaning ⎊ Capital Cost of Manipulation defines the minimum economic expenditure required to distort market prices for predatory gain within decentralized systems. ⎊ Term ## [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. ⎊ Term ## [Blockchain Based Marketplaces Growth Trends](https://term.greeks.live/term/blockchain-based-marketplaces-growth-trends/) Meaning ⎊ Marketplace Liquidity Expansion Protocols automate decentralized value exchange through smart contracts and algorithmic depth management to ensure global trade. ⎊ Term ## [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. ⎊ Term ## [Blockchain Based Marketplaces Growth](https://term.greeks.live/term/blockchain-based-marketplaces-growth/) Meaning ⎊ Blockchain Based Marketplaces Growth facilitates the transition from intermediated trade to sovereign algorithmic settlement via smart contracts. ⎊ Term ## [Blockchain Based Liquidity Provision](https://term.greeks.live/term/blockchain-based-liquidity-provision/) Meaning ⎊ Blockchain Based Liquidity Provision replaces traditional intermediaries with algorithmic reserves to ensure continuous, permissionless price discovery. ⎊ Term ## [Blockchain Based Liquidity Pools](https://term.greeks.live/term/blockchain-based-liquidity-pools/) Meaning ⎊ Blockchain Based Liquidity Pools replace traditional order books with automated, mathematical vaults that democratize market making and price discovery. ⎊ Term ## [Slippage Impact Modeling](https://term.greeks.live/term/slippage-impact-modeling/) Meaning ⎊ Execution Friction Quantization provides the mathematical framework for predicting and minimizing price displacement in decentralized liquidity pools. ⎊ Term ## [AMM-based Pricing](https://term.greeks.live/term/amm-based-pricing/) Meaning ⎊ AMM-based pricing utilizes deterministic invariants to provide automated, permissionless valuation and liquidity for decentralized derivative markets. ⎊ Term ## [Black Scholes Invariant Testing](https://term.greeks.live/term/black-scholes-invariant-testing/) Meaning ⎊ Black Scholes Invariant Testing validates the mathematical consistency of on-chain derivative pricing to prevent systemic arbitrage and capital loss. ⎊ Term ## [Constant Product Formula](https://term.greeks.live/definition/constant-product-formula/) A mathematical model ensuring liquidity by maintaining a constant product of asset quantities in a pool. ⎊ Term ## [Derivative Product Demand](https://term.greeks.live/definition/derivative-product-demand/) The increasing market interest in instruments that enable leverage, hedging, and price speculation. ⎊ Term ## [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. ⎊ Term ## [Constant Proportion Portfolio Insurance](https://term.greeks.live/definition/constant-proportion-portfolio-insurance/) A strategy that dynamically shifts assets between risky and safe investments to protect a minimum portfolio value. ⎊ Term ## [Automated Market Maker Curve Stress](https://term.greeks.live/term/automated-market-maker-curve-stress/) Meaning ⎊ Automated Market Maker Curve Stress represents the systemic risk where pricing algorithms fail to maintain equilibrium during extreme market volatility. ⎊ Term ## [Structured Product Analysis](https://term.greeks.live/term/structured-product-analysis/) Meaning ⎊ Structured Product Analysis evaluates the systemic risk and payoff mechanics of synthetic crypto derivatives within decentralized markets. ⎊ Term ## [Impermanent Loss Hedging](https://term.greeks.live/definition/impermanent-loss-hedging/) The use of derivatives to offset the value risk caused by price divergence in liquidity pools for providers. ⎊ Term ## [Solvency Invariant Proof](https://term.greeks.live/term/solvency-invariant-proof/) Meaning ⎊ Solvency Invariant Proof provides a cryptographic guarantee that protocol assets match liabilities, eliminating the need for trust in clearinghouses. ⎊ Term ## [Blockchain Innovation](https://term.greeks.live/term/blockchain-innovation/) Meaning ⎊ Automated Market Maker Options provide a transparent and decentralized framework for pricing and trading derivative risk without centralized intermediaries. ⎊ Term ## [Automated Market Efficiency](https://term.greeks.live/term/automated-market-efficiency/) Meaning ⎊ Automated Market Efficiency replaces human-intermediated order books with algorithmic liquidity to ensure continuous, trustless price discovery. ⎊ Term ## [Trading Pair Analysis](https://term.greeks.live/term/trading-pair-analysis/) Meaning ⎊ Trading Pair Analysis provides the structural diagnostic framework for evaluating liquidity, volatility, and risk within decentralized markets. ⎊ Term ## [Impermanent Loss Management](https://term.greeks.live/term/impermanent-loss-management/) Meaning ⎊ Impermanent Loss Management utilizes dynamic hedging to neutralize the value erosion caused by liquidity provision in volatile decentralized markets. ⎊ Term ## [Constant Product Formulas](https://term.greeks.live/definition/constant-product-formulas/) Mathematical algorithm where the product of asset quantities in a pool remains constant, driving price and liquidity. ⎊ Term ## [Constant Product Market Makers](https://term.greeks.live/term/constant-product-market-makers/) Meaning ⎊ Constant product market makers enable automated, permissionless liquidity through deterministic pricing curves, eliminating traditional order books. ⎊ Term ## [Decentralized Exchange Slippage](https://term.greeks.live/definition/decentralized-exchange-slippage/) The price difference between the expected and actual execution price caused by automated market maker pool depth. ⎊ Term ## [Decentralized Yield Farming](https://term.greeks.live/term/decentralized-yield-farming/) Meaning ⎊ Decentralized Yield Farming facilitates autonomous liquidity provision and incentive distribution through smart contract-based financial systems. ⎊ Term ## [Slippage Optimization](https://term.greeks.live/definition/slippage-optimization/) Algorithmic routing and execution strategies designed to minimize price impact and ensure the best trade execution. ⎊ Term ## [Slippage Control Strategies](https://term.greeks.live/term/slippage-control-strategies/) Meaning ⎊ Slippage control strategies define the mathematical boundaries for order execution to preserve capital integrity within decentralized market venues. ⎊ Term ## [Slippage Cost Modeling](https://term.greeks.live/term/slippage-cost-modeling/) Meaning ⎊ Slippage cost modeling quantifies the price deviation of trades, serving as the essential metric for assessing liquidity in decentralized markets. ⎊ Term --- ## Raw Schema Data ```json { "@context": "https://schema.org", "@type": "BreadcrumbList", "itemListElement": [ { "@type": "ListItem", "position": 1, "name": "Home", "item": "https://term.greeks.live/" }, { "@type": "ListItem", "position": 2, "name": "Area", "item": "https://term.greeks.live/area/" }, { "@type": "ListItem", "position": 3, "name": "Constant Product Invariant", "item": "https://term.greeks.live/area/constant-product-invariant/" }, { "@type": "ListItem", "position": 4, "name": "Resource 1", "item": "https://term.greeks.live/area/constant-product-invariant/resource/1/" } ] } ``` ```json { "@context": "https://schema.org", "@type": "FAQPage", "mainEntity": [ { "@type": "Question", "name": "What is the Formula of Constant Product Invariant?", "acceptedAnswer": { "@type": "Answer", "text": "The constant product invariant is a fundamental mathematical formula, typically expressed as x y = k, where x and y represent the quantities of two different assets in a liquidity pool, and k is a constant product. 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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/structured-product-analysis/", "url": "https://term.greeks.live/term/structured-product-analysis/", "headline": "Structured Product Analysis", "description": "Meaning ⎊ Structured Product Analysis evaluates the systemic risk and payoff mechanics of synthetic crypto derivatives within decentralized markets. ⎊ Term", "datePublished": "2026-03-11T22:36:20+00:00", "dateModified": "2026-03-11T22:36:50+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/deconstructing-collateral-layers-in-decentralized-finance-structured-products-and-risk-mitigation-mechanisms.jpg", "width": 3850, "height": 2166, "caption": "A detailed macro view captures a mechanical assembly where a central metallic rod passes through a series of layered components, including light-colored and dark spacers, a prominent blue structural element, and a green cylindrical housing. This intricate design serves as a visual metaphor for the architecture of a decentralized finance DeFi options protocol." } }, { "@type": "Article", "@id": "https://term.greeks.live/definition/impermanent-loss-hedging/", "url": "https://term.greeks.live/definition/impermanent-loss-hedging/", "headline": "Impermanent Loss Hedging", "description": "The use of derivatives to offset the value risk caused by price divergence in liquidity pools for providers. ⎊ Term", "datePublished": "2026-03-12T16:06:55+00:00", "dateModified": "2026-04-05T00:58:11+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-collateralized-debt-obligation-structure-for-advanced-risk-hedging-strategies-in-decentralized-finance.jpg", "width": 3850, "height": 2166, "caption": "A high-tech rendering of a layered, concentric component, possibly a specialized cable or conceptual hardware, with a glowing green core. The cross-section reveals distinct layers of different materials and colors, including a dark outer shell, various inner rings, and a beige insulation layer." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/solvency-invariant-proof/", "url": "https://term.greeks.live/term/solvency-invariant-proof/", "headline": "Solvency Invariant Proof", "description": "Meaning ⎊ Solvency Invariant Proof provides a cryptographic guarantee that protocol assets match liabilities, eliminating the need for trust in clearinghouses. ⎊ Term", "datePublished": "2026-03-13T02:02:04+00:00", "dateModified": "2026-03-13T02:02:29+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/interoperable-architecture-of-proof-of-stake-validation-and-collateralized-derivative-tranching.jpg", "width": 3850, "height": 2166, "caption": "A cutaway view reveals the inner workings of a multi-layered cylindrical object with glowing green accents on concentric rings. The abstract design suggests a schematic for a complex technical system or a financial instrument's internal structure." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/blockchain-innovation/", "url": "https://term.greeks.live/term/blockchain-innovation/", "headline": "Blockchain Innovation", "description": "Meaning ⎊ Automated Market Maker Options provide a transparent and decentralized framework for pricing and trading derivative risk without centralized intermediaries. ⎊ Term", "datePublished": "2026-03-13T08:42:11+00:00", "dateModified": "2026-03-13T08:42:50+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/advanced-decentralized-finance-yield-aggregation-node-interoperability-and-smart-contract-architecture.jpg", "width": 3850, "height": 2166, "caption": "The image portrays an intricate, multi-layered junction where several structural elements meet, featuring dark blue, light blue, white, and neon green components. This complex design visually metaphorizes a sophisticated decentralized finance DeFi smart contract architecture." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/automated-market-efficiency/", "url": "https://term.greeks.live/term/automated-market-efficiency/", "headline": "Automated Market Efficiency", "description": "Meaning ⎊ Automated Market Efficiency replaces human-intermediated order books with algorithmic liquidity to ensure continuous, trustless price discovery. ⎊ Term", "datePublished": "2026-03-13T13:05:31+00:00", "dateModified": "2026-03-13T13:05:48+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-algorithmic-mechanism-illustrating-decentralized-finance-liquidity-pool-smart-contract-interoperability-architecture.jpg", "width": 3850, "height": 2166, "caption": "A cutaway view reveals the inner workings of a precision-engineered mechanism, featuring a prominent central gear system in teal, encased within a dark, sleek outer shell. Beige-colored linkages and rollers connect around the central assembly, suggesting complex, synchronized movement." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/trading-pair-analysis/", "url": "https://term.greeks.live/term/trading-pair-analysis/", "headline": "Trading Pair Analysis", "description": "Meaning ⎊ Trading Pair Analysis provides the structural diagnostic framework for evaluating liquidity, volatility, and risk within decentralized markets. ⎊ Term", "datePublished": "2026-03-13T14:15:55+00:00", "dateModified": "2026-03-13T14:17:24+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/advanced-algorithmic-trading-system-for-high-frequency-crypto-derivatives-market-analysis.jpg", "width": 3850, "height": 2166, "caption": "The image displays a high-tech, multi-layered structure with aerodynamic lines and a central glowing blue element. The design features a palette of deep blue, beige, and vibrant green, creating a futuristic and precise aesthetic." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/impermanent-loss-management/", "url": "https://term.greeks.live/term/impermanent-loss-management/", "headline": "Impermanent Loss Management", "description": "Meaning ⎊ Impermanent Loss Management utilizes dynamic hedging to neutralize the value erosion caused by liquidity provision in volatile decentralized markets. ⎊ Term", "datePublished": "2026-03-15T10:48:37+00:00", "dateModified": "2026-03-21T15:13:23+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/precision-engineered-decentralized-derivatives-protocol-mechanism-illustrating-algorithmic-risk-management-and-collateralization-architecture.jpg", "width": 3850, "height": 2166, "caption": "This detailed rendering showcases a sophisticated mechanical component, revealing its intricate internal gears and cylindrical structures encased within a sleek, futuristic housing. The color palette features deep teal, gold accents, and dark navy blue, giving the apparatus a high-tech aesthetic." } }, { "@type": "Article", "@id": "https://term.greeks.live/definition/constant-product-formulas/", "url": "https://term.greeks.live/definition/constant-product-formulas/", "headline": "Constant Product Formulas", "description": "Mathematical algorithm where the product of asset quantities in a pool remains constant, driving price and liquidity. ⎊ Term", "datePublished": "2026-03-15T23:30:26+00:00", "dateModified": "2026-03-17T23:10:06+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-execution-interface-for-high-frequency-trading-and-smart-contract-automation-within-decentralized-protocols.jpg", "width": 3850, "height": 2166, "caption": "A high-resolution product image captures a sleek, futuristic device with a dynamic blue and white swirling pattern. The device features a prominent green circular button set within a dark, textured ring." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/constant-product-market-makers/", "url": "https://term.greeks.live/term/constant-product-market-makers/", "headline": "Constant Product Market Makers", "description": "Meaning ⎊ Constant product market makers enable automated, permissionless liquidity through deterministic pricing curves, eliminating traditional order books. ⎊ Term", "datePublished": "2026-03-15T23:31:27+00:00", "dateModified": "2026-03-23T01:04:39+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/abstract-representation-layered-financial-derivative-complexity-risk-tranches-collateralization-mechanisms-smart-contract-execution.jpg", "width": 3850, "height": 2166, "caption": "A stylized, high-tech illustration shows the cross-section of a layered cylindrical structure. The layers are depicted as concentric rings of varying thickness and color, progressing from a dark outer shell to inner layers of blue, cream, and a bright green core." } }, { "@type": "Article", "@id": "https://term.greeks.live/definition/decentralized-exchange-slippage/", "url": "https://term.greeks.live/definition/decentralized-exchange-slippage/", "headline": "Decentralized Exchange Slippage", "description": "The price difference between the expected and actual execution price caused by automated market maker pool depth. ⎊ Term", "datePublished": "2026-03-16T00:23:25+00:00", "dateModified": "2026-03-29T19:02:18+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/interlocking-architecture-of-collateralization-mechanisms-in-advanced-decentralized-finance-derivatives-protocols.jpg", "width": 3850, "height": 2166, "caption": "The visualization showcases a layered, intricate mechanical structure, with components interlocking around a central core. A bright green ring, possibly representing energy or an active element, stands out against the dark blue and cream-colored parts." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/decentralized-yield-farming/", "url": "https://term.greeks.live/term/decentralized-yield-farming/", "headline": "Decentralized Yield Farming", "description": "Meaning ⎊ Decentralized Yield Farming facilitates autonomous liquidity provision and incentive distribution through smart contract-based financial systems. ⎊ Term", "datePublished": "2026-03-16T15:48:06+00:00", "dateModified": "2026-03-16T15:49:34+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/multi-protocol-decentralized-finance-ecosystem-liquidity-flows-and-yield-farming-strategies-visualization.jpg", "width": 3850, "height": 2166, "caption": "The image depicts an abstract arrangement of multiple, continuous, wave-like bands in a deep color palette of dark blue, teal, and beige. The layers intersect and flow, creating a complex visual texture with a single, brightly illuminated green segment highlighting a specific junction point." } }, { "@type": "Article", "@id": "https://term.greeks.live/definition/slippage-optimization/", "url": "https://term.greeks.live/definition/slippage-optimization/", "headline": "Slippage Optimization", "description": "Algorithmic routing and execution strategies designed to minimize price impact and ensure the best trade execution. ⎊ Term", "datePublished": "2026-03-17T23:02:34+00:00", "dateModified": "2026-04-01T21:07:21+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-layered-architecture-collateralization-and-tranche-optimization-for-yield-generation.jpg", "width": 3850, "height": 2166, "caption": "A macro-level abstract visualization shows a series of interlocking, concentric rings in dark blue, bright blue, off-white, and green. The smooth, flowing surfaces create a sense of depth and continuous movement, highlighting a layered structure." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/slippage-control-strategies/", "url": "https://term.greeks.live/term/slippage-control-strategies/", "headline": "Slippage Control Strategies", "description": "Meaning ⎊ Slippage control strategies define the mathematical boundaries for order execution to preserve capital integrity within decentralized market venues. ⎊ Term", "datePublished": "2026-03-19T01:17:44+00:00", "dateModified": "2026-03-19T01:18:01+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-execution-protocol-activation-indicator-real-time-collateralization-oracle-data-feed-synchronization.jpg", "width": 3850, "height": 2166, "caption": "A high-resolution, close-up image captures a sleek, futuristic device featuring a white tip and a dark blue cylindrical body. A complex, segmented ring structure with light blue accents connects the tip to the body, alongside a glowing green circular band and LED indicator light." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/slippage-cost-modeling/", "url": "https://term.greeks.live/term/slippage-cost-modeling/", "headline": "Slippage Cost Modeling", "description": "Meaning ⎊ Slippage cost modeling quantifies the price deviation of trades, serving as the essential metric for assessing liquidity in decentralized markets. ⎊ Term", "datePublished": "2026-03-19T02:18:20+00:00", "dateModified": "2026-04-05T01:05:23+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-frequency-algorithmic-execution-logic-for-cryptocurrency-derivatives-pricing-and-risk-modeling.jpg", "width": 3850, "height": 2166, "caption": "The image displays a detailed cross-section of a high-tech mechanical component, featuring a shiny blue sphere encapsulated within a dark framework. A beige piece attaches to one side, while a bright green fluted shaft extends from the other, suggesting an internal processing mechanism." } } ], "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/interlocking-decentralized-finance-protocol-architecture-non-linear-payoff-structures-and-systemic-risk-dynamics.jpg" } } ``` --- **Original URL:** https://term.greeks.live/area/constant-product-invariant/resource/1/